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New Set of Mixed Questions!!! [#permalink]
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The next set of medium/hard PS questions. I'll post OA's with detailed explanations on Friday. Please, post your solutions along with the answers.1. The distance from the Yaxis to point K is 1/3 of the distance from the Xaxis to point K. If the coordinates of K are (3, y), what is the distance between point K and Xaxis?A. 1/2 B. 1 C. 3 D. 4.5 E. 9. Solution: https://gmatclub.com/forum/newsetofm ... l#p12084362. What is the area of a region enclosed by x/3+y/9=10?A. 675 B. 1350 C. 2700 D. 5400 E. 10800 Solution: https://gmatclub.com/forum/newsetofm ... l#p12084413. Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x?A. 1 B. 1.25 C. 2 D. 2.5 E. 4 Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084454. A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?A. 9 liters B. 18 liters C. 27 liters D. 36 liters E. 45 iters Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084495. For a certain set of numbers, if x is in the set, then both x^2 and x^3 are also in the set. If the number 1/2 is in the set , which of the following must also be in the set ? I. 1/64 II. 1/64 III. 1/2^(1/3) A. I only, B. II only, C. III only, D. I and II only E. I, II and III Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084546. A team contributes total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have?A. 37 B. 38 C. 39 D. 40 E. 41 Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084577. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat? A. 16% B. 25% C. 32% D. 48% E. 75% Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084598. Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school?A. 15 minutes B. 20 minutes C. 25 minutes D. 30 minutes E. 210 minutes Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084629. If x and y are integers and x + y = 12, which of the following must be true?A. Both x and y are negative B. xy > 0 C. If y < 0, then x > 0 D. If y > 0, then x < 0 E. x  y > 0 Solution: http://gmatclub.com/forum/newsetofmi ... l#p120846610. If n is a nonnegative integer and the remainder when 3^n is divided by 4 is a multiple of 3, then which of the following must be true?I. n^2 divided by 4 yields the reminder of 1 II. (2)^n is less than 0 III. n is a prime number A. I only B. II only C. III only D. I and II only E. II and III only Solution: http://gmatclub.com/forum/newsetofmi ... l#p1208471BONUS QUESTION: 11. Certain bowl contains 5 red marbles and 3 blue marbles only. One by one, every marble is drawn at random and without replacement. What is the probability that the seventh marble drawn is NOT blue?A. 7/8 B. 3/4 C. 2/3 D. 5/8 E. 3/8 Solution: http://gmatclub.com/forum/newsetofmi ... l#p1208473Kudos points for each correct solution!!!
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6. A team contributes total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have?
A. 37 B. 38 C. 39 D. 40 E. 41 Answer. C. 39To identify the maximum number each member of the team should have contributed closer or equal to minimum number (~$10) 37 members contributing $10 each will make $370. Since no one contributes $19, 2 members share the $29 between them which makes $399 from 39 members
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7. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat? A. 16% B. 25% C. 32% D. 48% E. 75% Say mar yeans $100 and spends $16 for meat and $64 for food. Percentage spent on meat in total food expenditure is 16/64 = 25% which makes 75% not spent meatAnswer E. 75% [b]
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8. Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school? A. 15 minutes B. 20 minutes C. 25 minutes D. 30 minutes E. 210 minutes [/b] Mary left 20 Minutes later and reached school 15 minutes later. Because of the 20% speed increase she has reached the distance 5 minutes earlier Substituting the value in each of the answer options, Speed difference between today and usual should be 20% ~Du/Tu – Dt/Tt = 20/100 = .2 Where, Du – Distance usual; Dt – Distance today; Tu – Time Usual; Tt – Time today Lets take mary’s speed is 1 unit/ minute Option A. 15 minutes => A)15/10 – 15/15 = 0.5 B)20/15 – 20/20 = 0.33 C)25/20 – 25/25 = 0.25 D)30/25 – 30/30 = 0.2 Answer= D. 30 minutes
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9. If x and y are integers and x + y = 12, which of the following must be true? A. Both x and y are negative B. xy > 0 C. If y < 0, then x > 0 D. If y > 0, then x < 0 E. x  y > 0 X and Y are integers X+Y = 12 A. Both x and y are negative => not true as there is a possibility for one of the number is higher negative (e.g., X = 14; Y =2) B. xy > 0 => not true; one number can be positive and one number can be negative to make the condition true C. If y < 0, then x > 0 => It is not necessary that only one number should be negative we need at least one to be negative to make the statement true; In this scenario x can be negative. D. If y > 0, then x < 0 => True as at least one number should be negative to get the negative summationE. x  y > 0 => not true in the case of x = 6 and y = 6 and so many other scenarios Answers D
