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Alice studies for a hours on each of Monday, Tuesday, and Thursday. Sh

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Math Revolution GMAT Instructor
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Alice studies for a hours on each of Monday, Tuesday, and Thursday. Sh  [#permalink]

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New post 23 Mar 2018, 00:21
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Question Stats:

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[GMAT math practice question]

Alice studies for a hours on each of Monday, Tuesday, and Thursday. She also studies for b hours on Wednesday, and for c hours on Friday. What is her median study time for the school week?

\(1) a=10\)
\(2) b+c=30\)

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Alice studies for a hours on each of Monday, Tuesday, and Thursday. Sh  [#permalink]

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New post 23 Mar 2018, 01:03
Information given in question
Day-------------------- Monday--------- Tuesday--------- Wednesday-----------Thursday-----------Friday
Study Time(hrs)--------- a--------------- a--------------------b-------------------------a-------------------c

Total number of days per school week = 5
Frequency of a = 3
for all possible value of a, b, c ; a will be median.

Statement 1: a=10hrs
It gives the value of a , hence sufficient
Statement 2: b+c=30
As there is no relation specified between a and b+c, Statement 2 is insufficient.

So Answer is A
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Re: Alice studies for a hours on each of Monday, Tuesday, and Thursday. Sh  [#permalink]

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New post 23 Mar 2018, 01:28
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MathRevolution wrote:
[GMAT math practice question]

Alice studies for a hours on each of Monday, Tuesday, and Thursday. She also studies for b hours on Wednesday, and for c hours on Friday. What is her median study time for the school week?

\(1) a=10\)
\(2) b+c=30\)



In a set having 5 elements, the median must be the middle value. We know from
the question stem that Alice studies for a hrs on a Monday, Tuesday, and Thursday
She studies b hrs on Wednesday and c hrs on Friday

1. If a = 10, the median study time is 10.
There are 6 possibilities
a>b>c - 10 10 10 b c
a>c>b - 10 10 10 c b
c>b>a - c b 10 10 10
b>c>a - b c 10 10 10
b<a<c c 10 10 10 b
c<a<b b 10 10 10 c

In each of these cases, the median study time is 10(Sufficient)

2. Here, we don't know the values of b,c, and a
We can't clearly give the median study time without
knowing the values of a (Insufficient) (Option A)

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Re: Alice studies for a hours on each of Monday, Tuesday, and Thursday. Sh  [#permalink]

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New post 25 Mar 2018, 18:19
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Depending on their values, it is possible to rearrange a, a, a, b, c into ascending order in the following ways:
a, a, a, b, c
a, a, a, c, b
b, a, a, a, c
c, a, a, a, b
b, c, a, a, a
c, b, a, a, a
In every order, the median (middle value) is a. So, the question asks for the value of a.

Thus, only condition 1) is sufficient.

Therefore, A is the answer.

Answer: A
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Re: Alice studies for a hours on each of Monday, Tuesday, and Thursday. Sh &nbs [#permalink] 25 Mar 2018, 18:19
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