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: https://www.gmatprepnow.com/articles/dat ... lug-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
