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 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
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