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Data Sufficiency - problem I don't seem to understand

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Data Sufficiency - problem I don't seem to understand

by jowe125 » Fri Dec 09, 2011 6:00 pm
Is the average (arithmetic mean) of a and b less than 40?

1. The average (arithmetic mean) of 3a and 3b is 117.

2. b=5a

The answer is A but I don't seem to understand how the first statement is sufficient to answer the question. I chose C when I was doing the problem thinking that you can replace b with 5a in the first statement's equation and solve for a therefore then solving for b and find the answer. I didn't do the math though.

Can someone help me understand this problem? Am I missing something stupid???

Thanks!!!!
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by fcabanski » Fri Dec 09, 2011 8:14 pm
Mean = sum of numbers / number of numbers

The problem asks if (a+b)/2 < 40

Multiply both sides by 2:

Is a+b < 80 ?

1. gives that (3a+3b)/2 = 117
3a + 3b = 234
a+b = 234/3 = 78

Thus a+b=78 < 80. 1 is sufficient.

2.

b=5a gives that the mean is (a+5a)/2 = 6a/2 = 3a. But without knowing the value of a, we can't know if 3a < 40. 2 is insufficient.

The answer is therefore a.
Last edited by fcabanski on Fri Dec 09, 2011 8:18 pm, edited 1 time in total.
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by rijul007 » Fri Dec 09, 2011 8:17 pm
jowe125 wrote:Is the average (arithmetic mean) of a and b less than 40?

1. The average (arithmetic mean) of 3a and 3b is 117.

2. b=5a

The answer is A but I don't seem to understand how the first statement is sufficient to answer the question. I chose C when I was doing the problem thinking that you can replace b with 5a in the first statement's equation and solve for a therefore then solving for b and find the answer. I didn't do the math though.

Can someone help me understand this problem? Am I missing something stupid???

Thanks!!!!
Statement 1:
Avg of 3a and 3b is 117
(3a+3b)/2 = 117
(a+b)/2 = 117/3 = 39
Avg of a and b is less than 40
SUFFICIENT

Statement 2:
b=5a
Avg = 5a+a/2 = 3a
INSUFFICIENT

Correct option A
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by Jeff@TargetTestPrep » Fri Jan 05, 2018 9:20 am
jowe125 wrote:Is the average (arithmetic mean) of a and b less than 40?

1. The average (arithmetic mean) of 3a and 3b is 117.

2. b=5a
We need to determine whether (a + b)/2 < 40, i.e., whether a + b < 80.

Statement One Alone:

The average (arithmetic mean) of 3a and 3b is 117.

Thus:

(3a + 3b)/2 = 117

3a + 3b = 234

a + b = 78

(a + b)/2 = 39

Statement one alone is sufficient to answer the question.

Statement Two Alone:

b = 5a

Since we do not know the values of a or b, we cannot determine whether a + b is less than 80.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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