DS - Decimals

[rajat27]

Is the number x between 0.3 and 0.6 ?
(1) 425x < 85
(2) 170x < 85

Please explain the logic ?

Thnx.

[Tommy Wallach]

Hey Rajat,

Use benchmarks to quickly do the math:

1) 425x < 85

If x = .3

.1 * 425 = 42.5 --> 3 * 42.5 = 117.5

That's already way bigger than 85, so x has to be less than .3. You could also do this in your head, if you notice that 42.5 is 1/10th of 85, which means that .2 * 425 = 85. Thus this statement is sufficient (x is definitively not

2) 170x < 85

This is easier. If x = .5, then 170x = 85. So x can't be .5, but it can be anything smaller. That makes this statement insufficient, as x could be more or less than .3.

The answer is A.

Hope that helps!

-t

P.S. While the GMAT doesn't require a calculator, it's very helpful to be sharp with benchmarking (Finding 10%, 20%, 30%, etc. very quickly). Practice makes perfect!

[Anurag@Gurome]

Is the number x between 0.3 and 0.6 ?
(1) 425x < 85
(2) 170x < 85

Statement 1: x < 85/425 ---> x < 1/5 ---> x < 0.2 < 0.3
Hence, x is definitely not between 0.3 and 0.6

Sufficient

Statement 2: x < 85/170 ---> x < 1/2 ---> x < 0.5
Now if x = 0.4 ---> x is between 0.3 and 0.6
But if x = 0.2 ---> x is not between 0.3 and 0.6

Not sufficient

The correct answer is A.

[ceilidh.erickson]

The question asks whether the number x will be within a given range. When we glance at the statements, we see that they each give an inequality. The only way that an inequality will answer a question about a range is if the inequality is completely outside the range. Consider:



We want to be able to compare the range to the inequalities. Tommy offered one way, but we could also try turning everything into FRACTIONS:

Rephrased question: Is (3/10) < x < (6/10) ?

(1) 425x < 85
Isolate x: x < (85/425)
Reduce: x < (17/85) --> x < (1/5)
Convert to tenths to compare to our range: x < (2/10)

2/10 is less than 3/10, so if x is less than the lowest point on our range, x cannot be within the range. We have a definitive "no" answer. Sufficient.

(2) 170x < 85
Isolate x: x < (85/170)
Reduce: x < (1/2)
Convert to tenths to compare: x < (5/10)

Something less than 5/10 could be within our range (e.g. 4/10), or it could be outside of the range (e.g. 0). We have an answer of "maybe." Insufficient.

The answer is A.