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Remainder when positive integer g is divided by 7?

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by das.ashmita » Fri Nov 02, 2012 1:51 am
Hi Saint
1. When g is divided by 14, the remainder is 8
From the above statement, g = 14x + 8
g/7 = 14x/7 + 8/7
14x/7 has remainder 0
8/7 has remainder 1.
Hence when g/7 has remainder 1 irrespective of the value of x. SUff
2. g is the sum of two distinct positive integers
The exact value of g cannot be determined. hence Insuff

Ans A
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by Brent@GMATPrepNow » Fri Nov 02, 2012 6:45 am
saintforlife wrote:What is the remainder when the positive integer g is divided by 7?
1. When g is divided by 14, the remainder is 8
2. g is the sum of two distinct positive integers
Target question: What is the remainder when g is divided by 7?[/color]

Statement 1: When g is divided by 14, the remainder is 8
There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2

In this statement, we're told that g divided by 14 equals some unknown value (say k) with remainder 8.
From this, we know that g = 14k + 8 for some integer k.
We can now rewrite this as g = (7)(2)(k) + 8
Or g = (7)(2)(k) + 7 + 1
Now we'll factor the 7 out of the first part to get: g = 7[2k + 1] + 1
This tells us that, when g is divided by 7, the remainder must be 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: g is the sum of two distinct positive integers
There are several values of g that meet this condition. Here are two:
Case a: g = 2+5 = 7, in which case g divided by 7 leaves remainder 0
Case b: g = 2+6 = 8, in which case g divided by 7 leaves remainder 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
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by GMATGuruNY » Fri Nov 02, 2012 7:14 am
saintforlife wrote:What is the remainder when the positive integer g is divided by 7?
1. When g is divided by 14, the remainder is 8
2. g is the sum of two distinct positive integers

OA: A
For some test takers, it might be easier to plug in values.

Statement 1: When g is divided by 14, the remainder is 8.
In other words, g is 8 more than a multiple of 14:
g = 14x + 8 = 8, 22, 36, 50...
When the values in this list are divided by 7:
8/7 = 1 R1.
22/7 = 3 R1.
36/7 = 5 R1.
50/7 = 7 R1.
In each case, the remainder is 1.
SUFFICIENT.

Statement 2: g is the sum of two distinct positive integers.
If g = 1+2 = 3, then g/7 = 3/7 = 0 R3.
If g = 1+6 = 7, then g/7 = 7/7 = 1 R0.
Since different remainders are possible, INSUFFICIENT.

The correct answer is A.
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