Positive integer Q gives a remainder of 5 when divided by 7. Find the

Question

Positive integer Q gives a remainder of 5 when divided by 7. Find the remainder when 2Q is divided by 7.

(A) 2
(B) 3
(C) 5
(D) 7
(E) 9

BrentGMATPrepNow · Accepted Answer

-------------ASIDE------------------
When it comes to remainders, we have a nice property that says: 
  If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.    
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc. 
--------------------------------------

Positive integer Q gives a remainder of 5 when divided by 7.  
So, the possible values of Q are:  5, 12, 19, 26, 33, . . .  etc

Find the remainder when 2Q is divided by 7.  
Let's test one of the possible values of Q. 
The easiest value to test is Q =  5 
So, 2Q = 2( 5 ) = 10, and 10 divided by 7 leaves remainder 3

Answer: B

RELATED VIDEO
 https://www.youtube.com/watch?v=XCxgIR042tE

GMATWhizTeam · Answer

Solution  :
We are given, 
 • Q is a positive integer.
• Q on dividing by 7 leaves a remainder of 5

So, Q can be written as:
 Q = 7k + 5, where k is a positive integer. 
Multiplying the above equation throughout by 2, we get
 2Q = 14k + 10

Now, we need to find the remainder when 2Q is divided by 7
i.e., we need to find the remainder when (14k + 10) is divided by 7.

• We know that, 14 is a multiple of 7 
 ⟹ 14k is a multiple of 7.
⟹ 14k on dividing by 7 leaves a remainder of  0  
• Also, 10 on being divided by 7 leaves a remainder of  3

Thus, (14k + 10) on being divided by 7 leaves a remainder of  (0 + 3) = 3

Hence the correct answer is   Option B  .

chetan2u · Answer

If you know that remainders get multiplied and added, the question can be answered in 10 seconds.

Q gives a remainder 5 when divided by 7.
2Q will give a remainder of 2*(5) or 10 when divided by 7.
But 10 is greater than 7 and, so will give a remainder 3 when divided by 7.

B

BrushMyQuant · Answer

Positive integer Q gives a remainder of 5 when divided by 7

Theory: Dividend = Divisor*Quotient + Remainder

Q -> Dividend
7 -> Divisor
a -> Quotient (Assume)
5 -> Remainders
=> Q = 7*a + 5 = 7a+5 ...(1)

Find the remainder when 2Q is divided by 7.

2Q = 2*(7a+5)  
=> 2Q = 14a + 10 = 14a + 7 + 3 = 7*(2a + 1) + 3
=> 2Q when divided by 7 gives 2a+1 as quotient and 3 as remainder

So,  Answer will be B 
Hope it helps!

Watch the following video to learn the Basics of Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

CrackverbalGMAT · Answer

Positive integer Q gives a remainder of 5 when divided by 7. Find the remainder when 2Q is divided by 7.

Q = 7k+ 5

2Q = 2(7k+5) = 14k +10

When 2Q is divided by 7, remainder will be same as the remainder of (14k+10)/7 = Remainder of (14k/7) + Remainder of (10/7) = 0 + 3 = 3

Since 14k is a multiple of 7, so the remainder will be 0 .

Option B is the answer.

Thanks,
Clifin J Francis

bumpbot · Answer

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Positive integer Q gives a remainder of 5 when divided by 7. Find the

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Positive integer Q gives a remainder of 5 when divided by 7. Find the

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