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x and h are both positive integers. When x is divided by 7, the quotie

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Bunuel
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x and h are both positive integers. When x is divided by 7, the quotie [#permalink] New post   13 Aug 2018, 05:04
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x and h are both positive integers. When x is divided by 7, the quotient is h with a remainder of 3. Which of the following could be the value of x?

(A) 7
(B) 21
(C) 50
(D) 52
(E) 57
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Re: x and h are both positive integers. When x is divided by 7, the quotie [#permalink] New post   13 Aug 2018, 05:41
From the question X = 7H+3.
Since H is an integer. Put H=0,1,2,3,4,5,6....etc.
Then X = 3,10,17,24,31,38,45,52,59.
Hence 52 is the answer.
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x and h are both positive integers. When x is divided by 7, the quotie [#permalink] New post   13 Aug 2018, 06:59
Bunuel wrote:
x and h are both positive integers. When x is divided by 7, the quotient is h with a remainder of 3. Which of the following could be the value of x?

(A) 7
(B) 21
(C) 50
(D) 52
(E) 57

\(x = 7h + 3\)

Now, The possible values of x are \({ 10, 17 , 24, 31, 38 , 45, 52....................}\)

Thus, Answer must be (D) 52
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Re: x and h are both positive integers. When x is divided by 7, the quotie [#permalink] New post   13 Aug 2018, 10:11
Bunuel wrote:
x and h are both positive integers. When x is divided by 7, the quotient is h with a remainder of 3. Which of the following could be the value of x?

(A) 7
(B) 21
(C) 50
(D) 52
(E) 57


This question can be translated into the following one:

\(\frac{x}{7} = h + 3\)


x = 7h + 3 .

Option D: 7*7 + 3 = 52

So, x is 52.

The best answer is D.
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Re: x and h are both positive integers. When x is divided by 7, the quotie [#permalink] New post   18 Aug 2018, 19:26
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Bunuel wrote:
x and h are both positive integers. When x is divided by 7, the quotient is h with a remainder of 3. Which of the following could be the value of x?

(A) 7
(B) 21
(C) 50
(D) 52
(E) 57


We can create the equation:

x = 7h + 3

We see x is 3 more than a multiple of 7, so x could be 52 since 7 x 7 + 3 = 52.

Answer: D
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Re: x and h are both positive integers. When x is divided by 7, the quotie [#permalink] New post   19 Oct 2022, 11:15
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When x is divided by 7, the quotient is h with a remainder of 3

Theory: Dividend = Divisor*Quotient + Remainder

x -> Dividend
7 -> Divisor
h -> Quotient
3 -> Remainder

=> x = 7*h + 3 = 7h + 3

=> x - 3 = 7h => x - 3 is a multiple of 7

Let's take each option choice and subtract 3 and see which one becomes a multiple of 7

(A) 7
7 - 3 = 4 => NOT DIVISIBLE by 7 => FALSE

(B) 21
21 - 3 = 18 => NOT DIVISIBLE by 7 => FALSE

(C) 50
50 - 3 = 47 => NOT DIVISIBLE by 7 => FALSE

(D) 52
52 - 3 = 49 => DIVISIBLE by 7 => TRUE
We don't need to check further, but I am checking to complete the solution.

(E) 57
7 - 3 = 4 => NOT DIVISIBLE by 7 => FALSE

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Remainders

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Re: x and h are both positive integers. When x is divided by 7, the quotie [#permalink]
19 Oct 2022, 11:15
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