Problem Solving Practice Questions - 1 | Practice Questions for GMAT PDF Download

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 (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 (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 (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 (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). 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 (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 (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 (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 (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.