GMAT Classic Mock Test - 9 - GMAT MCQ

The correct response is (D). The volume is the length x width x height. The building’s original volume is equal to lwh = 9600. The new footage will be 2.5l x 2.5w x 2.5h, or (lwh) x 2.5 x 2.5 x 2.5 = 15.625(lwh). Since lwh = 9600, the new volume will be 15.625(9600) = 150,000.

The correct response is (A). Let P be the number of Political Science majors and let R be the number of International Relations majors. "One fifth of the legislators are neither," so there are 1/5 *200 = 40 legislators who are neither. Hence, there are 200 – 40 = 160 Poly-Sci majors and IR majors, or P + R = 160. Translating the clause "the number of Poly-Sci majors is 50 less than 4 times the number of IR majors" into an equation yields P = 4R – 50.
Plugging this into the equation P + R = 160 yields:
4R – 50 + R = 160
5R – 50 = 160
5R = 210
R = 42

The correct response is (C). The need-to-know formula here is: Profit/Loss % = (Sales Price – Cost Price) / Cost Price x 100. The stem tells us that 20c = 25s, or 4c = 5s, so the ratio of the sales price to the cost price is 4/5.
Let’s simplify our Profit/Loss % formula by dividing each term by the cost price: Profit/Loss % = (S/C – C/C) x 100
P/L% = (S/C – 1) x 100 We know that S/C = 4/5 for this problem. So we can plug in and solve:
P/L% = (4/5 – 1) x 100
P/L% = (-1/5) x 100
P/L% = -20%. The answer is a 20% loss.

The correct response is (B). To find the "Average Rate" of the bus, we know we will need to find the Total Distance and the Total Time, so let's see how we can use the D = R x T formula to find the missing info.  

For the first part of the trip, we know that 30 miles = 15mph x T, so we know that T = 2 hours.  For the middle part of the trip, we know that D = 10mph x 3 hours, so we know that D = 30 miles. For the last part of the trip, we know that 40 miles = R x 2 hours, so we know that R = 20mph.  

Now we can find the Total Distance and the Total Time. Total Distance = 30 miles + 30 miles + 40miles = 100 miles. Total Time = 2 hours + 3 hours + 2 hours = 7 hours.  So the Average Rate = 100 miles/ 7 hours = 14.28mph.  (B) is the closest approximation.

The correct response is (C).
Time = Distance/Rate
Time spent going uphill = D /6
Time spent going downhill = D/14
Total Time = 1 hour

We can write the following equation, and solve for D:
Time taken on the uphill journey + Time taken on the downhill journey = Total Time

The correct response is (E). Remember that the probability of something NOT occurring is 1 – the probability of it occurring. So for this question, we can find the probability that those two doctors WILL be working together, then subtract it from one. Let’s start with the first group. If the first person we chose was from the first group, the odds that the second person would be their partner would be 1/8. This is because every doctor in the first group only has ONE partner, and we’d have 8 people to choose from after picking the first person (out of 9 total). 6/9*1/8 = 6/72 = 1/12.

If the first person we chose was from the second group (probability = 3/9), the odds that the second person would be one of their partners would be 2/8. The numerator is 2 this time because each person in the second group has two partners instead of one. 3/9*2/8 = 6/72 = 1/12.

Since EITHER of these outcomes (picking the first person from the first group OR the second group) produces our desired result, we’ll add these probabilities. 1/12 + 1/12 = 2/12 = 1/6.

Therefore, the probability that the two doctors are NOT working together is 1 – 1/6 = 5/6.

Another way to think of this question is to assign letters to each doctor and group them by clinical trial. So AB, CD, EF are from the first group, and GHI are from the second group. There are 6 ways of choosing a pair that are working together: AB, CD, EF, GH, GI, or HI. And we can quickly use the combination formula to find the total possible ways to choose 2 from 9. 9C2 = 9! / 2! 7! = 9 x 8/2 = 72/2 = 36. 6/36 = 1/6.

The correct response is (D). For questions with functions in the answer choices, use the given definitions to check each of the answer choices. For instance, since we want f(z) = f(1-z) we can assume z=4, and check each of the answer choices to see if f(4) = f(1-4), or, f(4) = f(-3).

