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exponents
Source: Beat The GMAT — Data Sufficiency |
I think 1 and 2 combined. In fact, if we know those numbers are integers, we know that only 1,7 or -1, -7 can have a product equal to 7. and if 1-7 or 7-1 are the same, -1-(-7) and -7-(-1) are both equal to 6 or -6, whose power of 4 is the same.
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Does stat (2) really matter? I couldnt think of any examples where a fraction (non integer values) would make the statement insufficient.
Could someone please explain or provide examples of non integer values that would make statement (1) insuff. Thanks!
Could someone please explain or provide examples of non integer values that would make statement (1) insuff. Thanks!
What is the value of (x - y)^4?
(1) The product of x and y is 7.
(2) x and y are integers.
(x - y)^4 = (x^2 - 2xy + y^2)(x^2 - 2xy + y^2)
(1)
(x^2 - 2*7 + y^2)(x^2 - 2*7 + y^2)
INSUFF
(2)
INSUFF
(1) and (2)
x and y are integers
xy = 7
either x=1, y=7
or x=7, y=1
also can be both negative, but here it does not matter - we have product and a square - they will be positive
(1^2 - 2*7 + 7^2)(1^2 - 2*7 + 7^2)
is the same as
(7^2 - 2*7 + 1^2)(7^2 - 2*7 + 1^2)
SUFF
C
(1) The product of x and y is 7.
(2) x and y are integers.
(x - y)^4 = (x^2 - 2xy + y^2)(x^2 - 2xy + y^2)
(1)
(x^2 - 2*7 + y^2)(x^2 - 2*7 + y^2)
INSUFF
(2)
INSUFF
(1) and (2)
x and y are integers
xy = 7
either x=1, y=7
or x=7, y=1
also can be both negative, but here it does not matter - we have product and a square - they will be positive
(1^2 - 2*7 + 7^2)(1^2 - 2*7 + 7^2)
is the same as
(7^2 - 2*7 + 1^2)(7^2 - 2*7 + 1^2)
SUFF
C
Just to clarify, stat 1 is Insuff becuase integer (1 and 7)and non integer values (1/7 and 7) will yield different results. Correct?
different x and y, even if their product is equal to 7, will yeld different result when expressed in (x-y)^4
consuder: x=2, y=3,5 (2-3,5)^4 = 5,0625
x=7, y=1 (7-1)^4 = 1296
consuder: x=2, y=3,5 (2-3,5)^4 = 5,0625
x=7, y=1 (7-1)^4 = 1296
