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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  a, b are positive integers. The remainder of a to be divided by 8 is 4

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Intern  B
Joined: 26 Jul 2014
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a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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Question Stats: 62% (02:14) correct 38% (02:22) wrong based on 281 sessions

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a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2.
Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20
Math Expert V
Joined: 02 Sep 2009
Posts: 55670
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2. Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20

The remainder of a to be divided by 8 is 4: a = 8q + 4. a could be 4, 12, 20, 24, ...
The remainder of b to be divided by 6 is 2: b = 6p + 2. b could be 2, 8, 14, 20, ...

If a =4 and b = 2, then ab = 8 and 8 divided by 48 yields the remainder of 8.

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a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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3
$$\frac{a}{8}$$ >>> Remainder = 4

$$\frac{b}{6}$$ >>> Remainder = 2

$$\frac{a*b}{8*6}$$ >> As numbers & divisors get multiplied, remainder will also get multiplied

Remainder = 4*2 = 8

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Manager  Joined: 31 Jul 2014
Posts: 127
GMAT 1: 630 Q48 V29 Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2.
Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20

Hi Bunuel
Could you please explain the solution?

I got up to this
a=8p+4
b=6q+2

a*b=48pq+16p+24q+8
when a*b is divided by 48,then 48pq is divisible by 48, 16p could be divisible by 48 (16*3) , 24 q could be divisible by 48 (24*2)
so 8 divided by 48 -> Possible reminder 8

Could you please confirm if this is a correct thinking?

Thanks !
Intern  B
Joined: 26 Jul 2014
Posts: 11
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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Bunuel wrote:
h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2. Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20

The remainder of a to be divided by 8 is 4: a = 8q + 4. a could be 4, 12, 20, 24, ...
The remainder of b to be divided by 6 is 2: b = 6p + 2. b could be 2, 8, 14, 20, ...

If a =4 and b = 2, then ab = 8 and 8 divided by 48 yields the remainder of 8.

I understand the case when a=4 b=2, but what about a=12 b=2, then ab=24. When this 24 is divided by 48, then the remainder is 24.
Math Expert V
Joined: 02 Sep 2009
Posts: 55670
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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h31337u wrote:
Bunuel wrote:
h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2. Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20

The remainder of a to be divided by 8 is 4: a = 8q + 4. a could be 4, 12, 20, 24, ...
The remainder of b to be divided by 6 is 2: b = 6p + 2. b could be 2, 8, 14, 20, ...

If a =4 and b = 2, then ab = 8 and 8 divided by 48 yields the remainder of 8.

I understand the case when a=4 b=2, but what about a=12 b=2, then ab=24. When this 24 is divided by 48, then the remainder is 24.

Yes but 24 is not among the options...
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Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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Bunuel wrote:
h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2. Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20

The remainder of a to be divided by 8 is 4: a = 8q + 4. a could be 4, 12, 20, 24, ...
The remainder of b to be divided by 6 is 2: b = 6p + 2. b could be 2, 8, 14, 20, ...

If a =4 and b = 2, then ab = 8 and 8 divided by 48 yields the remainder of 8.

HI
the series are 4,12,20....44
2,8,14....44
the first number happens to be 44 and the second one is 68, if we divide 68 by 48 we get the reminder 20 which is option E,
i ant denying option A cant be the ans but option E also could be the ans
Current Student B
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Location: United States (MI)
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Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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why will you divide 68 by 48?

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Manager  Joined: 03 May 2013
Posts: 67
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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i misunderstood the stem, thanks for prompt response
Math Expert V
Joined: 02 Aug 2009
Posts: 7757
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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h31337u wrote:
a, b are positive integers. The remainder of a to be divided by 8 is 4 and the remainder of b to be divided by 6 is 2.
Which is possible to be the remainder of a*b to be divided by 48

a) 2
b) 6
c) 8
d) 12
e) 20

Hi
Two ways to do it...
a=8x+4..
b=6y+2..

1) convenient way..
Take x and y as 0, and you will get a*b as 4*2=8
C.

2) a*b=(8x+4)(6y+2)=4(2x+1)*2(3y+1)=8(2x+1)(6y+2).....
So a*b is a multiple of 8..
Also the divider is a multiple of 8..
So remainder has to be a multiple of 8..
While doing this , I just thought of this method.
It should work for all cases, I believe.
Only C is a multiple of 8..
C
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Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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PareshGmat wrote:
$$\frac{a}{8}$$ >>> Remainder = 4

$$\frac{b}{6}$$ >>> Remainder = 2

$$\frac{a*b}{8*6}$$ >> As numbers & divisors get multiplied, remainder will also get multiplied

Remainder = 4*2 = 8

sorry, you are wrong.
you need to erase this post so that other people will not get wrong.
5/3 has remainder 2.
8/7 has remainder 1
but 40 / 21 does not have remainder 2
Manager  B
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Concentration: Social Entrepreneurship, Sustainability
a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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We can also apply the rule: remainder of a product is the product of remainders

thus in this case:

Rem(ab)--> rem(a) x rem(b) --> 4 x 2 --> 8

where a-->8p+4 and with p as 0, a is 4. and rem(4/48) is 4
same for b

the pitfall for me was that i got stuck with the algebra..which was not needed a, b are positive integers. The remainder of a to be divided by 8 is 4   [#permalink] 02 Nov 2018, 01:47
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