If you notice that, then it very easy to find the solution, replace each function with 4 and -3 instead of z, and see if f(4)=f(-3).

Let’s try choice (A):
F(-3) = 1 – (-3) = 4
F(4) = 1 - (4) = -3
They are NOT equal. Eliminate.

Repeat this process for the other answer choices, until you find one for which f(4) = f(-3). That choice is D:
F(-3) = (-3)² (1 – (-3))² = (9)(16)
F(4) = (4)² (1 – (4))² = (16)(9)
F(-3) = F(4).

The correct response is (A). If we know the longest side is “z,” we can label the other two sides as “z-4” and “z-2” respectively because we know that “consecutive even” means each side differs from its next-largest neighbor by 2. For example: 6, 8, 10.

We would use the Pythagorean Theorem to find the value of z:
a² + b² = c²
(z – 2)² + (z – 4)² = z²

Remember that “c” is always the hypotenuse, or the longest side. Only choice (A) matches this equation.

The correct response is (C). To find the circumference of a circle, we must find the radius. Let’s start with what we know:
The area of a rectangle is lw. Here we are told that lw = 8w. That means the length is 8. We also know that the distance from P to LM = 3, so the length of the rectangle must be 6. Let’s re-draw the shape:

The radius of the circle, LP, is the hypotenuse of a right triangle whose other two sides are half the length and half the width of the rectangle. Since it’s a classic Pythagorean triplet (3:4:5), we don’t need to use the Pythagorean theorem.
Plug the radius into the formula for circumference: C = 2πr. C = 2*π*5. The circumference is approximately 10π, or a number slightly larger than 30.

The correct response is (C). We can solve this problem by picking numbers:

We want x < w < z. Let’s pick x=3, w=4, z=6

For a job that took 4 hours, the client is charged $4/hour for the first 3 hours, then $6/hour for the last hour. The total cost would be $4(3) + $6(1) = $12 + $6 = $18.

For a job that took 6 hours, the client is charged $4/hour for the first 3 hours, then $6/hour for the last three hours. The total cost would be $4(3) + $6(3) = $12 + $18 = $30. The difference in price is $12.

Let’s plug our values into the expression: (w+2)(z-w) = (4+2)(6-4) = 6*2 = 12.

Here is the algebraic solution:

If the grass trimming job took z hours, the total cost is: wx + (z-x)(w+2)

If the grass trimming job took w hours, where x < w < z, the total cost is: wx + (w-x)(w+2)

The extra cost will be:

[wx + (z-x)(w+2)] – [wx + (w-x)(w+2)]
= (z-x)(w+2) - (w-x)(w+2)
= (w+2)[(z-x) – (w-x)]
= (w+2)(z-w)

The correct response is (C). For every 5 necklaces purchased by these ladies, 3 of them are Lady Edith’s and 2 of them are Lady Mary’s. We can set up an equation to find the total amount spent:

3(16) + 2(20) = Total Amount Spent for every 5 necklaces
88 = Total Amount Spent for every 5 necklaces

To find the average cost of the necklaces, we can simply divide 88 by 5. 88/5 = 17.6.

The correct response is (E). It is easier to use process of elimination on this type of question. Since all of the answer choices have at least one single-digit number in it, let’s look at the second requirement. If only one of the numbers was divisible by 3, we can eliminate answer choices that contain more than one multiple of 3: (A), (C), and (D).

The third requirement is that we have at least one even number. Between (B) and (E), only choice (E) contains an even number, 10.

The correct response is (D). Start by drawing the figure.

If the radius of P is 3, then its diameter is 6. Its circumference is 2πr = 6π. Q’s circumference is four times P’s circumference. Q’s circumference = 24π = 2πr. Q’s radius must be 12, and its diameter is 24.
The difference between the diameters is 24 – 6 = 18.

The correct response is (B). It’s important to first understand what this question is asking. “On the way to Beachside” means the way there. The question is asking the average speed for a portion of the total trip. To find it, we’ll need to know the distance for that part of the trip and the time spent on that part of the trip.

