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

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When the positive integer x is divided by 42, the remainder is 19. Wha  [#permalink]

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New post 27 Jun 2018, 21:43
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

82% (00:56) correct 18% (01:05) wrong based on 56 sessions

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Re: When the positive integer x is divided by 42, the remainder is 19. Wha  [#permalink]

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New post 27 Jun 2018, 21:52
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

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Re: When the positive integer x is divided by 42, the remainder is 19. Wha  [#permalink]

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New post 27 Jun 2018, 23:18
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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
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When the positive integer x is divided by 42, the remainder is 19. Wha  [#permalink]

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New post 28 Jun 2018, 10:17
Bunuel wrote:
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

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
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When the positive integer x is divided by 42, the remainder is 19. Wha &nbs [#permalink] 28 Jun 2018, 10:17
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