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If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY

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Bunuel
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If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY [#permalink] New post   10 Jul 2020, 04:58
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If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY is 90.

A. 2
B. 3
C. 5
D. 6
E. 10
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D
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Re: If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY [#permalink] New post   10 Jul 2020, 05:00
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(X + Y) - (X - Y) = 12
2Y = 12
Y = 6

XY = 90
=> X = 90/6 = 15

Smaller number = 6

Answer: D
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Re: If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY [#permalink] New post   10 Jul 2020, 05:06
Bunuel wrote:
If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY is 90.

A. 2
B. 3
C. 5
D. 6
E. 10


Given (X + Y) - (X - Y) is 12
=> 2Y = 12
=> Y=6

Also, XY = 90
=> X*6 = 90
=>X = 15

Smallest of X and Y = Y = 6

OA: D
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Re: If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY [#permalink] New post   10 Jul 2020, 05:18
Expert Reply
Bunuel wrote:
If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY is 90.

A. 2
B. 3
C. 5
D. 6
E. 10


Solution


    • We have, \( (X+Y) – (X-Y) = 12 ⟹ X + Y – X + Y = 12 ⟹ 2Y = 12 ⟹ Y= 6\)
    • Also, \( XY = 90 ⟹ X*6 = 90 ⟹X= 15\)
    • Hence smaller of X = 15 and Y= 6 is 6.
Thus, the correct answer is Option D.
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Re: If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY [#permalink] New post   10 Jul 2020, 08:47
If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY is 90.

A. 2
B. 3
C. 5
D. 6 --> correct: (X + Y) - (X - Y) = 12 =>2Y=12 => Y=6 and XY=90 => X=90/Y=90/6=15, min(X,Y)=min(6,15)=6
E. 10
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Re: If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY [#permalink] New post   11 Jul 2020, 00:07
Opening the brackets,
X+Y-X+Y = 12

X gets cancelled. 2Y = 12
Y=6

XY = 90
X*6 = 90
X = 90/6
X=15

Smaller value is Y=6
Answer D
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Re: If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY [#permalink] New post   11 Jul 2020, 18:42
Given:
(x + y) - (x - y) = 12

To solve
(x + y) - (x - y) = 12
x+y-x+y= 12
2y=12
y=6 --> since xy=90, we know that y< x -->the answer is D
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Re: If (X + Y) - (X - Y) is 12. Find the smaller of the two numbers if XY [#permalink]
11 Jul 2020, 18:42
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