Is the number x between 0.3 and 0.6 ?
(1) 425x < 85
(2) 170x < 85
Please explain the logic ?
Thnx.
DS - Decimals
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- Tommy Wallach
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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!
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!
Tommy Wallach, Company Expert
ManhattanGMAT
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Statement 1: x < 85/425 ---> x < 1/5 ---> x < 0.2 < 0.3rajat27 wrote:Is the number x between 0.3 and 0.6 ?
(1) 425x < 85
(2) 170x < 85
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.
Anurag Mairal, Ph.D., MBA
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- ceilidh.erickson
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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.
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.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education