Try yourself:Directions: Solve the problem and select the best of the answer choices given. Larry’s Lawn Service charges $w/hour for the first x hours of grass trimming, then w + 2 dollars for every hour of work over x hours. How much more will a homeowner be charged for a grass trimming job that took z hours if z > x than for a job which took only w hours if x < w < z?
A
x(z + w)
B
(w + 2) – zx
C
(w + 2) (z – w)
D
xw + 2 – (z – w)
E
xw + 2 – 1
Correct Answer: C
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)
Try yourself:Directions: Solve the problem and select the best of the answer choices given. At a medical research lab, nine doctors are conducting multiple clinical trials. Six of the doctors are working on a clinical trial with exactly one other doctor and three doctors are working on a clinical trial with exactly two other doctors. If two doctors are selected at random from the lab, what is the probability that those two doctors are NOT working together on a clinical trial?
A
1/12
B
2/12
C
5/12
D
7/12
E
10/12
Correct Answer: E
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.
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MULTIPLE CHOICE QUESTION
Try yourself:Directions: Solve the problem and select the best of the answer choices given. Clarissa spent all day on a sightseeing trip in Britain. Starting from her hotel, Clarissa boarded a bus, which traveled at an average speed of 15 miles per hour through a 30 mile section of the countryside. The bus then stopped for lunch in London before continuing on a 3 hour tour of the city's sights at a speed of 10mph. Finally, the bus left the city and drove 40 miles straight back to the hotel. Clarissa arrived at her hotel exactly 2 hours after leaving London. What was the bus's average rate, approximately, for the entire journey?
A
8
B
14
C
21
D
25
E
30
Correct Answer: B
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.
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MULTIPLE CHOICE QUESTION
Try yourself:Directions: Solve the problem and select the best of the answer choices given. In a university club of 200 people, the number of Political Science majors is 50 less than 4 times the number of International Relations majors. If one fifth of the club members are neither Political Science majors nor International Relations majors, and no club member is majoring in both Political Science and International Relations, how many of the club members are International Relations majors?
A
42
B
50
C
71
D
95
E
124
Correct Answer: A
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
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MULTIPLE CHOICE QUESTION
Try yourself:Directions: Solve the problem and select the best of the answer choices given. For which of the following functions g is g(z) = g(1 – z) for all z?
A
g(z) = 1 - z
B
g(z) = 1 – z2
C
g(z) = z2 – (1 – z)2
D
g(z) = z2(1 – z)2
E
g(z) = z / 1-z
Correct Answer: D
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).
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MULTIPLE CHOICE QUESTION
Try yourself:Directions: Solve the problem and select the best of the answer choices given. Meredith jogged to the top of a steep hill at an average pace of 6 miles per hour. She took the same trail back down. To her relief, the descent was much faster; her average speed rose to 14 miles per hour. If the entire run took Meredith exactly one hour to complete and she did not make any stops, how many miles, approximately, is the trail one way?
A
2
B
3
C
4
D
5
E
6
Correct Answer: C
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
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MULTIPLE CHOICE QUESTION
Try yourself:Directions: Solve the problem and select the best of the answer choices given. If the total cost of 20 pairs of shoes is equal to the total revenue generated from the sale of 25 pairs of shoes, what is the percent of profit or loss made on the sale of each pair of shoes, assuming each pair of shoes cost the same dollar amount and each pair of shoes sold for the same dollar amount?
A
25% loss
B
25% profit
C
20% loss
D
20% profit
E
5% profit
Correct Answer: C
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.
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MULTIPLE CHOICE QUESTION
Try yourself:Directions: Solve the problem and select the best of the answer choices given. The City Opera House is expanding. Currently the city block containing the opera house is rectangular-shaped with a total volume of 9600 feet. If the expanded Opera House is 2.5 times as long, wide, and deep as the original building, what would the new volume be?
A
24,000
B
60,000
C
72,000
D
150,000
E
245,000
Correct Answer: D
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.
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MULTIPLE CHOICE QUESTION
Try yourself: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
A
18 days
B
27 days
C
26.67 days
D
16 days
E
12 days
Correct Answer: A
A can complete a project in 20 days. So, A will complete 1/20th of the project in a day.
B can complete a project in 30 days. So, B will complete 1/30th of the project in a day.
Let the total number of days taken to complete the project be 'x' days. The value of x is the answer to the question.
B worked all x days. However, A worked for (x - 10) days because A quits 10 days before the project is completed.
In a day, A completes 1/20th of the project. Therefore, A would have completed (x - 10)/20th of the project in (x - 10) days.
In a day, B completes 1/30th of the project. Therefore, B would have completed x/30th of the project in x days.
Thus, (x - 10)/20 + x/30 = 1
3(x - 10) + 2x = 60
3x - 30 + 2x = 60
5x = 90 or x = 18
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MULTIPLE CHOICE QUESTION
Try yourself: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank?
A
1/2
B
2/3
C
4/7
D
3/4
E
2/7
Correct Answer: C
We are given that rate of work of 1 narrow pipe : rate of work of 1 wide pipe = 1:2
If we can find the ratio of rate of work of 2 wide pipes : rate of work of all pipes together, then we can easily get the ratio of time taken by 2 wide pipes : time taken by all pipes together. This is because ratio of time taken will be inverse of the ratio of rate of work since work done in both the cases is the same. (For a further explanation of this concept, check out the previous post)
In ratio terms, rate of work of 3 narrow pipes is 1*3 and rate of work of 2 wide pipes is 2*2
Therefore, rate of work of 3 narrow pipes : rate of work of 2 wide pipes = 3:4
Or we can say rate of work of 2 wide pipes : rate of work of all pipes together = 4 : (3+4) = 4:7
Then, time taken by 2 wide pipes : time taken by all pipes together = 7:4 (i.e. inverse of 4:7)
So all the pipes together will take 4/7 th of the time taken by the two wide pipes.
1. How do I approach quantitative reasoning questions in GMAT Problem Solving?
Ans. GMAT Problem Solving requires identifying what's being asked, eliminating distractors, and working systematically through algebraic or arithmetic methods. Read carefully to spot hidden assumptions, then test answer choices strategically-backsolving saves time on complex word problems. Master fundamentals in number properties, percentages, and ratio-proportion before tackling advanced problems.
2. What's the difference between algebraic and arithmetic problem-solving methods on the GMAT?
Ans. Arithmetic relies on direct calculation using basic operations, fractions, and percentages, while algebraic methods use variables and equations to model relationships. GMAT Problem Solving questions often allow both approaches, but algebra proves faster for multi-step scenarios. Practitioners benefit from recognizing when each method minimises computational errors and saves test time.
3. Why do I keep making careless mistakes in GMAT numerical problem-solving practice?
Ans. Common errors include misreading question stems, rushing through calculations, and neglecting units or constraints. Students often skip verifying answers against the original problem. Slow down, underline key information, double-check arithmetic, and confirm your solution addresses what was actually asked-not just what seems logical in Problem Solving sequences.
4. How should I practice GMAT quantitative word problems to improve accuracy?
Ans. Work through problem-solving practice questions systematically: first understand the problem structure, then solve without looking at options, and finally compare your answer to given choices. Review mistakes immediately to identify patterns. Use EduRev's worksheets, MCQ tests, and detailed solutions to reinforce weak areas and build consistent problem-solving habits across various question types.
5. What strategies help when I'm stuck on a difficult GMAT Problem Solving question during practice?
Ans. When stuck, try backsolving by testing answer choices from middle to extremes, or plug in simple numbers to eliminate impossible options. Redraw diagrams if geometry-based, restate the problem in simpler terms, or skip strategically and return later. These tactical approaches prevent time wastage while maintaining momentum in practice sessions focused on quantitative reasoning mastery.
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