When the positive integer x is divided by 42, the remainder is 19. Wha

Question

When the positive integer x is divided by 42, the remainder is 19. What is the remainder when x is divided by 7?

A. 0 
B. 2 
C. 3 
D. 4 
E. 5

C0achSteve · Answer

It's given that x=42(k) + 19 and asked x=7(s) + y.
What is the value of y?

Now for that as we know 42(k) is divisible by 7(s), hence no remainder from this

Now 19 divided by 7 will give us a remainder of 5 and that should be our remainder and the value of (y).

Hence E

Posted from my mobile device

EgmatQuantExpert · Answer

Solution

Given:  
 • When the positive integer x is divided by 42, the remainder is 19

To find:  
 • The remainder when x is divided by 7

Approach and Working:  
We can write the number x as 42q + 19, where q is the quotient of the division.

When x is divided by 7, we can write it as:
 •  \frac{x}{7} = \frac{42q + 19}{7} 
Or,  \frac{x}{7} = \frac{42q}{7} + \frac{19}{7}

Now, irrespective of the value of q, 42q will always be divisible by 7, as 42 is a multiple of 7

Therefore, the remainder we will get when we divide 19 by 7
 • Remainder ( \frac{19}{7} ) = 5

Hence, the correct answer is option E.

Answer: E

generis · Answer

Test values 
List a few values that  x  could be

42+19=61  
That is,  ((42*1) + 19)=61

After the first possibility, just add 42
 61+42=103  
That is,  ((42*2)+19)=103

103+42=145  
That is,  ((42*3)+19)=145

x=61, 103, 145  . . .

Remainder when  x  is divided by 7?

First  x  value:  \frac{61}{7}=8 , Remainder 5

x  divided by 7 = remainder of  5  should be the answer. Check

Next value of  x :  \frac{103}{7}=14 , Remainder 5

Last value  x :  \frac{145}{7}=20 , Remainder 5

When  x  is divided by 7, the remainder is 5

Answer E

BrushMyQuant · Answer

When the positive integer x is divided by 42, the remainder is 19

Theory: Dividend = Divisor*Quotient + Remainder

x -> Dividend
42 -> Divisor
a -> Quotient (Assume)
19 -> Remainders
=> x = 42*a + 19 = 42a + 19

What is the remainder when x is divided by 7

x = 42a + 19 = 7*6a + 14 + 5 = 7*61 + 7*2 + 5 = 7*(6a+2) + 5

=> x when divided by 7 gives 5 remainder

So,  Answer will be E 
Hope it helps!

Watch the following video to learn the Basics of Remainders

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

When the positive integer x is divided by 42, the remainder is 19. Wha

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

When the positive integer x is divided by 42, the remainder is 19. Wha

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards