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New Set of Mixed Questions!!!

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Math Expert
Joined: 02 Sep 2009
Posts: 39608
New Set of Mixed Questions!!! [#permalink]

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01 Apr 2013, 07:48
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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 Y-axis to point K is 1/3 of the distance from the X-axis to point K. If the coordinates of K are (-3, y), what is the distance between point K and X-axis?

A. 1/2
B. 1
C. 3
D. 4.5
E. 9.

Solution: new-set-of-mixed-questions-150204-100.html#p1208436

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

Solution: new-set-of-mixed-questions-150204-100.html#p1208441

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

Solution: new-set-of-mixed-questions-150204-100.html#p1208445

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

Solution: new-set-of-mixed-questions-150204-100.html#p1208449

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

Solution: new-set-of-mixed-questions-150204-100.html#p1208454

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 Solution: new-set-of-mixed-questions-150204-100.html#p1208457 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% Solution: new-set-of-mixed-questions-150204-100.html#p1208459 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 Solution: new-set-of-mixed-questions-150204-100.html#p1208462 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 Solution: new-set-of-mixed-questions-150204-100.html#p1208466 10. If n is a non-negative 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: new-set-of-mixed-questions-150204-100.html#p1208471 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 Solution: new-set-of-mixed-questions-150204-100.html#p1208473 Kudos points for each correct solution!!! _________________ Director Joined: 25 Apr 2012 Posts: 727 Location: India GPA: 3.21 WE: Business Development (Other) Re: New Set of Mixed Questions!!! [#permalink] Show Tags 02 Apr 2013, 06:03 1 This post received KUDOS 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?
ributed
A. 37
B. 38
C. 39
D. 40
E. 41

Sol: Since we need to find the greatest number of members, we should minimise the contribution of each member.
Min Contribution : $10 We can start by assuming no of members from any of the given options starting with C we have, 39*10+ y= 399--> y =$9. This $9 can be shared by any contributed by any of the members Lets take no. of members to be D then we have 400*10 > 399 and hence the case is not possible as Total contribution will exceed$ 399.

Assuming B as no of members we have 38*10+ y= 399----> y =$19 which can be given by eny of the remaining members (shared by 3 or more) Hence max no possible be 39. Ans should be C _________________ “If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.” Director Joined: 25 Apr 2012 Posts: 727 Location: India GPA: 3.21 WE: Business Development (Other) Re: New Set of Mixed Questions!!! [#permalink] Show Tags 02 Apr 2013, 06:06 1 This post received KUDOS 7. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat? A. 16% B. 25% C. 32% D. 48% E. 75% Sol: Let Mary's Salary be US$ 100
Spent on food : $64 Spent on meat :$ 16

A. 37
B. 38
C. 39
D. 40
E. 41

$$399 = 39*10 + 9$$ --> $$399 = 37*10 + 29$$ --> Thus, 37 members each gave $10 and 2 members gave a combination of 29 ( 16,13 or 12,17 or ...) So, the greatest number of members the club could have : 39 Answer : C _________________ KUDOS is the good manner to help the entire community. "If you don't change your life, your life will change you" Intern Joined: 06 Nov 2010 Posts: 41 Location: United States Concentration: Technology, Leadership GPA: 3.7 WE: Engineering (Other) Re: New Set of Mixed Questions!!! [#permalink] Show Tags 02 Apr 2013, 07:31 1 This post received KUDOS 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 SOLUTION: A marble can be drawn from the bowl in 8 ways. A red marble can drawn in 5 ways. So the probability that a marble is NOT blue is 5/8 _________________ Do not dwell in the past, do not dream of the future, concentrate the mind on the present moment. Push +1 kudos button please, if you like my post. Senior Manager Status: Final Lap Joined: 25 Oct 2012 Posts: 286 Concentration: General Management, Entrepreneurship GPA: 3.54 WE: Project Management (Retail Banking) Re: New Set of Mixed Questions!!! [#permalink] Show Tags 02 Apr 2013, 07:38 1 This post received KUDOS 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% Let$100 be her salary ;

