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If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th

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Bunuel
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If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th [#permalink] New post   22 Oct 2020, 11:43
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If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is the value of the sum of all possible values of y?

A. -1
B. 0
C. 1
D. 12
E. 24
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B
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B
Xolmuhammad
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If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th [#permalink] New post   Updated on: 02 Nov 2020, 03:17
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x-y and x+y are primes, we can only get 143 in two cases 13*11 or 11*13

1) x-y=13
x+y=11 x=12 y=-1

2) x-y=11
x+y=13 x=12 y=1

so y1+y2= 0

answer B

sorry for a typo!!!, now corrected!!!

Originally posted by Xolmuhammad on 22 Oct 2020, 12:39.
Last edited by Xolmuhammad on 02 Nov 2020, 03:17, edited 1 time in total.
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mayanksachdev7
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Re: If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th [#permalink] New post   01 Nov 2020, 21:31
Xolmuhammad wrote:

2) x-y=11
x+y=13 x=12 y=-1

answer B

2) x-y=11
x+y=13 x=12 y=1
if one of the y is one shouldn't the other be -1
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DanAustin
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If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th [#permalink] New post   01 Nov 2020, 23:21
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IMO B

143 = 11 X 13

this means x + y = 13 (or 11)
x - y = 11 (or 13)

Equating either one, we get the value of "Y" as -1 and +1

Hence Answer is B ie 0


(Please give kudos )
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yashvgupte
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Re: If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th [#permalink] New post   20 Nov 2020, 08:55
(x-y)(x+y)=143
(13)(11)= 143; (x-y)=13; (x+y)=11, solving both equations, x=12; y=-1
OR
(11)(13)=143; (x-y)=11; (x+y)=13, solving both equations, x=12; y =-1

In both cases, y+y = -1+-1 = -2.

Why does this logic not work here? Why is it assumed that y=+1 or -1?
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Re: If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th [#permalink] New post   24 Nov 2020, 07:26
Bunuel wrote:
If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is the value of the sum of all possible values of y?

A. -1
B. 0
C. 1
D. 12
E. 24


Given (x-y) and (x+y) are prime, we could have (13)(11) = 143 or (11)(13) = 143.


\(x - y = 11\)
\(x + y = 13\)
\(x = 12, y = - 1, 1\)

\(x - y = 13\)
\(x + y = 11\)
\(x = 12, y = -1, 1\)

\(-1 + 1 = 0\)

Answer is B.
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If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th [#permalink] New post   24 Nov 2020, 07:31
yashvgupte wrote:
(x-y)(x+y)=143
(13)(11)= 143; (x-y)=13; (x+y)=11, solving both equations, x=12; y=-1
OR
(11)(13)=143; (x-y)=11; (x+y)=13, solving both equations, x=12; y =-1

In both cases, y+y = -1+-1 = -2.

Why does this logic not work here? Why is it assumed that y=+1 or -1?


\((x-y)=11\); \((x+y)=13\)

x = 12; y = 1

\((x-y)=13\); \((x+y)=11\)

\(x = 12\); \(y = -1\)

\(y = 1, -1\)
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Re: If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th [#permalink] New post   24 Nov 2020, 10:47
Bunuel wrote:
If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is the value of the sum of all possible values of y?

A. -1
B. 0
C. 1
D. 12
E. 24

\((x − y)(x + y) = 143\)

Or, \((x − y)(x + y) = 11*13\)

Or, \((12 − 1)(12 + 1) = 11*13\) {x = 12 , y =1}

Hence, y can be -1 (As in 12 - 1 ) & y can be 1 (As in 12 + 1 )

Sum of all possible values of y = 0, Answer must be (B)
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Re: If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th [#permalink] New post   28 Nov 2020, 10:17
Expert Reply
Bunuel wrote:
If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is the value of the sum of all possible values of y?

A. -1
B. 0
C. 1
D. 12
E. 24

Solution:

Since 143 = 11 * 13, we could have 1) x - y = 11 and x + y = 13 OR 2) x - y = 13 and x + y = 11. In either case, let’s subtract the first equation from the second:

Case 1: 2y = 2 → y = 1

Case 2: 2y = -2 → y = -1

We see that the sum of the two possible values of y is 1 + (-1) = 0.

Answer: B
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Re: If (x − y)(x + y) = 143, and (x − y) and (x + y) are prime, what is th [#permalink]
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