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Divisibilty:

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Source: — Data Sufficiency |

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by [email protected] » Wed Aug 28, 2013 11:38 pm
Hi manpreet,

These types of DS questions are perfect for TESTing values.

We're told that A and B are integers. We're asked if (A + B)/7 = an integer? This is a YES/NO question.

Fact 1 tells us that A is NOT a multiple of 7, but doesn't tell us anything about B
Fact 1 is INSUFFICIENT.

Fact 2 tells us that (A - B)/7 = integer
If A = 7, B = 0, 7/7 = an integer and the answer to the question (7+0)/7 = 1 = YES
If A = 8, B = 1 7/1 = an integer and the answer to the question (8+1)/7 = 9/7 = NO
Fact 2 is INSUFFICIENT

Combining Facts, we could have
A = 8, B = 1 ---> NO.
A = 9, B = 2 ----> NO.
A = 10, B = 3 ----> NO.
A = 11, B = 4 -----> NO.
etc.
**NOTE: A CAN'T BE A MULTIPLE OF 7 (from Fact 1), so A CAN'T = 7, 14, 21, 28, etc.**
CONSISTENT = SUFFICIENT

Final Answer: C

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by sanju09 » Thu Aug 29, 2013 2:18 am
'manpreet singh wrote:Is the sum of integers a and b divisible by 7?

(1) a is not divisible by 7.
(2) a - b is divisible by 7.

ans c
Is (a + b) a multiple of 7?

I. If a is 4 (not divisible by 7) and b is 10, the sum of integers a and b is YES divisible by 7. But, if a is 4 (not divisible by 7) and b is 12, the sum of integers a and b is NO, not divisible by 7. Insufficient so DELETE choices A and D.

II. If a is 18 and b is 4, then a - b is divisible by 7 but a + b is NO, not. And when a is 21 and b is 7, then a - b is still divisible by 7 and a + b is YES divisible by 7. Insufficient so DELETE choice B also.

When taken together, now we know that given difference between two numbers divisible by 7, sum of these numbers will also be divisible by 7, if and only if each of the two numbers are divisible by 7. But, statement 1 says that this isn't the case; hence, the sum of integers a and b is NOT divisible by 7.

[spoiler]SUFFICIENT

Take C[/spoiler]
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by Brent@GMATPrepNow » Thu Aug 29, 2013 8:08 am
sanju09 wrote: When taken together, now we know that given difference between two numbers divisible by 7, sum of these numbers will also be divisible by 7, if and only if each of the two numbers are divisible by 7.
Hi sanju09,

It looks as though you're suggesting there's a rule that goes something like this: If the difference between two integers is divisible by k, then the sum of these integers will also be divisible by k, if and only if each of the two numbers is divisible by k.

While this rule certainly applies here, when k=7, I wouldn't want students to extrapolate and use it for all possible values of k. For example, the rule doesn't hold true when k=2.

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by sanju09 » Mon Sep 09, 2013 11:59 pm
Brent@GMATPrepNow wrote:
sanju09 wrote: When taken together, now we know that given difference between two numbers divisible by 7, sum of these numbers will also be divisible by 7, if and only if each of the two numbers are divisible by 7.
Hi sanju09,

It looks as though you're suggesting there's a rule that goes something like this: If the difference between two integers is divisible by k, then the sum of these integers will also be divisible by k, if and only if each of the two numbers is divisible by k.

While this rule certainly applies here, when k=7, I wouldn't want students to extrapolate and use it for all possible values of k. For example, the rule doesn't hold true when k=2.

Cheers,
Brent
Hi Brent!

I agree! Thanks for correcting me.
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