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A can be divided by 11 with no remainder. Which of the following expre

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Bunuel
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A can be divided by 11 with no remainder. Which of the following expre [#permalink] New post   05 Jul 2016, 12:27
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A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1?

A. A-20.
B. A-12.
C. A-9.
D. A-10.
E. A-13.
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Re: A can be divided by 11 with no remainder. Which of the following expre [#permalink] New post   05 Jul 2016, 13:00
[quote="Bunuel"]A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1?

A can be divided by 11
for easy calculations consider A = 22 (if u choose A=11, you shall need those extra miliseconds figuring -ve stats)
As remainder is 1 for the new expression 'say X' and all the answers include only -ve sign
=> Either X could be 12 = A-10 or X could be 1 = A-21
Ans - D. A-10.

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Re: A can be divided by 11 with no remainder. Which of the following expre [#permalink] New post   05 Jul 2016, 18:46
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We could use the following logic:
since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n).
The condition here should now be
11K + 1 = <operation> such that it gives us an integer
11k +1 = A -20 => A = 11K + 21 Not divisible by 11
11K +1 = A -12 => A = 11K + 31 Not Divisible by 11
11K +1 = A -9 => A = 11K + 10 Not Divisible by 11
11K +1 = A -10 => A = 11K + 11 Divisible by 11
11K +1 = A -13 => A = 11K + 14 Not Divisible by 11

Answer therefore is A -10 (D)
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A can be divided by 11 with no remainder. Which of the following expre [#permalink] New post   01 Oct 2017, 08:36
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Bunuel wrote:
A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1?

A. A-20.
B. A-12.
C. A-9.
D. A-10.
E. A-13.

If \(A = 11n + 0\), then A is a multiple of 11. A could be 11, 22, 33, 44, etc.

Looking at the answer choices' subtracted numbers, to avoid negative numbers and numbers less than 11, let A = 33.

We want \(\frac{(A - n)}{11}\) leaves remainder 1.

A) A-20. (33 - 20) = 13. NO. \(\frac{13}{11}\) has R2

B) A-12. (33 - 12) = 21. NO. \(\frac{21}{11}\) has R10

C) A-9. (33 - 9) = 24. NO. \(\frac{24}{11}\) has R2

D) A-10. (33 - 10) = 23. YES. \(\frac{23}{11}\) has R1

E) A-13. (33 - 13) = 20. NO. \(\frac{20}{11}\) has R9

Answer D
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Re: A can be divided by 11 with no remainder. Which of the following expre [#permalink] New post   02 Jul 2019, 10:17
1. The question stem states that A is a multiple of 11, so A=11n
2. To leave a remainder of 1, A should be "1 more than some multiple of 11" or "10 less than some multiple of 11".
3. So A will be equal to "11n+1" or "11n-10"

Only "A-10 or (11n-10)" is in the choices, hence the answer.
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Re: A can be divided by 11 with no remainder. Which of the following expre [#permalink]
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