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805+ (Hard)|   Remainders|      
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Bunuel
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A certain number, when successively divided by 8 and 11, leaves remain 17 Nov 2020, 08:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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95% (hard)

Question Stats:

37% (01:43) correct 63% (02:16) wrong based on 217 sessions

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A certain number, when successively divided by 8 and 11, leaves remainders of 3 and 7 respectively. What will be the remainder when the number is divided by the product of 8 and 11?

(A) 3
(B) 21
(C) 51
(D) 59
(E) 68

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D
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rajatchopra1994
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A certain number, when successively divided by 8 and 11, leaves remain 17 Nov 2020, 08:56
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Explanation:

Let number is x, when successively divided by 8 and 11.

x = 8 * Q (quotient) + 3 --- Eqn1

as it is a successive division, Quotient is divided by 11 and remainder is 7.
i.e. Q = 11k + 7
Putting Value of Q in Eqn 1
So, x = 8 * (11k + 7 ) + 3 = 88k + 56 + 3
= 88k + 59

x divided by 88, leaves a remainder of 59

IMO-D
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daniformic
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A certain number, when successively divided by 8 and 11, leaves remain 17 Nov 2020, 09:35
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D 8 11
R 3 7

8*7+3=59

Ans D

Bunuel am I wrong?

Thx
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ism1994
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A certain number, when successively divided by 8 and 11, leaves remain 22 Nov 2020, 09:08
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IMO:

x = 8*k + 3 = 11, 19, 27, 35, ..., 51, ....
x = 11*k' + 7 = 7, 18, 28, 40, 51, ....

x = 88*k'' + R = 51 -----> if k''=0 ------> R = 51

Answer: C
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theropesnyc
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A certain number, when successively divided by 8 and 11, leaves remain 22 Nov 2020, 10:47
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The number in question has the form \(x = r +k\cdot 88\) where \(r\) is one of the answer choices. Since \(88\) is a multiple of \(8\) and \(11\), \(r\) and \(x\) have the same remainder when divided by \(11\) (or \(8\)).
Only answer choice (C) yields \(7\) when divided by \(11\).

Reading rajatchopra1994 I realize that I most likely misunderstood the question (lol).
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Fdambro294
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A certain number, when successively divided by 8 and 11, leaves remain 23 Nov 2020, 01:06
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we are "successively dividing"

so we take the Number = N

(1st) Dividing N by 8 -------> get a quotient = A and a Remainder = 3


(2nd) Dividing the quotient of A we got above by 11 ---------> get another quotient = Q and a Remainder = 7



Starting from the 2nd Division and moving to the 1st Division -----

(Quotient = A) / 11 = Q + (7/11)

A = 11Q + 7 ------ (equation 1)



the 1st Division involving the Number = N -----

(N / 8) = A + (3 / 8)

N = 8A + 3

---substituting in (equation 1) for the Quotient Variable of A-----

N = 8(11Q + 7) + 3

N = 88Q + 56 + 3

N = 88Q + 59


When we Divide this Original Number of N by 88, it will leave a Remainder = 59

-D-
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versewriter
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A certain number, when successively divided by 8 and 11, leaves remain 01 Sep 2023, 09:16
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As per question, they are asking for a certain number, when successively divided by 8 and 11, leaves remainders of 3 and 7 respectively. This means that

N = 8*x + 3, where x = 11y + 7

So we put x value in equation 1.

N = 8 * (11y + 7) + 3
N = 88 y + 56 + 3
N = 88 y + 59

So if we divide 88y + 59 by product of 8 & 11 the remainder will be 59

So Option D is answer
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PA0037
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A certain number, when successively divided by 8 and 11, leaves remain 08 Oct 2024, 10:57
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Bunuel , I getting 51 as the answer, pls help with the official explanation
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