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Dipankar6435 wrote: g106 wrote: Answers for Questions 3  9
3. Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x?
A. 1 B. 1.25 C. 2 D. 2.5 E. 4
A, B, and C, can complete a certain task in 10, 5 and x hours respectively A completes 1/10 of the total work in 1 hr B Completes 1/5 of the total work in 1 hr C completes 1/x of the total work in 1 hr A starts working alone and 2 hours later B joins. After another 2 hours joins C. A completes 2/10 of the total work in 2 hrs later B joins A A&B together can complete 1/10 + 1/5 of the total work in 1 hr = 3/10 A&B work together for 2 hour and they complete 2 * 3/10 = 6/10 of the total work
By the time C joins A&B 8/10 of the total work is complete
To complete 2/10 of the work A, B & C together take 15 minutes (1/4 hr) 2/10 = ¼( 1/10 + 1/5+ 1/x) 8/10 = 3/10 + 1/X 5/10 = 1/X X = 2 Answer = C
4. A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?
A. 9 liters B. 18 liters C. 27 liters D. 36 liters E. 45 iters
Draining pipe takes 4 hr to empty the pool Rain inflow = 3lt/hr Time taken to drain the water from the pool on rainy day = 6
It takes 2 hr to drain the additional water added due to rain Water accumulation in six hrs of rain = 3*6 = 18lts
It takes 2 hrs to drain 18 lts => in 4 hours 36 lts of water will be drained from the pool and the capacity of the pool is 36 liters
Answer:D 36 liters
5. For a certain set of numbers, if x is in the set, then both x^2 and x^3 are also in the set. If the number 1/2 is in the set , which of the following must also be in the set ?
I. 1/64 II. 1/64 III. 1/2^(1/3)
A. I only, B. II only, C. III only, D. I and II only E. I, II and III
X = ½ X^2 = ¼ = X1 X^3 = 1/8 = X2
X1^2 = 1/16 X1^3 = 1/64 (I)
X2^2 = 1/64 (II)
Ans D. I and II only
6. A team contributes total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have?
A. 37 B. 38 C. 39 D. 40 E. 41
Answer. C. 39
To identify the maximum number each member of the team should have contributed closer or equal to minimum number (~$10)
37 members contributing $10 each will make $370. Since no one contributes $19, 2 members share the $29 between them which makes $399 from 39 members
7. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat?
A. 16% B. 25% C. 32% D. 48% E. 75%
Say mar yeans $100 and spends $16 for meat and $64 for food.
Percentage spent on meat in total food expenditure is 16/64 = 25% which makes 75% not spent meat
Answer E. 75%
8. Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school?
A. 15 minutes B. 20 minutes C. 25 minutes D. 30 minutes E. 210 minutes
Mary left 20 Minutes later and reached school 15 minutes later. Because of the 20% speed increase she has reached the distance 5 minutes earlier
Substituting the value in each of the answer options, Speed difference between today and usual should be 20% ~Du/Tu – Dt/Tt = 20/100 = .2 Where, Du – Distance usual; Dt – Distance today; Tu – Time Usual; Tt – Time today Lets take mary’s speed is 1 unit/ minute
Option A. 15 minutes => A)15/10 – 15/15 = 0.5 B)20/15 – 20/20 = 0.33 C)25/20 – 25/25 = 0.25 D)30/25 – 30/30 = 0.2
Answer= D. 30 minutes
9. If x and y are integers and x + y = 12, which of the following must be true?
A. Both x and y are negative B. xy > 0 C. If y < 0, then x > 0 D. If y > 0, then x < 0 E. x  y > 0
X and Y are integers X+Y = 12
A. Both x and y are negative => not true as there is a possibility for one of the number is higher negative (e.g., X = 14; Y =2) B. xy > 0 => not true; one number can be positive and one number can be negative to make the condition true C. If y < 0, then x > 0 => It is not necessary that only one number should be negative we need at least one to be negative to make the statement true; In this scenario x can be negative. D. If y > 0, then x < 0 => True as at least one number should be negative to get the negative summation E. x  y > 0 => not true in the case of x = 6 and y = 6 and so many other scenarios
Answers D BANG ON!!!!!! Just some issue with Q5 5. For a certain set of numbers, if x is in the set, then both x^2 and x^3 are also in the set. If the number 1/2 is in the set , which of the following must also be in the set ? I. 1/64 II. 1/64 III. 1/2^(1/3) A. I only, B. II only, C. III only, D. I and II only E. I, II and III X = ½ X^2 = ¼ = X1X^3 = 1/8 = X2 X1^2 = 1/16X1^3 = 1/64 (I) X2^2 = 1/64 (II) Ans D. I and II only IMO x^2 should be \(\frac{1}{4}\) Likewise X2^2 will be \(\frac{1}{64}\) And we will never get +ve values. Thus only possible soln is A I assumed –X^2 as (x)^2 You are right it should be –(x^2), but the answer remains same X = ½ X^2 = ¼ = X1 X^3 = 1/8 = X2 X1^2 = 1/16 X1^3 = +1/64 (I) X2^2 = 1/64 (II)
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11. D Since there are repeats, to calculate no of arrangements we use the formula
n!/[(no of repeats in group 1)! * (no of repeats in group 2)!]
[By fixing position of blue ball in the 7th place]
No of ways that we can get blue ball in 7th turn = 7! / (5! * 2!) = 21
No of ways that the 8 balls can be arranges = 8! ( 5! * 3!) = 56
Therefore : p(blue ball in 7th turn) = 21/56 = 3/8
Therefore : p(no blue ball in 7th turn) = 5/8
Please let me know if this answer is right!



