Data Sufficiency

swerve wrote:What is the value of a positive integer k?

(1) When k is divided by 5, the remainder is 3.
(2) When k is divided by 3, the remainder is 2.

The OA is E.

I tried as follows,

Both the statements combined will give you a 2 var eq. That you can solve but don't need to since it is a DS question.

2eq. Are cal using for. --> i=d.q+r.

Therefore, eq1= 5q+3=k
And eq2 = 3q+2=k
Both combined can give value of k.

Hence, the correct answer should be C but this isn't the OA <i class="em em-disappointed"></i>.

Please, can anyone explain this DS question? I need help. Thanks.

There is a mistake in your approach. You assumed the same quotient q for both the statements; however, it is not so.

For Statement I: k = 5p + 3 and for Statement II: k = 3q + 2, where p and q are quotient (p and q need not be same)

So, from both the relationships (k = 5p + 3 and k = 3q + 2), we have 5p + 3 = 3q + 2

=> 3q = 1 + 5p

q = (1 + 5p)/3

For q to be an integer, 1 + 5p must be a multiple of 3; a couple of probable values of p are 1 and 4.

At p = 1, k = 8;
At p = 4, k = 23

No unique value of k. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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