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If d represents the hundredths

This topic has 1 expert reply and 0 member replies

If d represents the hundredths

Post Wed Dec 06, 2017 4:23 am
If d represents the hundredths digit and e represents the thousandths digit in the decimal 0.4de, what is the value of this decimal rounded to the nearest tenth?

(1) d - e is equal to a positive perfect square.
(2) √d > e^2

Can some experts identify how to get the best option?

OA E

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Top Reply
Post Wed Dec 06, 2017 7:15 am
Quote:
If d represents the hundredths digit and e represents the thousandths digit in the decimal 0.4de, what is the value of this decimal rounded to nearest tenth?

(1) d-e is equal to a positive perfect square.
(2) √d > e²
Target question: What is the value of this decimal rounded up to nearest tenth?

Statement 1: d-e is equal to a positive perfect square.
This statement doesn't FEEL sufficient, so I'm going to TEST some values.
There are several values of d and e that satisfy statement 1. Here are two:
Case a: d = 5 and e = 1, in which case d - e = 5 - 1 = 4, and 4 is a perfect square. In this case, when we round 0.451 to the nearest tenth, we get 0.5
Case b: d = 2 and e = 1, in which case d - e = 2 - 1 = 1, and 1 is a perfect square. In this case, when we round 0.421 to the nearest tenth, we get 0.4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values

Statement 2: √d > e²
This one doesn't feel sufficient either, so let's test some values.
There are several values of d and e that satisfy statement 2. Here are two:
Case a: d = 5 and e = 1, in which case √5 > 1². In this case, when we round 0.451 to the nearest tenth, we get 0.5
Case b: d = 2 and e = 1, in which case √2 > 1².. In this case, when we round 0.421 to the nearest tenth, we get 0.4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT


Statements 1 and 2 combined
Notice that the numbers we used above satisfy BOTH statements. We have:
Case a: d = 5 and e = 1. In this case, when we round 0.451 to the nearest tenth, we get 0.5
Case b: d = 2 and e = 1. In this case, when we round 0.421 to the nearest tenth, we get 0.4
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

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Brent Hanneson – Founder of GMATPrepNow.com
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