If d represents the hundredths digit and e represents the

Question

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

Bunuel · Accepted Answer

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?

To answer the question we should know whether  d\geq{5} .

(1) d – e is equal to a positive perfect square --> easy to get two different result:  0.4de=0.451  (5-1=4=2^2), then 0.4de rounded to the nearest tenth will be  0.5  but if  0.4de=0.421  (2-1=1=1^2), then 0.4de rounded to the nearest nearest tenth will be  0.4 . Not sufficient.

(2)  \sqrt{d}>e^2  --> also easy to get two different result: if  \sqrt{d}=\sqrt{5}>1^2=e^2  or  \sqrt{d}=\sqrt{2}>1^2=e^2 . Not sufficient.

(1)+(2) 0.451 and 0.421 satisfy both statements and give different values of 0.4de when rounded to the nearest tenth: 0.5 and 0.4. Not sufficient.

Answer: E.

Rounding rules 
Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep.

Example:
5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5.
5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5.
5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.

Hope it helps.

fluke · Answer

E
0.451. Decimal rounded tenth=0.5
0.421. Decimal rounded tenth=0.4

pbull78 · Answer

can anyone help me with detailed explanation ?

LalaB · Answer

0.4de . question -0.x?

st1-d-e =perfect square.
let d-e=4 (d=4; e=0) or d-e=9 (d=9 e =0) insuff

st2- sqrootd>e^2 
sqroot4>0 or sqroot9>0. again insuff. as everyone can understand, together these stmnts are also insuff

gmat6nplus1 · Answer

we are allowed to use numbers < 10.

1. there are only 3 perfect squares in the available range. 1; 4; 9.

Pick 4. If d-e=4 then d might be 4 and e 0 or d might be 7 and e 3. If d=4 then our decimal remains 0.4; If d=7 our decimal becomes 0.5

NS.

2. since we know for sure that we are dealing with positive integers+0 we can safely say that if the square root of a number is greater than another number to the power of n, then the number under square root must be greater than the number to the power of n. This conveys us that d>e.

NS

1+2) Both cases on statement 1) hold. (E)

stonecold · Answer

Amazing Question
Let n=0.4de
Here when we round n to nearest thousandths we will get either=>
0.4 for d≤4
OR
0.5 for d≥5
hence in this question we are concerned about the value of d.
statement 1
d-e=positive perfect square
numerous values are possible
e.g=>
n=0.454
n=0.487
n=0.421
n=9.451
Hence insufficient as we can have d<5 so ≥5.
Statement 2
hmm since d and e are both positive and we can square on both sides of any inequality for which both of its sides are positive
we get=> d>e^4
hmm numerous values are possible 
e.g=>
n=0.421
n=0.491
n=0.451
etc
hence insufficient 
combining the two statements we can still get two-bound cases
n=0.421
n=0.451
hence E

firas92 · Answer

Bunuel

Are we allowed to assume e=0? I ask because if e=0, the decimal can be represented as 0.4d in which case we wouldn't have a thousandth digit

Posted from my mobile device

iamdc22 · Answer

As a test case for statement (2), could we say that e may be negative? For example, e=-1 and d=4 would make the value of the decimal negative.

ScottTargetTestPrep · Answer

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

minustark · Answer

we need to find whether d >= 5 or not.
1) d -e can be 1, 4 , 9. so depending on the value of e, d can be greater or lower than 5. not sufficient
2) d's value depends on e. not sufficient.
Combined, e has to be 1 to satisfy stmnt 1. so the value of d can be either 2 or 5.Not sufficient.
E is the answer.

CEdward · Answer

Bunuel, what about 'carry-over' rounding?

Suppose the decimal is 5.3445 and we are asked to round to the nearest hundredth. Is it 5.34 or 5.35?

Bunuel · Answer

5.3445 rounded to the nearest hundredth = 5.35.

puneetfitness · Answer

Hi Bunuel can e be equal to zero so that d-e= 4-0=2^2

What i am trying to ask as question stem does not say d and e are not equal to zero can zero be considered decimal place.

Posted from my mobile device

Bunuel · Answer

___________________________
Yes, in (1) both d and e can be 0.

unraveled · Answer

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. 
A) d - e = 9
I) d = 9, e = 0

0.4de = 0.490 = 0.5

B) d - e = 4
I) d = 9, e = 5
0.4de = 0440 = 0.4

II) d = 5, e = 1
0.4de = 0.451 = 0.5

III) d = 4. e = 0
0.4de = 0.495 = 0.5

Similarly, 
d - e = 1
for which there are so many cases.

INSUFFICIENT.

(2) √d > e^2
Taking same values as taken for St. 1
A) I) d = 9, e = 0
0.4de = 0.490 = 0.5

B) III) d = 4, e = 0
0.4de = 0.440 = 0.4

And there can be so many more cases.

INSUFFICIENT.

Together 1 and 2
From above we see both are insufficient together as well.

Answer E.

finisher009 · Answer

The core of the question is whether to round `0.4de` to 0.4 or 0.5. This only depends on the hundredths digit, `d`.
• If `d` is 5 or more, it rounds to 0.5.
• If `d` is 4 or less, it rounds to 0.4. The question is simply: “Is d >= 5?”

Let’s test the statements by picking numbers to see if we can get both a “yes” and a “no.”

1. Statement (1): d - e = a positive perfect square.
• Can `d` be >= 5? Let’s test `d = 5`. If `e = 1`, then `d - e = 4`, which is a perfect square. This works. The number rounds to 0.5.
• Can `d` be < 5? Let’s test `d = 4`. If `e = 3`, then `d - e = 1`, a perfect square. This works. The number rounds to 0.4.
• Since we get two different answers, Statement (1) is Insufficient.

2. Statement (2): sqrt(d) > e^2.
• Can `d` be >= 5? Let’s reuse `d = 5, e = 1`. `sqrt(5)` (which is about 2.2) is greater than `1^2`. This works. The number rounds to 0.5.
• Can `d` be < 5? Let’s reuse `d = 4, e = 1`. `sqrt(4)` (which is 2) is greater than `1^2`. This works. The number rounds to 0.4.
• Again, two different answers. Statement (2) is Insufficient.

3. Statements (1) and (2) Together:
• We already found two pairs that work for both statements:
• `d=5, e=1` satisfies both conditions and rounds to 0.5.
• `d=4, e=1` (since `4-1=3` is not a perfect square, let’s try `d=2, e=1`. `d-e=1`, which is a perfect square. `sqrt(2) > 1^2` is true). `d=2` works for both conditions and rounds to 0.4.
• Since we still have two possible outcomes, the combined statements are Insufficient.

The correct answer is E.

If d represents the hundredths digit and e represents the

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