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BONUS QUESTION: 11. Certain bowl contains 5 red marbles and 3 blue marbles only. One by one, every marble is drawn at random and without replacement. What is the probability that the seventh marble drawn is NOT blue?
A. 7/8 B. 3/4 C. 2/3 D. 5/8 E. 3/8
There are 8 marbles in total. The first thing we have to do is to calculate the number of outcomes of the first 6 drawn marbles. 1. R R R B B B (20 outcomes) (3 red 3 blue marbles can be arranged in 20 different ways) 2. R R R R B B (16 outcomes) (4 red 2 blue marbles can be arranged in 16 different ways) 3. R R R R R B (6 outcomes) (5 red 1 blue marbles can be arranged in 6 different ways) We need to find the probability of the seventh marble is RED. case 1. two remaining marbles are red (seventh always red) case 2. two remaining marbles are either blue or red (50% red) case 3. two remaining marbles are blue (always blue) So, the probability that the seventh marble drawn red is ((20+(16/2)+0))/(20+16+6)=28/42=2/3



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1. The distance from the Yaxis to point K is 1/3 of the distance from the Xaxis to point K. If the coordinates of K are (3, y), what is the distance between point K and Xaxis?
A. 1/2 B. 1 C. 3 D. 4.5 E. 9.
Coordinate of K is (3,y). ==> Distance of K from Yaxis is 3. ==> Distance of K from Xaxis is 9.
Correct answer is E.



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2. What is the area of a region enclosed by x/3+y/9=10?
A. 675 B. 1350 C. 2700 D. 5400 E. 10800
Area is enclosed by following four lines: 3x + y = 90 Passing through (0, 90) and (30, 0) 3x  y = 90 Passing through (0, 90) and (30, 0)  3x + y = 90 Passing through (0, 90) and (30, 0)  3x  y = 90 Passing through (0, 90) and (30, 0) This makes rhombus area with diagonals of length 60 and 180. Area of the region = d1*d2/2 = 60*180/2 = 5400
Correct answer is D.



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3. Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x?
A. 1 B. 1.25 C. 2 D. 2.5 E. 4
Time spent on the work is 4.25 hrs by A, 2.25 hrs by B, and .25 hr by C. Let’s say the work as w. A does w in 10 hrs ==> In 4.25 hrs, A does 0.425w B does w in 5 hrs ==> In 2.25 hrs, B does 0.45w C does w in x hrs ==> In 0.25 hrs, C does 0.25w/x ==> 0.425w + 0.45 w + 0.25w/x = w ==> 0.25w/x = w  0.425w  0.45 w = 0.125w ==> x = 2
Correct answer is C.



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4. A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?
A. 9 liters B. 18 liters C. 27 liters D. 36 liters E. 45 iters
Rain inflow in 6 hrs = 18 lt. ==> Draining pipe took extra 2 hrs to drain out extra 18 lt. water ==> Draining pipe can clear 36 lt. in 4 hrs. ==> Capacity of the pool is 36 liters.
Correct answer is D.



