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GMAT Sample Questions & Answers

GMAT sample questions and answers written by our admissions experts

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Verbal

Sentence correction

Critical reasoning

 

Quantitative

Data sufficiency

Problem Solving


GMAT Sample Questions: Verbal


Sentence correction: Comparisons


Question:

Unlike the nests of leaf cutters and most other ants, situated underground or in pieces of wood, raider ants make a portable nest by entwining their long legs to form "curtains" of ants that hang from logs or boulders, providing protection for the queen and the colony larvae and pupae.

A. The nests of leaf cutters and most other ants,

B. The nests of leaf cutters and most other ants, which are

C. Leaf cutters and most other ants, whose nests are

D. Leaf cutters and most other ants in having nests

E. Those of leaf cutters and most other ants with nests

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Answer:

The first question you should ask when you see a comparison in the GMAT, is ‘what is the sentence comparing?’. You want to check that the comparison is logical, in that it must compare similar things. Apples to apples so to speak. You cannot compare an apple to a person for example. Likewise, you cannot compare nests to a type of ant. Although we might do this in everyday conversation, it is technically illogical. Words like ‘just as’, ‘like’ and ‘unlike’ indicate a direct comparison.

In this sentence the part that is not underlined mentions raider ants. The part that is underlined is the part that you can change, and the one you will have to match to that.

Scanning the answer choices, you’ll see that answer choice A, B and E are still illogically comparing nests to ants. C and D are the only options that make a logical comparison. Remember for sentence correction questions, the aim is to find four wrong answers so that you are left with the right one. Finding the correct answer is a process of elimination.

Now that you have narrowed down the answer choices, you can focus on the differences between C and D.  

Answer choice D intuitively looks wrong. The reason is that the phrase ‘in having nests’ makes it look like the raider ants’ nests are underground or in pieces of wood.

C makes it clear (with the correct possessive phrase whose nests) that it is the nests of the leaf cutters and most other ants that are underground or in pieces of wood. Answer choice C is the correct answer.


Read: How To Score 700+ On The GMAT—Top Test Prep Tips From The MBAs Who’ve Done It

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Sentence correction: Modifiers, Parallelism


Question:

Despite its covering the entire planet, Earth has a crust that is not seamless or stationary, rather it is fragmented into mobile semi-rigid plates.

A. Despite its covering the entire planet, Earth has a crust that is not seamless or stationary, rather it is

B. Despite the fact that it covers the entire planet, Earth's crust is neither seamless nor is it stationary, but is

C. Despite covering the entire planet, Earth's crust is neither seamless nor is it stationary, but rather

D. Although it covers the entire planet, Earth's crust is neither seamless nor stationary, but rather

E. Although covering the entire planet, Earth has a crust that is not seamless or stationary, but

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Answer:

Like most GMAT Sentence correction questions, this one tests multiple grammar points. Incorrect answer choices have more than one error. You can start where you feel most confident and narrow down the choices. You will find the correct answer through a process of elimination.

In the original sentence the modifier ‘Despite its covering the entire planet’ is describing the closest subject to it – Earth. This is illogical as it indicates that Earth is covering itself.

This modifier should be directly next to ‘Earth’s crust’, as that is what it is describing.

You can eliminate answer choices A and E based on this illogical construction.

The correct parallel structure is ‘neither X nor Y’, or ‘neither seamless nor stationary’. Like all parallel structures (including lists) it is incorrect to break up the structure by including random words that interrupt the formation. Hence B and C’s ‘neither seamless nor is it stationary’ is unparallel and incorrect. D is the correct answer.

You could have also narrowed down the answer choices based on the words ‘Despite’ vs ‘Although’. Despite is a preposition and should be followed by a noun (for example: Despite the rain, we walked on) while although is a conjunction and should be followed by a subject and verb (for example: Although it rained, we walked on).


Sentence correction: Parallelism


Question:

Obtaining an investment-grade rating will keep the county's future borrowing costs low, protect its already-tattered image, and increase its ability to buy bond insurance.

(A) Obtaining an investment-grade rating will keep the county's future borrowing costs low, protect

(B) To obtain an investment-grade rating will keep the county's future borrowing costs low, and protect

(C) Having obtained an investment-grade rating will, in keeping the county's future borrowing costs low, protect

(D) To obtain an investment-grade rating would keep the county's future borrowing costs low, protecting

(E) Obtaining an investment-grade rating, keeping the county's borrowing costs low, would be protecting

Answer:

This is a classic parallelism question. What makes this one slightly more complex is the fact that it tests your ability to see which parts of the sentences need to be parallel.

