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x and h are both positive integers
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Updated on: 16 Oct 2018, 10:01
Updated on: 16 Oct 2018, 10:01
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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
Originally posted by ruposh6240 on 16 Oct 2018, 05:41.
Last edited by Carcass on 16 Oct 2018, 10:01, edited 1 time in total.
Last edited by Carcass on 16 Oct 2018, 10:01, edited 1 time in total.
Edited by Carcass
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Posts: 6218
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Re: Divisibility
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16 Oct 2018, 07:21
16 Oct 2018, 07:21
2
ruposh6240 wrote:
25. 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
Which of the following could be the value of x?
(A) 7
(B) 21
(C) 50
(D) 52
(E) 57
When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
GIVEN: When x is divided by 7, the quotient is h with a remainder of 3
So, the possible values of x are: 3, 10, 17, 24, 31, etc
Notice that each possible value of x is THREE MORE than some multiple of 7.
Now check the answer choices....
(A) 7 This is a multiple of 7. ELIMINATE
(B) 21 This is a multiple of 7. ELIMINATE
(C) 50 This is ONE MORE than a multiple of 7 (49). ELIMINATE
(D) 52 This is THREE MORE than a multiple of 7 (49). PERFECT!!!
Answer: D
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Re: x and h are both positive integers
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19 Oct 2022, 10:16
19 Oct 2022, 10:16
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
