Data Sufficiency

Hi ziyuenlau,

We're told that the sum of 7 POSITIVE INTEGERS is LESS than 12. Since that sum has to be so small, there are a limited number of possibilities for the 7 integers. For example....

We could have....
Seven 1s - and the sum would be 7
Five 1s and two 2s - and the sum would be 9
Six 1s and one 4 - and the sum would be 10
Four 1s, two 2s and one 3 - and the sum would be 11
Etc.

We're asked for the RANGE of the 7 integers.

1) The sum of the 7 integers is 11

With a sum of 11, we could have....
Four 1s, two 2s and one 3 - and the RANGE = 2
Six 1s and one 5 - and the RANGE = 4
Fact 1 is INSUFFICIENT

2) The median of the 7 integers is 2

With a MEDIAN of 2, we must have three numbers less than/equal to 2 and three other numbers greater than/equal to 2...

_ _ _ 2 _ _ _

Since we're dealing with POSITIVE INTEGERS, there's only one way for this to occur...

1 1 1 2 2 2 2

Thus, the range MUST equal 1.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

ziyuenlau wrote:If the sum of the 7 positive integers is smaller than 12, what is the range of the 7 integers?

1) The sum of the 7 integers is 11
2) The median of the 7 integers is 2

Source : Math Revolution
Official Answer : B

Hi ziyuenlau,

These types of questions require you to play with numbers and do some hit and trial.

We have: Sum of the 7 positive integers < 12

We have to find the range of the 7 positive integers

Let's take each statement one by one.

S1: The sum of the 7 integers is 11.

We can at least a couple of extreme cases.

Case 1: The 7 integers are: 1, 1, 1, 1, 1, 1, 5. Range = 5 - 1 = 4.

Case 2: The 7 integers are: 1, 1, 1, 2, 2, 2, 2. Range = 2 - 1 = 1. No unqiue answer. Insufficient.

There can be other cases too.

S2: The median of the 7 integers is 2.

Say the integers arranged in ascending order are: a, b, c, 2, d, e, f

Since the 4th integer is the median, the minimum value d, e, and f each can take is 2.

Thus, the integers arranged in ascending order are: a, b, c, 2, 2, 2, 2

We have to make sure that a+b+c+2+2+2+2 < 12

=> a+b+c+8 < 12

=> a+b+c < 4

Since a, b and c are positive integers, the minimum and only value each can take is 1.

Thus, the integers are: 1, 1, 1, 2, 2, 2, 2. Range = 2 - 1 = 1. Sufficient.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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