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x and h are both positive integers. When x is divided by 7,
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12 Aug 2018, 15:45
12 Aug 2018, 15:45
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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
(A) 7
(B) 21
(C) 50
(D) 52
(E) 57
Re: x and h are both positive integers. When x is divided by 7,
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17 Aug 2018, 16:03
17 Aug 2018, 16:03
Expert Reply
Explanation
Division problems can be interpreted as follows: dividend = divisor × quotient + remainder.
This problem is dividing x by 7, or distributing x items equally to 7 groups. After the items are distributed among the 7 groups, there are 3 items left over, the remainder. This means that the value of x must be some number that is 3 larger than a multiple of 7, such as 3, 10, 17, 24, etc.
The only answer choice that is 3 larger than a multiple of 7 is 52.
Division problems can be interpreted as follows: dividend = divisor × quotient + remainder.
This problem is dividing x by 7, or distributing x items equally to 7 groups. After the items are distributed among the 7 groups, there are 3 items left over, the remainder. This means that the value of x must be some number that is 3 larger than a multiple of 7, such as 3, 10, 17, 24, etc.
The only answer choice that is 3 larger than a multiple of 7 is 52.
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Re: x and h are both positive integers. When x is divided by 7,
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19 Oct 2022, 10:15
19 Oct 2022, 10:15
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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
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
