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# Number of chocolates with Daniel is X and the number of chocolates wit

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

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Updated on: 06 Mar 2018, 21:25
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Question Stats:

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

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

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05 Mar 2018, 07:25
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
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Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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06 Mar 2018, 21:28
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.
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Re: Number of chocolates with Daniel is X and the number of chocolates wit  [#permalink]

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07 Mar 2018, 01:13
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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07 Mar 2018, 01:27
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.

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

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07 Mar 2018, 01:59
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.

Therefore the answer is A.

"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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07 Mar 2018, 07:19
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.

Therefore the answer is A.

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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07 Mar 2018, 07:22
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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07 Mar 2018, 16:51
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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07 Mar 2018, 22:35
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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09 Mar 2018, 00:14
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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09 Mar 2018, 08:06
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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Re: Number of chocolates with Daniel is X and the number of chocolates wit   [#permalink] 09 Mar 2018, 08:06
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