So, she spent $64 of her salary on food (including meat) and$16 of her salary on meat.
Hence, she spent 64-16, which is $48 on food not spent on meat. Percent of the salary spent on food were not spend on meat = [Amount spent on food and not spent on meat] / [Total amount spent on food] = 48/64 = 0.75 Answer : E _________________ KUDOS is the good manner to help the entire community. "If you don't change your life, your life will change you" Senior Manager Status: Final Lap Joined: 25 Oct 2012 Posts: 286 Concentration: General Management, Entrepreneurship GPA: 3.54 WE: Project Management (Retail Banking) Re: New Set of Mixed Questions!!! [#permalink] Show Tags 02 Apr 2013, 08:40 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 The data are organized in the figure below; Notice that the distance that takes Holly to arrive from home to school as usual is the same as today; Hence, $$(1.2x-6)=x$$ -->$$x=30minutes$$ Answer: D Attachments Rock3.jpg [ 18.22 KiB | Viewed 2314 times ] _________________ KUDOS is the good manner to help the entire community. "If you don't change your life, your life will change you" Senior Manager Status: Final Lap Joined: 25 Oct 2012 Posts: 286 Concentration: General Management, Entrepreneurship GPA: 3.54 WE: Project Management (Retail Banking) Re: New Set of Mixed Questions!!! [#permalink] Show Tags 02 Apr 2013, 09:05 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 Lets consider this two pairs that match with the equation above : (x,y) = (-3,-9) (x,y) = (-13,1) A- Not always true ; -3 and -9 both are negative BUT -13 is negative whereas 1 is positive B- Not always true; (-3)*(-9) = 27>0 BUT (-13)*(1)<0 C- Not always true; If y = -9 <0 then x = -3<0 so x is not positive D- True; If y>0 then -12-x>0 then x<-12 and hence x must be negative E- Not always true; x-y = -3-9 = -12 <0 Answer : D _________________ KUDOS is the good manner to help the entire community. "If you don't change your life, your life will change you" Manager Joined: 20 Apr 2010 Posts: 210 Schools: ISB, HEC, Said Re: New Set of Mixed Questions!!! [#permalink] Show Tags 02 Apr 2013, 13:09 Bunuel wrote: 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. II only, D. I and II only E. I, II and III Answers B and C are same Math Expert Joined: 02 Sep 2009 Posts: 39608 Re: New Set of Mixed Questions!!! [#permalink] Show Tags 02 Apr 2013, 13:20 prashantbacchewar wrote: Bunuel wrote: 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. II only, D. I and II only E. I, II and III Answers B and C are same Thank you, edited. C should read: III only. _________________ Manager Joined: 21 Aug 2010 Posts: 188 Location: United States GMAT 1: 700 Q49 V35 Re: New Set of Mixed Questions!!! [#permalink] Show Tags 02 Apr 2013, 19:13 1 This post received KUDOS 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 _________________ ------------------------------------- Last edited by g106 on 03 Apr 2013, 07:48, edited 1 time in total. Manager Status: Breaking my head!! Joined: 27 Jan 2013 Posts: 71 Location: India Concentration: General Management, Operations GMAT 1: 740 Q50 V40 GPA: 3.51 WE: Other (Transportation) Re: New Set of Mixed Questions!!! [#permalink] Show Tags 03 Apr 2013, 02:34 Zarrolou wrote: 2. What is the area of a region enclosed by |x/3|+|y/9|=10? We can analize the function x/3 + y/9 = 10 first. y=90-3x This intersect the Y-axis is 90 and the X-axis in 30. The original function ( with the absolute values) has the same graph as y=90-3x, only symmetric for value of x<0 and values of y <0. So the answer is: it defines a triangle of Area=$$\frac{90*30}{2}=1350$$ IMO B Sound reasoning but IMO you missed the last step. What you have calculated is only the part of the figure that lies when x>0 and y>0. Thus only the first quadrant. Since the expression is symmetrical in terms of -x and -y (Substituting -x for x and/or -y for y will not change the expression) the figure will be symmetrical about the x and y axes. You just need to multiply 1350 by 4 to get the area enclosed by the figure. Manager Status: Breaking my head!! Joined: 27 Jan 2013 Posts: 71 Location: India Concentration: General Management, Operations GMAT 1: 740 Q50 V40 GPA: 3.51 WE: Other (Transportation) Re: New Set of Mixed Questions!!! [#permalink] Show Tags 03 Apr 2013, 07:17 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

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

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

BANG ON!!!!!!
Just some issue with Q-5
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

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
Re: New Set of Mixed Questions!!!   [#permalink] 03 Apr 2013, 07:17

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