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There are three different hoses used to fill a pool: hose x,

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There are three different hoses used to fill a pool: hose x,

by BTGmoderatorLU » Thu Sep 06, 2018 6:53 pm

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Source: Veritas Prep

There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3

A. I only
B. III only
C. I and III only
D. II only
E. I, II and III

The OA is C.
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by Jay@ManhattanReview » Thu Sep 06, 2018 9:41 pm
BTGmoderatorLU wrote:Source: Veritas Prep

There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?

I. d < c
II. d > b
III. c/3 < d < a/3

A. I only
B. III only
C. I and III only
D. II only
E. I, II and III

The OA is C.
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by Jay@ManhattanReview » Thu Sep 06, 2018 9:48 pm
BTGmoderatorLU wrote:Source: Veritas Prep

There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?

I. d < c
II. d > b
III. c/3 < d < a/3

A. I only
B. III only
C. I and III only
D. II only
E. I, II and III

The OA is C.
If there were only z hose in operation, the pool would fill in c days; however, since two more hoses are helping hose z, the pool would fill in less than c days; thus, d < c. Statement I is correct.

Also, since b > c and d < c, we have d < b; thus, Statement II is incorrect.

Assuming that a, b and c are nearly equal to each other, thus, the pool would fill in c/3 days, or d = c/3; however, it is not so since a > b > c, thus, a/3 > d > c/3. So, statement III is also correct.

The correct answer: C

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Mon Sep 17, 2018 5:36 pm

There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?

I. d < c
II. d > b
III. c/3 < d < a/3

A. I only
B. III only
C. I and III only
D. II only
E. I, II and III
Roman numeral I is true. When all three hoses work together, the number of days it takes must be less than the number of days it takes for any individual hose to complete the job by itself. Using the same argument, we see that Roman numeral II can't be true.

If each hose works as fast as hose z, it will take exactly c/3 days. However, since they do not, and since hose z is the fastest, they must take more than c/3 days. That is, d > c/3. Similarly, if each hose works as fast as hose x, it will take exactly a/3 days. However, since they do not, and since hose x is the slowest, they must take less than a/3 days. That is, d < a/3. We see that c/3 < d < a/3, which means Roman numeral III is true also.

Answer: C

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