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Need Help in DS problems - 4

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Need Help in DS problems - 4

by phoenix9801 » Thu Jun 10, 2010 2:30 am
Would you please use Picking Numbers and/or Straightforward Math to solve these questions Please be simple. (not Algebra). Thanks.


8- If m and n are nonzero integers, is m^n an integer?

(1) n^m is positive

(2) n^m is an integer


9- What us the value of XY ?

(1) x+ Y = 10

(2) x -y = 6
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Source: — Data Sufficiency |
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by Rich@VeritasPrep » Thu Jun 10, 2010 3:14 am
You want to know if m^n is an integer if m and n are nonzero integers...

(1) n^m is positive

If n=2 and m=3, for example, then m^n = 3^2 = 9, which is an integer.

If n=-2 and m=2, for example, then m^n = 2^(-2) = 1 / 2^2 = 1/4, which is not an integer.

INSUFFICIENT

(2) n^m is an integer

Use the same examples. INSUFFICIENT

We used the same examples for each statement, so we can certainly use these examples when combining the statements, and that's enough to show that even when combined, Sts (1) and (2) are still insufficient.
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by Rich@VeritasPrep » Thu Jun 10, 2010 3:19 am
9- What us the value of XY ?

(1) x+ Y = 10

Could have x=7 and y=3, or could have x=6 or y=4. Each option gives you a different value of XY. INSUFFICIENT

(2) x -y = 6

Could have x=7 and y=1, or could have x=8 or y=2. Each option gives you a different value of XY. INSUFFICIENT

If you combine (1) and (2) and start picking numbers, you'd find that only x=8 and y=2 work, which gives you a definite value of XY. SUFFICIENT.

You could also reach this conclusion by adding the two equations together in a system:

X+Y=10
+(X-Y=6)
-----------
2X + (Y + -Y) = 16

2X + 0 = 16

X = 8

X+Y=10

8+Y=10

Y=2
Rich Zwelling
GMAT Instructor, Veritas Prep
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