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IF X and Y are positive integers then what is the least value of their

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IF X and Y are positive integers then what is the least value of their  [#permalink]

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New post Updated on: 22 Apr 2016, 17:42
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Question Stats:

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If x and y are positive integers, then what is the least value x*y?

(1) x divided by y leaves a remainder 10.
(2) 10<x<12 ; 9<y<20

Interesting Question? Smash that kudos then ..!

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Originally posted by stonecold on 22 Apr 2016, 10:17.
Last edited by stonecold on 22 Apr 2016, 17:42, edited 2 times in total.
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Re: IF X and Y are positive integers then what is the least value of their  [#permalink]

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New post 22 Apr 2016, 16:50
1
X and Y are positive integers
To find: least value of their product
The phrasing of the question makes you believe that the value of X and Y can be in a range

Statement [A] : X divided by Y leaves a remainder 10.
If X is less than Y , then remainder is the entirety of X.
With that in mind, the least value of X= 10 and that of Y =11
Product XY = 110
Sufficient

Statement [B] : 10<X<12 ; 9<Y<20
As the numbers are integers, X = 11
In order to get the least product , Y = 10
Product XY = 110
Sufficient

Answer : D
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Re: IF X and Y are positive integers then what is the least value of their  [#permalink]

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New post 22 Apr 2016, 17:23
ronny123 wrote:
X and Y are positive integers
To find: least value of their product
The phrasing of the question makes you believe that the value of X and Y can be in a range

Statement [A] : X divided by Y leaves a remainder 10.
If X is less than Y , then remainder is the entirety of X.
With that in mind, the least value of X= 10 and that of Y =11
Product XY = 110
Sufficient

Statement [B] : 10<X<12 ; 9<Y<20
As the numbers are integers, X = 11
In order to get the least product , Y = 10
Product XY = 110
Sufficient

Answer : D


For Part 1 What you did was hit and trial.
here the reasoning => The Least value of a divisor (given that both X and Y are integer ) is always one more than remainder.
Rule => Divisor>Remainder and Remainder≥0

Your explanation is fine as long as you know the above rule plus it will be used in every remainder problem around.
Regards
StoneCold
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Re: IF X and Y are positive integers then what is the least value of their  [#permalink]

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New post 11 Mar 2018, 05:05
stonecold wrote:
If x and y are positive integers, then what is the least value x*y?

(1) x divided by y leaves a remainder 10.
(2) 10<x<12 ; 9<y<20

Interesting Question? Smash that kudos then ..!


Just a small point to this question , both the statements should give the same value for x and y .
Here from statement 1, x=10 and y= 11
from statement 2 , x=11 and y =10

This should not happen , both the statements should not contradict each other.

Hope this helps.
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Re: IF X and Y are positive integers then what is the least value of their  [#permalink]

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New post 11 Mar 2018, 11:09
It has to be B i guess coz even 118/12 gives 10 bt the product is different


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Re: IF X and Y are positive integers then what is the least value of their &nbs [#permalink] 11 Mar 2018, 11:09
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