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GMAT Past Paper Test - Algebra

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by Nisha1218 » Sun Aug 12, 2007 4:34 pm
Can anyone help with the answer to the following question:

If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?

a. 4
b. 5
c. 6
d. 7
e. 8

The answer is C and paper test does not offer explanations. Can someone explain why the answer is C? Thnx!
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by beny » Sun Aug 12, 2007 6:26 pm
You are increasing in increments of 3:

5, 8, 11, 14, ...

Every 2 increments is an increment of 6. Because the first and second terms are not divisible by 6, the entire sequence will never be divisible by 6.
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by Nisha1218 » Sun Aug 12, 2007 6:56 pm
Thanks Beny!

In your response, what do you mean by the first and second termm (3x??)?
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by beny » Sun Aug 12, 2007 11:17 pm
The first term is 5 (x=1) and the second term is 8 (x=2).

If the sequence increases by multiples of 3, one of the first two terms must be divisible by 6 or else the entire sequence never will.

I.e.

3, 6, 9, 12

6, 9, 12, 15

9, 12, 15, 18

Clearly every other term would also be a multiple of 6 (since it's increasing by 6 every 2 increments). From the sequence given, you can quickly see no term will ever be divisible by 6.
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by Nisha1218 » Mon Aug 13, 2007 9:13 am
Thanks Beny! Now I fully understand.
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by mayonnai5e » Mon Sep 10, 2007 1:21 pm
There's another explanation:

The equation for any number represented by a quotient, divisor and remainder is:

Y = Xq + r where q is the quotient and r is the remainder

for example: 8/3 = (3)2 + 2

y = 3x + 2 fits this equation perfectly. In other words y divided x has a quotient of 3 and a remainder of 2. What does this tell you? Y is not divisible by 3. If Y is not divisible by 3, it cannot be divisible by 6. So the answer is C.

This explanation is more complicated, but the ideas behind it help in more advanced number property type questions.
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by samirpandeyit62 » Mon Sep 10, 2007 11:21 pm
If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?

we have y = 3x +2

now 3x is a multiple of 3 hence divisible by 3

so 3x+2 will be 2 greater than 3x i.e 3x+2, hence not divisible by 3

so that means any nos having prime factor as 3 is the ans as it would not divide 3x +2

In the answer choices only 6 = 3 * 2 has 3 as a prime factor

so ans is C
Regards
Samir
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