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When both positive integers a and b are divided by 7

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sairam595
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When both positive integers a and b are divided by 7 [#permalink] New post   24 Apr 2016, 07:33
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When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?
A. 6
B. 5
C. 4
D. 3
E. 2

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Re: When both positive integers a and b are divided by 7 [#permalink] New post   24 Apr 2016, 09:55
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smartguy595 wrote:
When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?
A. 6
B. 5
C. 4
D. 3
E. 2


The question has confusing wording and is of a poor quality. You can ignore it and move on.

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Re: When both positive integers a and b are divided by 7 [#permalink] New post   Updated on: 24 Apr 2016, 09:01
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I took a&b to be 4
so 443/7 = 2 E but its wrong :(

when I took a&b to be 11
so 11113/7 = remainder 4 (b) correct answer

Originally posted by paidlukkha on 24 Apr 2016, 08:59.
Last edited by paidlukkha on 24 Apr 2016, 09:01, edited 1 time in total.
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Re: When both positive integers a and b are divided by 7 [#permalink] New post   24 Apr 2016, 09:01
paidlukkha wrote:
I took a&b to be 4
so 443/7 = 2 E but its wrong :(


I got ans '6' but OA says ans->4
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Re: When both positive integers a and b are divided by 7 [#permalink] New post   24 Apr 2016, 09:06
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smartguy595 wrote:
When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?
A. 6
B. 5
C. 4
D. 3
E. 2


Let a = 4 and b = 11

Both will produce remainder 4 when divided by 7

ab3 = 4113 { Nowhere it is mentioned about digits , the question states integers and 11 is an integer }

Further the question states a and b are 2 distinct integers , so we can not assume a = b = 11 as smartguy595 has assumed.. :-D

4113 = 587 + remainder 4

Hence answer will be (C) 4
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Re: When both positive integers a and b are divided by 7 [#permalink] New post   24 Apr 2016, 09:15
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Abhishek009 wrote:
smartguy595 wrote:
When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?
A. 6
B. 5
C. 4
D. 3
E. 2


Let a = 4 and b = 11

Both will produce remainder 4 when divided by 7

ab3 = 4113 { Nowhere it is mentioned about digits , the question states integers and 11 is an integer }

Further the question states a and b are 2 distinct integers , so we can not assume a = b = 11 as smartguy595 has assumed.. :-D

4113 = 587 + remainder 4

Hence answer will be (C) 4


Dear Abhishek009,

Thanks for the explanation provided. I assumed both a & b can be same integer! my bad :(
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Re: When both positive integers a and b are divided by 7 [#permalink] New post   24 Apr 2016, 09:20
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Abhishek009 and smartguy595
Hey
I Strongly Disagree with your solution abhishek..!
I Don't see anywhere written that x and y are distinct integers...!!!!!

secondly why would you assume that ab3 are place digits and not a*b*3
Remember xy = x*y and not xy as place digits...!!!
here the correct answers are multiple.
For me it is an ILLEGAL Question.

E.g let a=b=4
no we dont know if 443 is 443 or 4*4*3


I hope i made a valid point..!!

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Re: When both positive integers a and b are divided by 7 [#permalink] New post   24 Apr 2016, 09:39
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Actually, it is not that clear that a<>b.
Also, it could be 4113/7, which is 4, or 1143/7, which is 2.
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Re: When both positive integers a and b are divided by 7 [#permalink] New post   24 Apr 2016, 09:46
what I fail to understand is why 2 diff numbers
& why not (a*b*3)/7?

how do we deduce these 2?

source of the Q please??
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Re: When both positive integers a and b are divided by 7 [#permalink] New post   24 Apr 2016, 09:47
Razuvaev wrote:
Actually, it is not that clear that a<>b.
Also, it could be 4113/7, which is 4, or 1143/7, which is 2.


Diagree..!
It can be 4*11*3 too..!!!
who told us that ab3 is not a*b*3 but the digits..!!

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Re: When both positive integers a and b are divided by 7 [#permalink] New post   24 Apr 2016, 09:49
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paidlukkha wrote:
what I fail to understand is why 2 diff numbers
& why not (a*b*3)/7?

how do we deduce these 2?

source of the Q please??

Exactly what i mean..!!!
But wait AB3 can be place digits too.
Let the writer clarify

CC- chetan2u Abhishek009
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Re: When both positive integers a and b are divided by 7 [#permalink]
24 Apr 2016, 09:49
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