If the average speed of the entire journey was 2/3 miles per hour, then every 3 hours 2 miles were travelled. Since the total distance was 2 miles, the total time must have been 3 hours. If the way back took half as much time as the way there, then for every 3 hours, 2 hours was spent on the way there, and 1 hour was spent on the way back.

Average Speed = Distance/Time = 1 mile / 2 hours. The average speed for the way to Beachside was ½ mph.

The correct response is (C). This is a great question for plugging in your own values. Let’s say the value of the original radius was 10. The original area would be equal to πr² = (10)²π = 100π. If the diameter increased by 80%, the new radius would be 18, and the new area would be equal to πr2 = (18)²π = 324π.

The increase is 324π - 100π = 224π. An increase of 224/100, or approximately 225%.

Given the length of one side of a triangle, it is known that the sum of the lengths of the other two sides is greater than that given length. The length of either of the other two sides, however can be any positive number.
(i) Only the length of one side, XY, is given,
and that is not enough to determine the
length of YZ; NOT sufficient.
(ii) Again, only the length of one side, XZ, is
given and that is not enough to determine
the length of YZ; NOT sufficient.

Even by using the triangle inequality stated above, only a range of values for YZ can be determined from (1) and (2). If the length of side YZ is represented by k，then it is known both that 3 + 5 > k and that 3 + k> 5,or k > 2. Combining these inequalities to determine the length of k
yields only that 8 > k > 2.

Recognize that a right triangle can be formed with the junction creating the 90° angle and the two municipalities at the other two vertices.

Therefore, only two of the distances between the locations will be necessary to find the third by way of the Pythagorean Theorem.

(1) This provides the distance for one of the two legs of the right triangle only; NOT sufficient.

(2) This provides the distance for the hypotenuse of the right triangle only; NOT sufficient.

(Together) Complete the theorem as 12²+b² = 15² to find that the shorter leg distance is 9. From there, 12 + 9 = 21 is 6 kilometers further than 15 kilometers; SUFFICIENT.

( 1) Dividing both sides of the inequality by z yields x > y. However, there is no information relating z to either x or y; NOT sufficient.
(2) Dividing both sides of the inequality by y yields only that x > z, with no further information relatingy to either x or z; NOT sufficient. From (1) and (2) it can be determined that xis greater than bothy and z. Since it still cannot be determined which of y or z is the least, the correct ordering of the three numbers also cannot be determined. The correct answer is E.

Note that the slope of a line with equation y=mx+b ism.

(1) A line passing through the point (1, 8) can have any value for its slope, so it is impossible to determine the slope of line d.

For example, the line y=x+7 intersects y=6x+2 at (1, 8) with a slope of 1, while the line y=2x+6 intersects y=6x+2 at (1, 8) with a slope of 2; NOT sufficient.

(2) Parallel lines have the same slope, and it is possible to solve for the slope as m=2–m, 2m=2, and m=1; SUFFICIENT.

Since (x - y)² = (x² + y²) - 2xy and it is given that x² + y² = 29, it follows that (x - y)² = 29 - 2xy. Therefore, the value of (x - y )2 can be determined if and only if the value of xy can be determined. (1) Since the value of xy is given, the value of (x - y)² can be determined; SUFFICIENT. (2) Given only that x = 5, it is not possible to determine the value of xy. Therefore, the value of (x - y)² cannot be determined; NOT sufficient. The correct answer is A

A  includes all multiples of 2; B includes all multiples of 3. A∪B comprises all multiples of either 2 or 3.

Knowing n is a perfect square is neither necessary nor helpful, as, for example, 9∈B⊆A∪B, but 25∉A∪B (as 25 is neither a multiple of 2 nor a multiple of 3).

If you know that n is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means n∈B⊆A∪B

(1) Since x² is always nonnegative, it follows
that here x must also be nonnegative, that is,
greater than or equal to 0. If x = 0 or 1, then
x² = x. Furthermore, if x is greater than 1,
then x² is greater than x. Therefore, x must
be between O and 1; SUFFICIENT.
(2) If x³ is positive, then x is positive, but x can
be any positive number; NOT sufficient.

The question asks whether Jimmy is an element of M.

