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What is the difference between the number of chocolates with Alice and

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Retired Moderator
Joined: 22 Aug 2013
Posts: 1435
Location: India
What is the difference between the number of chocolates with Alice and  [#permalink]

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19 Jul 2018, 11:22
2
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:40) correct 38% (02:24) wrong based on 39 sessions

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What is the difference between the number of chocolates with Alice and Bob, if each of them has at least one chocolate and Alice has 25% more chocolates than Bob?

(1) Together Alice and Bob have less than 30 but more than 20 chocolates.

(2) Difference between the squares of number of chocolates with Alice and Bob is 27 times the difference between the number of chocolates with Alice and Bob.
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: What is the difference between the number of chocolates with Alice and  [#permalink]

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19 Jul 2018, 19:32
1
What is the difference between the number of chocolates with Alice and Bob, if each of them has at least one chocolate and Alice has 25% more chocolates than Bob?

A=1.25B=5B/4

(1) Together Alice and Bob have less than 30 but more than 20 chocolates.
So 20<A+B<30........20<B+5B/4<30........20<9B/4<30.........
Since B is an integer, Only possibility of 9B/4 is 27....B=27*4/9=12
A = 1.25*12=15
Difference=15-12=3
Sufficient

(2) Difference between the squares of number of chocolates with Alice and Bob is 27 times the difference between the number of chocolates with Alice and Bob.
Straight way a+B=27
$$a^2-b^2=27(a-b)..................(a-b)(a+b)=27(a-b).....................(a+b)=27$$
We know total is 9B/4=27.....B=12
Sufficient

D
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Re: What is the difference between the number of chocolates with Alice and   [#permalink] 19 Jul 2018, 19:32
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