Parallelism makes sentences easier to read by making clear how the different parts relate to one another. Items in a list or sequence need to be in the same form. In this case, this sentence contains a list of what will happen if the country obtains an investment grade rating. This investment-grade rating will do three things 1) KEEP the country’s future borrowing costs low 2) PROTECT its already-tattered image and 3) INCREASE its ability to buy bond insurance.

The list should be keep protect and increase, or keeping protecting and increasing.

As the word increase is not underlined (and cannot be changed in the answer choices), keep and protect are the right form of these words to match it.

The only answer choices consistent with this are A and B.

B is probably the most common wrong answer to this question. It is tempting to change Obtaining to Obtain to match increase, keep and protect, but actually obtaining is not part of the list (of what the investment-grade rating would do).

In fact, in A Obtaining is a gerund – a part of speech that may look like a verb at first glance due to its -ing structure, but is actually a noun. It is correct to have a noun as the subject of the sentence rather than to have an infinitive verb ‘To Obtain’ as the subject. A verb cannot be the subject of a sentence.

Note also that the additional and in B breaks up the parallel structure. The structure of a list should be ‘A, B and C’ and not ‘A and B and C’.


Read more: How To Create The Perfect GMAT Study Plan

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Critical reasoning: Assumptions


Question:

Farmer: Worldwide, just three grain crops—rice, wheat, and corn—account for most human caloric intake. To maintain this level of caloric intake and also keep pace with global population growth, yields per acre from each of these crops will have to increase at least 1.5 percent every year, given that the supply of cultivated land is diminishing. Therefore, the government should increase funding for research into new ways to improve yields.

Which of the following is an assumption on which the farmer's argument depends?

A. It is solely the government's responsibility to ensure that the amount of rice, wheat, and corn produced worldwide keeps pace with global population growth.

B. Increasing government funding for research into new ways to improve the yields per acre of rice, wheat, and corn crops would help to increase total worldwide annual production of food from these crops.

C. Increasing the yields per acre of rice, wheat, and corn is more important than increasing the yields per acre of other crops.

D. Current levels of funding for research into ways of improving grain crop yields per acre have enabled grain crop yields per acre to increase by more than 1.5 percent per year worldwide.

E. In coming decades, rice, wheat, and corn will become a minor part of human caloric intake, unless there is government-funded research to increase their yields per acre.

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Answer:

In this question we are looking for an assumption on which the argument DEPENDS. Remember, there can be hundreds of unspoken assumptions in an argument, but the assumption we are looking for here, is one that HAS to be true, for the argument to stand.

Let’s consider the logic of the argument. The argument is saying that yields for these three crops (that make up for most of human caloric intake) have to increase (by at least 1.5% per year) because a) population growth is increasing and b) cultivated land is diminishing. Therefore, the government should increase funding into new ways to improve yields.

One way to go about answering this question is to look at whether or not each answer choice has to be 100% true for the argument to be true. If it doesn’t really matter either way, then you can eliminate the answer choice.  In other words: Does it matter to the argument whether or not this statement is exactly true? If the argument could stand either way, then that’s not the assumption you are looking for. If the argument would collapse if the statement was not true – that’s the one you’re looking for.

A. It is solely the government's responsibility to ensure that the amount of rice, wheat, and corn produced worldwide keeps pace with global population growth.

Answer choice A is a good example of a statement that does not affect the logic of the argument. Whether or not it is the government’s sole responsibility, or a shared responsibility does not matter to the argument. The argument could still be true either way. In other words, the argument does not DEPEND on this assumption.

B. Increasing government funding for research into new ways to improve the yields per acre of rice, wheat, and corn crops would help to increase total worldwide annual production of food from these crops.

Answer choice B speaks directly to the logic of the argument. If it is not true that government funding into new ways to improve yields would help increase food production from these crops, then it can’t be true that government should increase funding into new ways to improve yields.

Let’s hang on to B for now but take a look at the other answer choices.

C. Increasing the yields per acre of rice, wheat, and corn is more important than increasing the yields per acre of other crops.

Answer choice C is tempting. It seems like it would bolster the argument to say that funding research related to these crops specifically are important. But that is not what the question wants you to consider. The question is asking for an assumption that must be true for the argument to be true. Whether these crops are as important, slightly more important or slightly less important than other crops are not the difference between a good argument, and one that falls apart.

