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Retired Moderator P
Joined: 22 Aug 2013
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Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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1
2 00:00

Difficulty:   95% (hard)

Question Stats: 24% (01:50) correct 76% (02:15) wrong based on 76 sessions

### HideShow timer Statistics Number of chocolates with Daniel is X and the number of chocolates with Maria is Y. If X and Y are distinct, what is the number of chocolates with the one having lesser chocolates, out of Daniel and Maria?

(1) Sum of X and Y is greater than the positive difference between X and Y by 20.

(2) Maria has more chocolates than Daniel.

Originally posted by amanvermagmat on 05 Mar 2018, 05:17.
Last edited by amanvermagmat on 06 Mar 2018, 21:25, edited 1 time in total.
Changed value from 5 to 20
Retired Moderator P
Joined: 07 Jan 2016
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GMAT 1: 710 Q49 V36 Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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amanvermagmat wrote:
Number of chocolates with Daniel is X and the number of chocolates with Maria is Y. If X and Y are distinct, what is the number of chocolates with the one having lesser chocolates, out of Daniel and Maria?

(1) Sum of X and Y is greater than the positive difference between X and Y by 5.

(2) Maria has more chocolates than Daniel.

X and Y are distinct

Using 1

X+Y - X-Y = 5

but here x>y or y< x

we need this relation

insufficient

using 2

y>x

combining

x+y - ( y -x ) = 5

we can find y and x

(C) imo
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1435
Location: India
Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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Hatakekakashi wrote:
amanvermagmat wrote:
Number of chocolates with Daniel is X and the number of chocolates with Maria is Y. If X and Y are distinct, what is the number of chocolates with the one having lesser chocolates, out of Daniel and Maria?

(1) Sum of X and Y is greater than the positive difference between X and Y by 5.

(2) Maria has more chocolates than Daniel.

X and Y are distinct

Using 1

X+Y - X-Y = 5

but here x>y or y< x

we need this relation

insufficient

using 2

y>x

combining

x+y - ( y -x ) = 5

we can find y and x

(C) imo

Hi

Sorry there was a flaw in the question. I changed the value from 5 to 20 now.
Intern  B
Joined: 13 Dec 2017
Posts: 5
Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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amanvermagmat wrote:
Number of chocolates with Daniel is X and the number of chocolates with Maria is Y. If X and Y are distinct, what is the number of chocolates with the one having lesser chocolates, out of Daniel and Maria?

(1) Sum of X and Y is greater than the positive difference between X and Y by 20.

(2) Maria has more chocolates than Daniel.

Can we have a solution for this please?
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Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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3
shiying wrote:
Can we have a solution for this please?

Hey shiying ,

Here you go:

Question is asking if X < Y, what is X? and if Y < X, what is Y?

So, basically we need to determine the value of the lowest.

Let's look options now.

1. Let's consider X < Y

X + Y = Y - X + 20

=> X = 10.

Now consider Y < X

X + Y = X - Y + 20

Y = 10.

Hence, For both the scenarios, I got the lowest value = 10. Hence, sufficient.

Now, Consider Statement 2:

It says X < Y. But we don't know anything about the values.

Hence, insufficient.

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Joined: 13 Dec 2017
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Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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abhimahna wrote:
shiying wrote:
Can we have a solution for this please?

Here you go:

Question is asking if X X = 10.

Now consider Y < X

X + Y = X - Y + 20

Y = 10.

Hence, For both the scenarios, I got the lowest value = 10. Hence, sufficient.

Now, Consider Statement 2:

It says X < Y. But we don't know anything about the values.

Hence, insufficient.

"what is the number of chocolates with the one having lesser chocolates, out of Daniel and Maria?". I actually thought we were suppose to find the sum of the chocolates held by Daniel and Maria. Silly me. Thanks for the reply!
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Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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abhimahna wrote:
shiying wrote:
Can we have a solution for this please?

Hey shiying ,

Here you go:

Question is asking if X X = 10.

Now consider Y < X

X + Y = X - Y + 20

Y = 10.

Hence, For both the scenarios, I got the lowest value = 10. Hence, sufficient.

Now, Consider Statement 2:

It says X < Y. But we don't know anything about the values.

Hence, insufficient.

Hi , Isn't it mentioned that X and Y are distinct? Then how can we conclude that both are 10 ?

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Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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rocko911 wrote:
Hi , Isn't it mentioned that X and Y are distinct? Then how can we conclude that both are 10 ?

Hi rocko911 ,

I never mentioned both are 10. I said when X < Y , I am getting X = 10 and when I am taking Y < X , I am getting Y = 10

This means whichever is the lowest, the value will be 10.

Does that make sense?
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Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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You're going to have to explain this a little more. I don't see how we can conclude the lowest to be 10
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Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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mphil124 wrote:
You're going to have to explain this a little more. I don't see how we can conclude the lowest to be 10

Hello

Statement 1

Lets assume X < Y. Now we are given that sum of chocolates is greater than difference between the chocolates by 10. Here sum of chocolates = X+Y or = Y+X and difference between the chocolates = Y-X. So we are given that:
(Y+X) - (Y-X) = 10. When you solve it, you get 2X = 20 or X=10. So the one having lesser chocolates has '10' chocolates.

Now lets assume Y < X. Again, sum of chocolates is greater than difference between the chocolates by 10. Sum = X+Y or Y+X and difference between them= X-Y. So: (X+Y) - (X-Y) = 20. Solving it, we get 2Y = 20 or Y=10. Again the one having lesser chocolates has '10' chocolates.

We are not asked the value of either X or Y. We are asked the lesser value between X and Y. In either case, the one with lesser chocolates has '10' chocolates. So the lesser value between X and Y is '10' in any case.
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Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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Statement 1:
X + Y = 20 + |X-Y|
Let X > Y => Y is smaller
X + Y = 20 + X - Y => Y = 10
Let X < Y => X is smaller
X + Y = 20 - X + Y (as |x| = -x , if x < 0)
X = 10

in either case, smallest is 10 (which is what the question asks) sufficient

Statement 2: clearly insuff

(A)
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Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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I really liked statement A.

According to statement A, X+Y - |X-Y| = 20. This actually means, the sum of the 2 numbers is equal to 20 if they were equal, so one number is 10 and other is 30. Really nice.
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GMAT1 650 Q48 V32. Re: Number of chocolates with Daniel is X and the number of chocolates wit   [#permalink] 09 Mar 2018, 08:06
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