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Inequality Question

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Source: — Data Sufficiency |
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by pemdas » Fri Jul 15, 2011 10:37 am
st(1) (10^2)^(1-a)<1/1000, 1/100^(a-1)<1/1000, 100^(a-1)>1000, 10^(2a-2)>10^3, 2a-2>3, 2a>5, a>2.5 Not sufficient, as a can be < or > 4;
st(2) 1/(10^2a)<1/(10^4), 10^2a>10^4, 2a>4, a>2. Not sufficient, as a can be < or > 4;
combined st(1&2): still Not sufficient, as a can be < or > 4;
e
akshatgupta87 wrote:Q.) If a is an integer, is a<4 ?
1) (10)^(-2a+2) < 0.001
2) (10)^(-2a) < 0.0001
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by shoot4greatness » Fri Jul 15, 2011 3:00 pm
Statement 1 - rewrite the decimal into exponent. 10^(-2a+2)<10^-3. Then -2a+2<-3. -2a<-5. a>5/2. Insufficient.
Statement 2 - 10^(-2a)<10^-4. -2a<-4. a>2

1 and 2. We know that a>2. Not sufficient.

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