D. Current levels of funding for research into ways of improving grain crop yields per acre have enabled grain crop yields per acre to increase by more than 1.5 percent per year worldwide.

Answer choice D is a common wrong answer. If the question was asking you to weaken the argument it would be spot on. But the question is asking for something that must be true for the argument to be true. It doesn’t matter if current levels of research are increasing yields by 1%, or 1.5% or 0.7341%, or making no difference. None of these options (including 1.5%) must be true for the argument to make sense.  

E. In coming decades, rice, wheat, and corn will become a minor part of human caloric intake, unless there is government-funded research to increase their yields per acre.

If there was no government-funded research, its plausible that these crops could become a minor part of human caloric intake. It’s equally plausible that they would remain the major part of human caloric intake and a bunch of smaller, more obscure plants would fill the gap. It doesn’t matter either way.

Based on the above, B would be the correct answer choice. Remember to find 4 wrong answers along with your right one. You should be able to think through the logic of what the question is asking and why the incorrect answers are incorrect. While it’s not always helpful to dwell on the question type – for assumption questions in particular, make sure you not getting the right answer to the wrong question.  


Read More: 5 GMAT Vocabulary Tips For Non-Native English Speakers

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Critical reasoning: Strengthening


Question:

A company has developed a new sensing device that, according to the company's claims, detects weak, ultralow-frequency electromagnetic signals associated with a beating heart. These signals, which pass through almost any physical obstruction, are purportedly detected by the device even at significant distances. Therefore, if the company's claims are true, their device will radically improve emergency teams' ability to locate quickly people who are trapped within the wreckage of collapsed buildings.

Which of the following, if true, most strengthens the argument?

A. People trapped within the wreckage of collapsed buildings usually have serious injuries that require prompt medical treatment.

B. The device gives a distinctive reading when the signals it detects come from human beings rather than from any other living beings.

C. Most people who have survived after being trapped in collapsed buildings were rescued within two hours of the building's collapse.

D. Ultralow-frequency signals are not the only electromagnetic signals that can pass through almost any physical obstruction.

E. Extensive training is required in order to operate the device effectively.

This does not strengthen the argument. It does not increase the likelihood of the argument’s conclusion: that the device will speed up rescues.

Answer:

Let’s jump in by taking a look at the argument. The argument’s conclusion is that the device will radically improve emergency teams’ ability to locate quickly people who are trapped within the wreckage of collapsed buildings. The device can enable this, according to the argument because it detects the signals associated with a beating heart- even at distances or behind physical barriers.

For critical reasoning questions, the conclusions are very specific. This one is focused on the emergency teams’ ability to locate people quickly. Before getting to the answer choices, its helpful to remind yourself about that specific conclusion, and that other aspects about the device – eg cost, are beside the point.

A. People trapped within the wreckage of collapsed buildings usually have serious injuries that require prompt medical treatment.

This answer choice speaks to the device’s usefulness and importance. But it does not strengthen the argument – that emergency teams can locate people more quickly.

B. The device gives a distinctive reading when the signals it detects come from human beings rather than from any other living beings.

This may be relevant. The device would certainly help pull humans out faster if it was not picking up frequencies from other living beings. It very slightly strengthens. Let’s keep this one.

C. Most people who have survived after being trapped in collapsed buildings were rescued within two hours of the building's collapse.

This does not strengthen the argument. We don’t get extra information on whether or not the device will improve this time or not.

D. Ultralow-frequency signals are not the only electromagnetic signals that can pass through almost any physical obstruction.

We don’t really care. There may be hundreds of technologies that can contribute to lessening rescue times. The argument is about this one device, and its ability to do so.

E. Extensive training is required in order to operate the device effectively.

This does not strengthen the argument. It does not increase the likelihood of the argument’s conclusion: that the device will speed up rescues.

Given the answer choices we have, B is the correct answer. It is the only one that speaks to the conclusion and gives extra evidence to support the conclusion. Remember, the GMAT is asking for an answer choice that MOST strengthens the argument. B is not an outstanding answer, but by using a process of elimination we are able to narrow it down. B only slightly strengthens the argument, but its still the answer choice that strengthens it the most.


Critical reasoning: Paradox


Question:

Beginning in 1966 all new cars sold in Morodia were required to have safety belts and power steering. Previously, most cars in Morodia were without these features. Safety belts help to prevent injuries in collisions, and power steering helps to avoid collisions in the first place. But even though in 1966 one-seventh of the cars in Morodia were replaced with new cars, the number of car collisions and collision-related injuries did not decline.

