Decimals

[prachi18oct]

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 up to nearest tenth?
(1) d-e is equal to a positive perfect square.
(2) d^1/2 > e^2

Reasoning:-

[spoiler]
FRom (1) d-e can be 1,4,9 ( Can we assume the last digit to be zero? if yes, then only d-e can be 9)
d, e can be 2,1 ; 3,2 ; 4,3; 5;4, 6,5 ; 7,6 ; 8,7 ; 9,8 => rounded up value can be 0.4 or 0.5
or 5,1 ; 6,2 ; 7,3 ; 8;4 ; 9,5 => rounded up value will always be 0.5
INSUFFICIENT
From 2, d > 1 INSUFFICIENT

Combining, d,e can be 2,1 ; 3,2 ; 4,3; 5;4, 6,5 ; 7,6 ; 8,7 ; 9,8 etc INSUFFICIENT


[/spoiler]

Please advise if the reasoning is ok.

[Brent@GMATPrepNow]

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 up to nearest tenth?

Are you sure the word up is supposed to be there? If so, then we don't even need the statements. Rounded UP, 0.4de becomes 0.5

I assume the question is worded as follows:

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

[Brent@GMATPrepNow]

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 up to nearest tenth?
(1) d-e is equal to a positive perfect square.
(2) d^1/2 > e^2

Reasoning:-


FRom (1) d-e can be 1,4,9 ( Can we assume the last digit to be zero? if yes, then only d-e can be 9)
d, e can be 2,1 ; 3,2 ; 4,3; 5;4, 6,5 ; 7,6 ; 8,7 ; 9,8 => rounded up value can be 0.4 or 0.5
or 5,1 ; 6,2 ; 7,3 ; 8;4 ; 9,5 => rounded up value will always be 0.5
INSUFFICIENT
From 2, d > 1 INSUFFICIENT

Combining, d,e can be 2,1 ; 3,2 ; 4,3; 5;4, 6,5 ; 7,6 ; 8,7 ; 9,8 etc INSUFFICIENT




Please advise if the reasoning is ok.

Your reasoning looks great.

Cheers,
Brent

[Matt@VeritasPrep]

Another thought here:

The question is essentially: is d ≥ 5 ?

S1:: d - e = x², where x is a positive integer. Since 9 ≥ d ≥ 0 and 9 ≥ e ≥ 1, we have d - e = 4 or 1. So we could have d = 2 and e = 1, or d = 5 and e = 1; insufficient.

S2:: √d > e², or d > e�. This tells us e = 1 and d > 1. Big whoop!

Together, we still have d = 2, e = 1 and d = 5, e = 1, so E.

[Scott@TargetTestPrep]

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 up to nearest tenth?
(1) d-e is equal to a positive perfect square.
(2) d^1/2 > e^2

Solution:

If d is a digit greater than or equal to 5, the decimal 0.4de will be rounded to 0.5. If d is a digit less than or equal to 4, the decimal 0.4de will be rounded to 0.4. So we need to determine whether d ≥ 5 or d ≤ 4.

Statement One Alone:

d – e is equal to a positive perfect square.

We see that if e = 1, d could be either 2 or 5. Since d could be either ≥ 5 or ≤ 4, we can’t determine the value of 0.4de when rounded to nearest tenth. Statement one alone is not sufficient.

Statement Two Alone:

√d > e^2

Again, if e = 1, d could be either 2 or 5. Statement two alone is not sufficient.

Statements One and Two Together:

Even with the two statements, d could be either 2 or 5 (when e = 1). So the two statements together are still not sufficient.

Answer: E