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exponents

Expert replies
Source: — Data Sufficiency |

by mjjking » Mon Sep 29, 2008 1:50 am
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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by beater » Mon Sep 29, 2008 5:57 am
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!
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by 4meonly » Mon Sep 29, 2008 8:20 am
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
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by beater » Mon Sep 29, 2008 8:32 am
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?
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by 4meonly » Mon Sep 29, 2008 8:50 am
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
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by beater » Mon Sep 29, 2008 8:54 am
Thanks dude.
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