c is a positive integer, and d is a prime number. When c is divided by

Question

c is a positive integer, and d is a prime number. When c is divided by 4d, the remainder is d. What is the value of d?

(1) c is even
(2) c > 4d

Archit3110 · Answer

given c is +ve integer and d is prime number
c= 4d*x+d
or say that
 c=d and x = 0
#1
c is even
d has to be 2 as its only even prime number
sufficient
#2
c>4d
least value of c is 43 and d is 2 
c is 44 and d is 3
insufficient
option A

gmatophobia · Answer

"c" can be represented as

c = 4d * q + d

c = d (4q + 1)

q = quotient when c is divided by 4d.

Statement 1     : c is even

4q + 1 = odd ; even + odd = odd

So for c to be even d must be even.

Also we know d is a prime number.

The only even prime number is 2. Hence this statement is sufficient.

Statement 2     : c > 4d

c = d (4q + 1)

For different values of q and c we can have different values of d.

Hence, this statement is not sufficient on its own.

Option A

Chanovski · Answer

Why do you know that 4q+1 = odd?

BrentGMATPrepNow · Answer

Given : c is a positive integer, and d is a prime number. When c is divided by 4d, the remainder is d.

-----ASIDE---------------------
There's a nice rule that says, "  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
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
----------------------------------

Since the quotient isn't given, let's let Q = the quotient when c is divided by 4d. 
On other words:   When c is divided by 4d, the quotient is Q and the remainder is d  
So, from the above   rule  , we can write:  c = (4d)(Q) + d 
Factor to get:  c = d(4Q + 1)

Target question :    What is the value of d?

Statement 1 : c is even  
Since  c = d(4Q + 1) , we can conclude that  d(4Q + 1)   is even .
Since 4Q is even for all integer values of Q, we know that 4Q + 1  is odd 
So, if  d(4Q + 1)  is even, it must be the case that  d is even .
Since d is a prime number,   d must equal  2  (since 2 is the only even prime).

Statement 2 : c > 4d 
This information doesn't help us answer the target question. 
There are several values of c and d that satisfy statement 2 (and the given information). Here are two: 
 Case a : c = 10 and d = 2. In this case, the answer to the target question is  d = 2 
 Case b : c = 15 and d = 3. In this case, the answer to the target question is  d = 3 
Since we can’t answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

gmatophobia · Answer

As 'q' is the quotient, its an integer.

Therefore 4*q is even

1 is odd.

So 4q + 1 = even + odd

even + odd = odd

Therefore 4q + 1 = odd.

Hope this clarifies !

vv65 · Answer

q is an integer
==> 4q is even
==> 4q+1 is odd

- multiply any integer by an even number, we get an even number
- add 1 to any even number, we get an odd number

Posted from my mobile device

bumpbot · Answer

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c is a positive integer, and d is a prime number. When c is divided by

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c is a positive integer, and d is a prime number. When c is divided by

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