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# XY and YX represent 2-digit numbers. What is the value of X × Y?

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Intern
Joined: 17 Mar 2019
Posts: 6
XY and YX represent 2-digit numbers. What is the value of X × Y?  [#permalink]

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12 Apr 2019, 22:06
1
1
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Difficulty:

55% (hard)

Question Stats:

59% (01:56) correct 41% (01:42) wrong based on 29 sessions

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XY and YX represent 2-digit numbers. What is the value of X × Y?

(1) XY – YX = 9
(2) XY + YX = 187
Senior Manager
Joined: 28 Jul 2016
Posts: 312
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
Re: XY and YX represent 2-digit numbers. What is the value of X × Y?  [#permalink]

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12 Apr 2019, 22:17
2
(1) XY – YX = 9
Using statement 1
10x+y-10y-x= 9
9(x-y)= 9
x-y =1
Any values of x and y will satisfy hence not sufficient
(2) XY + YX = 187
10x+y+10y+x= 187
11(x+y)= 187
x+y = 17
only 9 and 8 satisfy the values
thus 9*8 = 72
thus B is sufficient

Hence B
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Joined: 02 Aug 2009
Posts: 7575
Re: XY and YX represent 2-digit numbers. What is the value of X × Y?  [#permalink]

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12 Apr 2019, 22:26
1
XY and YX represent 2-digit numbers. What is the value of X × Y?

This tells us that X and Y are single digits and greater than 0. We can write XY as 10X+Y, and YX as 10Y+X

(1) XY – YX = 9
$$10X+Y-10Y-X=9........9(X-Y)=9......X-Y=1$$
So XY could be 21, 32, 43, and so on
Isuff

(2) XY + YX = 187
$$10X+Y+10Y+X=187........11(X+Y)=187......X+Y=17$$
Now, the only possible values are 8 and 9. If we decrease 8 to 7, 9 will become 10 ans so a 3-digit number..
Hence number could be 89 or 98, but X*Y will remain same, that is 9*8=72
Suff

B
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Joined: 18 Jun 2018
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XY and YX represent 2-digit numbers. What is the value of X × Y?  [#permalink]

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18 Apr 2019, 08:45
OA:B

(1) XY – YX = 9
{10X+Y}-{10Y+X}=9
9{X-Y}=9
X-Y=1

taking Y=1, then X will be 2.
XY will be 2.

taking Y=2. then X will be 3
XY will be 6

There is no unique value of XY, so Statement 1 alone is not sufficient.

(2) XY + YX = 187
10X+Y+10Y+X=187
11X+11Y=187
X+Y=17
and X and Y can be only 1~9,
Two different values of X,Y are possible.
Case 1: X=8 ,Y=9
XY=72
Case 2: X=9 ,Y=8
XY=72

In both case, XY=72
So Statement 2 alone is sufficient to give a unique value of XY.
XY and YX represent 2-digit numbers. What is the value of X × Y?   [#permalink] 18 Apr 2019, 08:45
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