Which of the following, if true about Morodia, most helps to explain why the number of collisions and collision-related injuries in Morodia failed to decline in 1966?

A. Because of a driver-education campaign, most drivers and passengers in cars that did have safety belts used them in 1966.

B. Most of the new cars bought in 1966 were bought in the months of January and February.

C. In 1965, substantially more than one-seventh of the cars in Morodia were replaced with new cars.

D. An excessive reliance on the new safety features led many owners of new cars to drive less cautiously in 1966 than before.

E. The seat belts and power steering put into new cars sold in 1966 had to undergo strict quality-control inspections by manufacturers, whether the cars were manufactured in Morodia or not.

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Answer:

The key to answering this question is knowing what the question is asking. The argument gives you two pieces of information that appear to conflict – the fact that new safety features were introduced but that the number of collisions and collision-related injuries did not decline as you might expect. This question is asking for an answer choice that helps to explain this apparent paradox. The correct answer will provide some information explaining how these seemingly contradictory statements can both be true.

A. Because of a driver-education campaign, most drivers and passengers in cars that did have safety belts used them in 1966.

This answer choice does not explain why the number of collisions and collision-related injuries did not decline. In fact, it gives us more reason to question how it could be possible that the new safety features did not lead to fewer collisions and related injuries.

B. Most of the new cars bought in 1966 were bought in the months of January and February.

The earlier in the year the new cars were bought the more of a decline we would expect to see over the year. This answer choice does not resolve the paradox

C. In 1965, substantially more than one-seventh of the cars in Morodia were replaced with new cars.

The number of new cars purchased in 1965 is beyond the scope of the argument. These cars would have the same safety standards as any older car bought before 1966. This would not explain the limited impact the cars that were purchased in 1966 had on the number of collisions and collision-related injuries

D. An excessive reliance on the new safety features led many owners of new cars to drive less cautiously in 1966 than before.

This answer choice does provide an explanation of how the new safety features in cars would not result in fewer collisions and related injuries. The effect of drivers driving less cautiously would counteract the benefit of the new features. This answer choice helps to explain why there was no drop in collisions, despite the new features. This is the correct answer choice.

E. The seat belts and power steering put into new cars sold in 1966 had to undergo strict quality-control inspections by manufacturers, whether the cars were manufactured in Morodia or not.

This does not help us explain why the number of collisions did not decline as expected. If anything, this eliminates any doubt that the safety features were in every car and of good quality.

Answer choice D is the only one that resolves the paradox, by explaining statements that at first glance, do not appear to be consistent.


Critical reasoning: Bold, Roles


Question:

Chaco Canyon, a settlement of the ancient Anasazi culture in North America, had massive buildings. It must have been a major Anasazi center. Analysis of wood samples shows that some of the timber for the buildings came from the Chuska and San Mateo mountains, 50 miles from Chaco Canyon. Only a major cultural center would have the organizational power to import timber from 50 miles away.

In the argument given, the two portions in boldface play which of the following roles?

A. The first is a premise used to support the argument's main conclusion; the second is the argument's main conclusion.

B. The first is the argument's main conclusion; the second is a premise used to support that conclusion.

C. The first is one of two premises used to support the argument's main conclusion; the second is the other of those two premises.

D. The first is a premise used to support the argument's main conclusion; the second is a premise used to support another conclusion drawn in the argument.

E. The first is inferred from another statement in the argument; the second is inferred from the first.

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Answer:

This type of question typically takes a little longer on average to complete. The question is asking how the two portions in boldface relate to the argument overall, and what roles they play in the argument.

The best place to start with this type of question is to read the argument and find the main conclusion. This will help you to see how the different parts in bold relate to it. In this case the first statement is the conclusion of the argument. It is the main claim that the author is making, and the rest of the argument supports it. One way to check that you have found the correct conclusion is to ask yourself if there is evidence or reasons to support it. Unsupported statements cannot be conclusions. The second statement in bold is giving a reason why the Chaco Canyon must have been a cultural centre.

The best way to approach these questions is to eliminate the answer choices that are obviously wrong, and then to take a closer look at the remaining choices.

In fact, in this question only answer choice B correctly identifies the first statement as the main conclusion of the argument.

In order to solve this question, you would have to understand the argument and identify the conclusion, even through it is not placed at tge end of the argument. Once you correctly identify the argument’s conclusion, this question is quite straightforward. 


Read More: What Is A Good GMAT Score?

