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DS Multiple

by karthikpandian19 » Thu Jun 07, 2012 9:49 pm
If a, b and c are integers, is (a·b) a multiple of 18?

(1) 2a=3b

(2) 2b=3c
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by Anurag@Gurome » Thu Jun 07, 2012 10:19 pm
karthikpandian19 wrote:If a, b and c are integers, is (a·b) a multiple of 18?

(1) 2a=3b
(2) 2b=3c
Statement 1: 2a = 3b
As a and b are integers, a must be a multiple of 3 and b must be a multiple of 2. Hence, ab must be a multiple of (2*3) = 6. But may or may not be a multiple of 18.

For example,
  • 1. a = 3 and b = 2 --> 2a = 6 = 3b --> ab = 6 --> NO
    2. a = 9 and b = 6 --> 2a = 18 = 3b --> ab = 54 --> YES
Not sufficient


Statement 2: 2b = 3c
Only thing we can conclude is b is multiple of 3 and c is multiple of 2.
No information about a.

Not sufficient

1 & 2 Together: a is a multiple of 3 and b is a multiple of both 2 and 3. Hence, b is a multiple of (2*3) = 6.

Therefore, ab must be a multiple of (3*6) = 18.

Sufficient

The correct answer is C.
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by karthikpandian19 » Thu Jun 07, 2012 11:04 pm
OA is C
Anurag@Gurome wrote:
karthikpandian19 wrote:If a, b and c are integers, is (a·b) a multiple of 18?

(1) 2a=3b
(2) 2b=3c
Statement 1: 2a = 3b
As a and b are integers, a must be a multiple of 3 and b must be a multiple of 2. Hence, ab must be a multiple of (2*3) = 6. But may or may not be a multiple of 18.

For example,
  • 1. a = 3 and b = 2 --> 2a = 6 = 3b --> ab = 6 --> NO
    2. a = 9 and b = 6 --> 2a = 18 = 3b --> ab = 54 --> YES
Not sufficient


Statement 2: 2b = 3c
Only thing we can conclude is b is multiple of 3 and c is multiple of 2.
No information about a.

Not sufficient

1 & 2 Together: a is a multiple of 3 and b is a multiple of both 2 and 3. Hence, b is a multiple of (2*3) = 6.

Therefore, ab must be a multiple of (3*6) = 18.

Sufficient

The correct answer is C.
Regards,
Karthik
The source of the questions that i post from JUNE 2013 is from KNEWTON

---If you find my post useful, click "Thank" :) :)---
---Never stop until cracking GMAT---
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