Statement 1 alone - that Jimmy is an element of T′ - provides insufficient information, since T′ contains elements that are and are not elements of M. By a similar argument, Statement 2 alone is insufficient.

Now assume both statements to be true. Then Jimmy is an element of T′∩E′, shaded in the Venn diagram below:

It can be seen that T′∩E′ shares no elements with M, so Jimmy cannot be an element of M. Jimmy is not a Mason.

(1) Given x + y = 10, or y = 10 - x, it follows that xy = x(10 - x), which does not have a unique value. For example, if x = 0, then xy = (0)(10) = 0, but if x = 1, then xy = (1)(9) = 9; NOT sufficient.
(2) Given x - y = 6, or y = x - 6, it follows that xy = x(x - 6), which does not have a unique value. For example, if x = 0, then xy = (0) (-6) = 0, but if x = 1, then xy = (1)(-5) = -5; NOT sufficient.
Using (1) and (2) together, the two equations can be solved simultaneously for x and y. One way to do this is by adding the two equations, x + y = 10 and x - y = 6, to get 2x = 16, or x = 8.
Then substitute into either of the equations to obtain an equation that can be solved to get y = 2. Thus, xy can be determined to have the value (8)(2) = 16. Alternatively, the two equations
correspond to a pair of nonparallel lines in the (x,y) coordinate plane, which have a unique point incommon.
The correct answer is C

The question is whether or not Craig is an element of T.
Assume both statements to be true. Craig is an element of the set M′∩E′, shaded in this Venn diagram:

There are elements of this set that both are and are not elements of T. Therefore, the two statements together do not prove or disprove Craig to be an element of T, a Toastmaster.

Assume both statements are true. If x is the number of students enrolled in both courses, we can fill in the Venn diagram for the situation with the expressions shown:

No further information is given in the problem, however, so there is no way to calculate x.

The question asks if Cary is an element of M.

Assume Statement 1 alone. From the Venn diagram, it can be seen that T and M are disjoint sets. Since Cary is an element of T, he cannot be an element of M - Cary is not a Male.

Assume Statement 2 alone. From the Venn diagram, it can be seen that M⊆T - that is, if Cary is an element of M, then she is an element of T. Restated, if Cary is a Male, then he is a Teenagers. The contrapositive also holds - if Cary is not a teenager - which is given in Statement 2 - then Cary is not a male.

(1) Given x² > 1, it follows that either x > l or x < -1. If x > l, then multiplying both sides of the inequality by the positive number x gives x² > x. On the other hand, if x < -l, then x is negative and x² is positive (because x² > 1), which also gives x² > x; SUFFICIENT. (2) Given x > -l, x² can be greater than x (for example, x = 2) and x² can fail to be greater than x (for example, x = O); NOT sufficient.
The correct answer is A

By expanding the product (x - l)(y- 1), the question is equivalent to whether xy - y - x + 1 = 1, or xy - y - x = 0, when xy > 0.
(1) If x + y = xy, then xy -y -x = 0, and hence by the remarks above, (x -l)(y-1) = 1; SUFFICIENT.
(2) If x = y, then (x - 1)(y- 1) = 1 can be true (x = y = 2) and (x - 1)(y- 1) = 1 can be false (x = y = 1); NOT sufficient.

Consider the Venn diagram below in which x represents the number of businesses that reported a net profit and had investments in foreign markets. Since 21 businesses reported a net profit, 21 - x businesses reported a net profit only. Since 15 businesses had investments in foreign markets, 15 - x businesses had investments in foreign markets only. Finally, since there is a total of 30 businesses, the number of businesses that did not report a net profit and did not invest in foreign markets is 30 - (21- x + x + 15 - x) = x - 6.
Determine the value of x - 6, or equivalently, the value of x.

(1) It is given that 12 = x; SUFFICIENT.
(2) It is given that 24 = (21 - x) + x + (15 - x). Therefore, 24 = 36 - x, or x = 12. Alternatively, the information given is exactly the number of businesses that are not among those to be counted in answering the question posed in the problem, and therefore the number of businesses that are to be counted is 30 - 24 = 6; SUFFICIENT.
The correct answer is D