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5. For a certain set of numbers, if x is in the set, then both x^2 and x^3 are also in the set. If the number 1/2 is in the set , which of the following must also be in the set ?
I. 1/64 II. 1/64 III. 1/2^(1/3)
A. I only, B. II only, C. III only, D. I and II only E. I, II and III
If x is in the set, then both x^2 and x^3 are also in the set ==> There cannot be any other +ve number derived from the presence of 1/2 (as both x^2 and x^3 are –ve) ==> Option II and option III are not must
1/2 is in the set ==> 1/4 and 1/8 are in the set ==> 1/16, 1/64, and 1/512 are in the set ==> Option I is correct
Correct answer is A.



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6. A team contributes total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have?
A. 37 B. 38 C. 39 D. 40 E. 41
Greatest number of members can be obtained by contributing least amount by most of the members. So, maximum number of members = upper round ($399) / 10 – 1 = 400/10 – 1 = 40 – 1 = 39
Correct answer is C.



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7. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat?
A. 16% B. 25% C. 32% D. 48% E. 75%
Assuming salary as $100, $64 is spend on food and $16 spent on meat. So, 16/64 = 1/4 = 25% of the food expenditure was spent on meat. This means 75% of the salary spent on food was not spent on meat.
Correct answer is E.



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8. Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school?
A. 15 minutes B. 20 minutes C. 25 minutes D. 30 minutes E. 210 minutes
Assuming usual time for Holly is t min. By increasing speed by 20%, today Holly took t/1.2 min. As found from the given data, today Holly has spend 5 mins less on commuting. So, t – 5 = t/1.2 ==> 1.2t – 6 = t ==> 0.2t = 6 ==> t = 30 min
Correct answer is D.



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9. If x and y are integers and x + y = 12, which of the following must be true?
A. Both x and y are negative B. xy > 0 C. If y < 0, then x > 0 D. If y > 0, then x < 0 E. x  y > 0
A. Not mandatory. X,y can have the values as 6,6 or 20,8. Condition is true for first case and false for second case. B. Not mandatory. If x,y is 6,6, xy >0. If x,y is 20,8, xy < 0. Condition is true for first case and false for second case. C. Not mandatory. X,y can be 6,6 or 8,20. Condition is true for second case and false for first case. D. As the sum of two numbers is –ve, if one is +ve, other one must be –ve. This is correct condition. E. Not mandatory. If x,y is 20,8, xy < 0. If x,y is 8,20, xy > 0. Condition is true for second case and false for first case.
Correct answer is D.



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10. If n is a nonnegative integer and the remainder when 3^n is divided by 4 is a multiple of 3, then which of the following must be true?
I. n^2 divided by 4 yields the reminder of 1 II. (2)^n is less than 0 III. n is a prime number
A. I only B. II only C. III only D. I and II only E. II and III only
When 3^n is divided by 4, remainder is a multiple of 3 ==> n is odd. I. For all odd n’s, remainder will be 1 if n^2 is divided by 4. Correct. II. As n is odd, (2)^n is –ve. Correct. III. n can be 9 or 15 or some other composite odd number. Incorrect.
Correct answer is D.



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11. Certain bowl contains 5 red marbles and 3 blue marbles only. One by one, every marble is drawn at random and without replacement. What is the probability that the seventh marble drawn is NOT blue?
A. 7/8 B. 3/4 C. 2/3 D. 5/8 E. 3/8
Total number of marbles is 8. For any given position, probability for red marble is 5/8 and blue marble is 3/8. So, the probability that the seventh marble drawn is NOT blue is 5/8
Correct answer is D.



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2. What is the area of a region enclosed by x/3+y/9=10?A. 675 B. 1350 C. 2700 D. 5400 E. 10800 Find the x and y intercepts. When y=0, then x=30 or x=30. When x=0, then y=90 or x=90. So, we have 4 points: (30, 0), (30, 0) (0, 90), (0, 90). When joining these points we get the rhombus: Attachment:
2.png [ 7.85 KiB  Viewed 29580 times ]
The area of a rhombus is \(\frac{d_1*d_2}{2}\) (where \(d_1\) and \(d_2\) are the lengths of the diagonals), thus the area of the enclosed figure is 60*180/2=5,400. Answer: D.
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New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




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