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# If two integers p and q are in the ratio 4: 5 and their least common m

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If two integers p and q are in the ratio 4: 5 and their least common m  [#permalink]

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09 Oct 2018, 05:01
1
00:00

Difficulty:

65% (hard)

Question Stats:

53% (01:24) correct 47% (02:14) wrong based on 30 sessions

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If two integers p and q are in the ratio 4: 5 and their least common multiple is 800, what is their greatest common divisor?

A. 20
B. 40
C. 80
D. 100
E. 160
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If two integers p and q are in the ratio 4: 5 and their least common m  [#permalink]

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09 Oct 2018, 05:28
1
1
rencsee wrote:
If two integers p and q are in the ratio 4: 5 and their least common multiple is 800, what is their greatest common divisor?

A. 20
B. 40
C. 80
D. 100
E. 160

The product of two integers= GCD*LCM
So $$4x*5x=800*G......20x^2=800G.....x^2=40G$$
Now X as common ratio means G is x
So x^2=40x or X=40
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: If two integers p and q are in the ratio 4: 5 and their least common m  [#permalink]

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09 Oct 2018, 06:06
We have:
P = 4 * x
Q = 5 * x
LCM = 800 = 2^5 * 5^2
=> 4 * 5 * x = 2^2 * 5 * 2^3 * 5
=> x = 2^3 * 5 = 8 * 5 = 40
Because 4 and 5 have no common multiple -> x is the GCD = 40
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Joined: 13 Jan 2016
Posts: 9
Re: If two integers p and q are in the ratio 4: 5 and their least common m  [#permalink]

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09 Oct 2018, 21:09
VodkaHelps wrote:
We have:
P = 4 * x
Q = 5 * x
LCM = 800 = 2^5 * 5^2
=> 4 * 5 * x = 2^2 * 5 * 2^3 * 5
=> x = 2^3 * 5 = 8 * 5 = 40
Because 4 and 5 have no common multiple -> x is the GCD = 40

if they have no common multiple then shouldn't GCF be 1 ?
Re: If two integers p and q are in the ratio 4: 5 and their least common m   [#permalink] 09 Oct 2018, 21:09
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