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

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Joined: 02 Sep 2009
Posts: 51072
When the positive integer x is divided by 42, the remainder is 19. Wha  [#permalink]

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27 Jun 2018, 20:43
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Difficulty:

15% (low)

Question Stats:

85% (01:08) correct 15% (01:24) wrong based on 62 sessions

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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

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

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27 Jun 2018, 20:52
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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27 Jun 2018, 22:18
1

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.

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

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28 Jun 2018, 09:17
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

When the positive integer x is divided by 42, the remainder is 19. Wha &nbs [#permalink] 28 Jun 2018, 09:17
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