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GMAT Sample Questions: Quantitative


Data Sufficiency


Question:

At a bakery, all donuts are priced equally and all bagels are priced equally. What is the total price of 5 donuts and 3 bagels at the bakery?

(1) At the bakery, the total price of 10 donuts and 6 bagels is $12.90.

(2) At the bakery, the price of a donut is $0.15 less than the price of a bagel.

A. If statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

B. If statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

C. If BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;

D. If EACH statement ALONE is sufficient to answer the question asked;

E. If statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

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Answer:

Here we need to evaluate how sufficient the statements (1) and (2) are to answer the question asked, and choose the correct alternative accordingly.

If we let d be the price of 1 Donut and b be the price of 1 Bagel, statements (1) and (2) can be re-expressed as:

1. 10d + 6b = 12.90

2. d = b - 0.15

Mathematically, the only way to get the values of d and b is to use the equations from both statements at the same time and solve a typical school-exercise of simultaneous equations. This will help us get the values of d and b. We would then be enabled to answer any question related to those variables.

However, we are faced with twi facts that should be examined carefully:

Fact 1) The only alternative above that considers using both statements being used together is (C) If BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

Fact 2) The question is actually not asking for the values of b and d; rather it requires the price of a combo: 5d + 3b.

Let’s look attentively to statement 1, in the question, on its own:  10d + 6b = 12.90.

If we divide both sides by 2, we will have 5d + 3b = 6.45

This means that the price for 5 donuts and 3 bagels is $6.45!! That’s the answer we were looking for!

Statement (1) alone allows us to answer the question proposed; statement (2) alone only informs us about the difference in prices between a donut and bagel is clearly not sufficient to answer the question asked.

Final Answer:

A. If statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked


Problem solving: Arithmetic


Question:

If 893 × 78 = p, which of the following is equal to 893 × 79?

(A) p + 1

(B) p + 78

(C) p + 79

(D) p + 893

(E) p + 894

Answer:

1.              Common approach

The unprepared approach to this question would lead us to determine the value of p.

Indeed, we could obtain p after some strenuous calculations. p would be 893 x 78 which leads to the value of p: p = 69654.

Then we need to move on to another hard, time-consuming sum: 893 x 79, which gives us 70547. If that’s not enough work, we need now to relate both numbers, as all the answers (including the correct one!)  require us to express the new number (70547) in terms of p.

Since 70547 – 69654 = 893, we conclude that 70547 = 69654 + 893, which is the same as saying that 70547 is p + 893. Alternative (D) is the correct one.  

2.              The GMAT approach

As a rule of thumb, we should know that no question on GMAT is either too easy or too hard. They are suited for the test constraints: calculators are not allowed and the average time available per questions is no more than 2 minutes! There must be another way!

Indeed, the luxury of calculators makes us forget that some basic algebraic operations could be perfectly used with numbers just as well.

When it comes to Algebra, almost everyone recalls the multiplication property a(b + c) = ab +ac. The good news is that we could replicate this simple model here! After all:  893 x 79 = 893 x (78 +1) = 893 x 78 + 893 x 1. Having in mind that that question told us that 893 x 78 = p, then we have that:

893 x 79 = p + 893 and alternative (D) is correct. No big numbers and the question is straight-forwardly addressed.


Problem solving: Geometry, Circles


Question:

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In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

(A) 4

(B) 3

(C) 2

(D) √3

(E)  √2

Answer:

Before we examine the different approaches to this question, we should have a clear idea of what is happening in this case:

There are two circles; a small one and a big one and the small one is completely contained within the big circle.

The shaded area represents the difference in the area between them:

Area of big circle = Area of small circle + shaded area

The shaded area, according to the question, is 3 times the area of the small circle:

Shaded area = 3 x area of small circle.

Substituting in the above equation:

Area of big circle = Area of small circle + 3 x area of small circle

Thus: area of big circle = 4 x area of small circle

So how many times is the circumference of the big circle greater than circumference of the small circle?

The academic approach

We need to recall the basic formulas that relate to circles:

Area of circle: A=πR^2

Circumference of circle: C=2πR

Where r is the radius of the circle.

In terms of the areas, we saw above that: area of big circle = 4 x area of small circle

We can now say that: πR_BIG^2=4× πR_SMALL^2  

Cancelling p in both sides, we will have R_BIG^2=4× R_SMALL^2  

Taking the square root on both sides: RBIG = 2 x RSMALL

Now, the circumference of big circle is 2πR_BIG

But if we replace RBIG with 2 x RSMALL, we will have:  

Circumference of big circle is 2π2×R_SMALL.

