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An amount of money was divided between some people in such a way that if there had been 4 more people, everyone would have $16 less. but if there had been 4 less people, everyone would have got $24 more. How many people were there in group? ?

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17 Aug 2017, 02:49

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Bunuel wrote:

An amount of money was divided between some people in such a way that if there had been 4 people, everyone would have $16 less. but if there had been 4 less people, everyone would have got $24 more. How many people were there in group? ?

A. 12 B. 16 C. 20 D. 24 E. 32

Let n be the number of people with p dollars total = pn

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17 Aug 2017, 03:25

Ans : C

Solution - Let the no of people be x and the amount that each one gets be y . Thus the total amount - xy

Given Condition 1 - (x+4)(y-16) = xy (The total amount remains the same because there is a change in the no of people and the amount that each one gets according to the given condition).

SOlving - y-4x=16

GIven condition 2 - (x-4)(y+24) = xy. Solving , -y+6x=24.

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17 Aug 2017, 03:31

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Bunuel wrote:

An amount of money was divided between some people in such a way that if there had been 4 people, everyone would have $16 less. but if there had been 4 less people, everyone would have got $24 more. How many people were there in group? ?

A. 12 B. 16 C. 20 D. 24 E. 32

hi Bunuel , I think there is typo in the question: it says "If there had been 4 people" perhaps you meant if there had been 4 people MORE ?

An amount of money was divided between some people in such a way that if there had been 4 people, everyone would have $16 less. but if there had been 4 less people, everyone would have got $24 more. How many people were there in group? ?

A. 12 B. 16 C. 20 D. 24 E. 32

hi Bunuel , I think there is typo in the question: it says "If there had been 4 people" perhaps you meant if there had been 4 people MORE ?

______________________ Edited the typo. Thank you.
_________________

An amount of money was divided between some people in such a way that [#permalink]

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17 Aug 2017, 04:34

Bunuel wrote:

dave13 wrote:

Bunuel wrote:

An amount of money was divided between some people in such a way that if there had been 4 people, everyone would have $16 less. but if there had been 4 less people, everyone would have got $24 more. How many people were there in group? ?

A. 12 B. 16 C. 20 D. 24 E. 32

hi Bunuel , I think there is typo in the question: it says "If there had been 4 people" perhaps you meant if there had been 4 people MORE ?

______________________ Edited the typo. Thank you.

you are welcome:) Bunuel you know I dont understand why i always write wrong equations when it comes to such problems. here is what i did, --- logically my approach should be correct ...

Let X be a total sum N = number of persons y = sum each owns after division

An amount of money was divided between some people in such a way that if there had been 4 more people, everyone would have $16 less. but if there had been 4 less people, everyone would have got $24 more. How many people were there in group? ?

A. 12 B. 16 C. 20 D. 24 E. 32

We can let the number of people = n and the amount of money each originally received = m; thus, the total original amount of money is mn.

If there had been 4 more people, everyone would have $16 less:

(n + 4)(m - 16) = mn

nm + 4m - 16n - 64 = mn

4m - 16n - 64 = 0

4m = 16n + 64

m = 4n + 16

And, had there been 4 fewer people, everyone would have received $24 more:

(n - 4)(m + 24) = mn

nm - 4m + 24n - 96 = mn

-4m + 24n - 96 = 0

-4m = -24n + 96

m = 6n - 24

Since m = 4n + 16 and m = 6n - 24, we have:

4n + 16 = 6n - 24

40 = 2n

20 = n

Answer: C
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

An amount of money was divided between some people in such a way that [#permalink]

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22 Aug 2017, 10:09

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dave13 wrote:

Bunuel wrote:

An amount of money was divided between some people in such a way that if there had been 4 people, everyone would have $16 less. but if there had been 4 less people, everyone would have got $24 more. How many people were there in group? ?

A. 12 B. 16 C. 20 D. 24 E. 32

Bunuel you know I dont understand why i always write wrong equations when it comes to such problems. here is what i did, --- logically my approach should be correct ...

Let X be a total sum N = number of persons y = sum each owns after division