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John distributed a total of 625 chocolates among a group of boys and

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Joined: 05 Oct 2017
Posts: 20
John distributed a total of 625 chocolates among a group of boys and  [#permalink]

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05 Oct 2018, 23:32
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95% (hard)

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40% (03:39) correct 60% (02:03) wrong based on 52 sessions

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John distributed a total of 625 chocolates among a group of boys and girls. Find the total number of boys and girls in the group? There is at least one member in their respected group.

(1) Each boy received as many chocolates as the number of boys and each girls received as many chocolates as the number of girls.

(2) Each child received as many chocolates as the total number of boys and girls in the group.
Math Expert
Joined: 02 Aug 2009
Posts: 6956
Re: John distributed a total of 625 chocolates among a group of boys and  [#permalink]

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06 Oct 2018, 00:17
1
John distributed a total of 625 chocolates among a group of boys and girls. Find the total number of boys and girls in the group?
There is at least one member in their respected group.

Let there be total t and boys B and girls g

1) Each boy received as many chocolates as the number of boys and each girls received as many chocolates as the number of girls.
so b*b+g*g=625
$$b^2+g^2=25^2$$
You can try values or if you are aware of right angled triangle you would know 3-4-5 ratio.
So 15:20:25 and $$15^2+20^2=25^2......225+400=625$$ total =15+20=35
Also 7-24-25 and $$7^2+24^2=25^2........49+576=625$$ total = 7+24=31
Insufficient

2) Each child received as many chocolates as the total number of boys and girls in the group.
So t*t=625.....t=25
Sufficient

B

Note .. statement I and II will not give you same total
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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

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Re: John distributed a total of 625 chocolates among a group of boys and  [#permalink]

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06 Oct 2018, 20:16
aa008 wrote:
John distributed a total of 625 chocolates among a group of boys and girls. Find the total number of boys and girls in the group? There is at least one member in their respected group.

(1) Each boy received as many chocolates as the number of boys and each girls received as many chocolates as the number of girls.

(2) Each child received as many chocolates as the total number of boys and girls in the group.

At first look 625 looks a perfect square.Possible factors of 625 are 25*25 and 125*5
Looking at statement 2 ,we can tell it is 25*25 ,since total children is equal to chocolate per child.

From statement 1,it can be different possibilities since the first statement gives information about chocolate per boy and chocolate per girl.Possible that 15 boys or 7 boys .So insufficient.

Ans:B
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Re: John distributed a total of 625 chocolates among a group of boys and &nbs [#permalink] 06 Oct 2018, 20:16
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John distributed a total of 625 chocolates among a group of boys and

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