However, π2×R_SMALL= 2πR_SMALL, which is the circumference of the small circle.

Therefore, the circumference of the big circle is 2 x the circumference of the small circle and the correct answer is C.

A simpler approach: similarity

The small and big circles have identical shape (quite obviously!). We could see the big circle as a ‘magnified version’ of the small circle. When this happens, we have ‘similarity’: all linear measures of both circles are proportional: radii, diameters, circumferences.

That means if the radius of the big circle is k times bigger than the radius of the small circle, then:

The diameter of the big circle will be k times bigger that the diameter of the small circle

The circumference of the big Circle will be k times bigger that the circumference of the small circle

What about the two areas? They will also be proportional, but to k2. Therefore:

The area of the big circle will be k2 times bigger that the area of the small circle.

Thus, in our case, k2 = 4 and k = 2. So, the circumference of the big circle is 2x the circumference of the small one. The correct answer is C.


Read More: How Can You Score 800 On The GMAT?

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Problem solving: Algebra, Plug-in numbers, Quant


Question:

If 1 < x < y < z, which of the following has the greatest value?

A. z(x + 1)

B. z(y + 1)

C. x(y + z)

D. y(x + z)

E. z(x + y)

Answer:

Method 1: Algebraic Approach

As we are dealing with numbers greater than 1, there are 2 rules that must be noted:

  • The product of two numbers is greater than each one of them;

  • The larger the numbers, the larger the product

Thus if 1 < x < y < z, we can derive the following inequailities:

  • xy < xz < yz

  • x < y < z < xz

When we open up the multiplications on each alternative:

A. z(x + 1) = xz + z
B. z(y + 1) = yz + z
C. x(y + z) = xy + xz
D. y(x + z) = xy + yz
E. z(x + y) = xz + yz

We have the following conclusions:

  1. (B) is greater than (A) as yz > xz

  2. Comparing (C), (D) and (E), (E) will be the greatest, as xy < xz < yz

  3. (E) is greater than (B), as xz > z

Answer (E)

Method 2: Plug-in numbers

Recalling the fact that the GMAT doesn’t regard the workings towards the correct answer, we could experiment with numbers instead of letters, since the alternatives have to be true for any values of x, y and z, as long as the condition 1 < x < y < z is respected:

Let’s try with x = 2, y = 3 and z = 4 and check which alternative gives us the largest number:

A. z(x + 1) = 4(2 + 1) = 4 × 3 = 12
B. z(y + 1) = 4(3 + 1) = 4 × 4 = 16
C. x(y + z) = 2(3 + 4) = 2 × 7 = 14
D. y(x + z) = 3(2 + 4) = 3 × 6 = 18
E. z(x + y) = 4(2 + 3) = 4 × 5 = 20

And we can quickly spot (E) as the correct alternative!


Problem solving: Quant, Quantitative, Estimation


Question:

Over the past 7 weeks, the Smith family had weekly grocery bills of $74, $69, $64, $79, $64, $84, and $77. What was the Smiths' average (arithmetic mean) weekly grocery bill over the 7-week period?

A. $64

B. $70

C. $73

D. $74

E. $85

Answer:

Method 1: The regular Approach

It’s quite well known that average of a set of numbers is the sum of those numbers divided by the quantity of those numbers. In our case we have:

Average = (74 + 69 + 64 + 79 + 64 + 84 + 77)÷7

While this is a straight-forward problem, performing 74 + 69 + 64 + 79 + 64 + 84 + 77 without a calculator will be time-consuming job during which distractions could most likely happen!

At any rate, since: 74 + 69 + 64 + 79 + 64 + 84 + 77=511

And 511 ÷ 7 = 73

Answer (C)

Method 2: Estimations Method

An alternative approach to decrease the amount of calculations with “big numbers” is to estimate (guess) what the average would be and add it to the average of the differences of every number

Let’s say that, from glancing at the numbers in the question, one would estimate their average to be 75.

Let’s calculate the differences between each number and 75

74 – 75 = -1

69 – 75 = -6

64 – 75 = -11

79 – 75 = 4

64 – 75 = -11

84 – 75 = 9

77 – 75 = 2

Since the sum of -1, -6, -11, 4, -11, 9 and 2 will be -14 and -14 ÷ 7 = -2, it comes out that the average of the differences is -2.

Therefore 75 - 2 = 73  – the correct answer is C!


These questions have been written by Cara Skikne and Shimon Goldchmit.

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