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

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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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09 Nov 2014, 07:21
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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
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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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13 Nov 2014, 01:29
4
1
$$\frac{a}{8}$$ >>> 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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Joined: 31 Jul 2014
Posts: 137
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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09 Nov 2014, 09:42
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 !
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Joined: 02 Sep 2009
Posts: 47168
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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10 Nov 2014, 01:20
1
3
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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Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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12 Nov 2014, 07:28
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.
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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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12 Nov 2014, 07:46
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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12 Sep 2016, 19:19
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
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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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12 Sep 2016, 20:16
why will you divide 68 by 48?

Sent from my iPhone using GMAT Club Forum mobile app
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Joined: 03 May 2013
Posts: 72
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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12 Sep 2016, 20:50
i misunderstood the stem, thanks for prompt response
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Posts: 6274
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4  [#permalink]

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12 Sep 2016, 22:38
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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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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06 Sep 2017, 15:38
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
Re: a, b are positive integers. The remainder of a to be divided by 8 is 4 &nbs [#permalink] 06 Sep 2017, 15:38
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