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Value; tenths digit of a decimal

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by crackgmat007 » Thu May 07, 2009 10:21 am
What is the value of (2x – 5)^3 ?
(1) (2x)^3 = 216
(2) (2x + 3)^2 = 81

IMO - E. Can anyone help me understand how statement 1 alone is sufficient?

In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

IMO - D. Can anyone help me understand why statement 1 is not sufficient?
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Source: — Data Sufficiency |
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by scoobydooby » Thu May 07, 2009 11:51 am
Q.1
stmt1) 2x)^3 = 216
let 2x be y=> y^3=216=>y=6
or 2x=6=>x=3
with a unique value of x, we get adefinite value for (2x – 5)^3=1
sufficient.

stmnt 2)
(2x + 3)^2 = 81
=>2x+3=9 or 2x+3=-9
=>x=3 or x=-6
as there is no unique value for x, we do not get a definite value for
(2x – 5)^3. not sufficient
hence, A


Q2.
stmnt1) 16x=integer say k
=>x=k/16
if k=4, x=4/16=1/4=0.25 => tens digit not 0
if k=1, x=1/16=0.0625=> tens digit 0
not sufficient

stment2) 8x=integer say k
=>x=k/8
if k=4, x=4/8=1/2=0.50 => tens digit not 0
if k=1, x=1/8=0.125=>tens digit not 0
(the least k can be is 1)
sufficient

hence, B
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