If X and Y each represent single digits in the decimal above

Question

3.2XY6

If X and Y each represent single digits in the decimal above, what digit does X represent?

(1) When the decimal is rounded to the nearest tenth, 3.2 is the result.

(2) When the decimal is rounded to the nearest hundredth, 3.24 is the result.

mcelroytutoring · Accepted Answer

Here is a visual that should help.

harshavmrg · Answer

i feel that the answer should be B, but GMAT-PREP wont give me wrong answer..correct...so can somebody explain it to me why the answer is E.

My analysis
=============
1. to round it to 3.2, @ would be either 0,1,2,3,4 ..hence unique value of @ cant be decided , hence No

2. to round it to 3.24, & would be either 5,6,7,8,9 and @ to be 3 and then when it is rounded off it became 4 as in 3.24 ....hence @=3
is this not correct?

jamifahad · Answer

3.2@&6
Consider this number: 3.2416. &=1 and @=4. rounded to hundredth it became 3.24

Now take both statement.
1. when the decimal is rounded to the nearest tenth, 3.2 is the result.
2. when the decimal is rounded to the nearest hundredth , 3.24 is the result.

let &=2 so number 3.2@26
rounded 3.2@3
@=4. hence number 3.2426
let &=6 so number 3.2@66
rounded 3.2@7
@=3. hence number 3.2366. 
Hence no unique value of @.

OA E.

suraabhi · Answer

Hey I have stumbled across this question and still confused.

Dont you think 3.2416 should be 3.23 when rounded to 100?

fluke · Answer

It is hundreDTHs, not hundreds;

Answer: No.

3.2416 rounded to hundredths place will be 3.24 because thousandths place is 1.

Units  Decimal  Tenths  Hundredths  Thousandths  Ten Thousandths  
  3  .  2  4  1  6

3.2416
Rounded to Tenths place=3.2 because hundredths place is 4(<=5)
Rounded to Hundredths place=3.24 because thousandths place is 1(<=5)
Rounded to Thousandths place=3.242 because ten thousandths place is 6(>=5)

stonecold · Answer

clearly x=3,4 satisfy both and hence no unique value => E

law258 · Answer

E is correct.

(1) When the decimal is rounded to the nearest tenth, 3.2 is the result. --> NOT SUFFICIENT; we can have the following possibilities off of this statement: 3.24, 3.23, 3.22, etc.

(2) When the decimal is rounded to the nearest hundredth, 3.24 is the result. --> NOT SUFFICIENT; We could already have 3.24 and y could be 3 or we could have 3.235 (rounded to 3.24 as well).

(1) + (2) - NOT SUFFICIENT - We still don't know that value of y (which would help us lock down a value for x)

stonecold · Answer

Wonderful little Question from GREP prep.
Here let N=3.2XY6
we need to get X
Using Digit constraints => X,Y can take valued out of 10 available values=> {0,1,2,,,9}
Note here that we aren't told that X,Y are non zero. In some questions its can make a huge impact.
Statement 1
Here When N will be rounded to nearest tenths => we will get 3.2 or 3. 3 depending on whether the value of X is ≤4 or >5 respectively.
Since the answer is 3.2 
WE can say with confidence that the vale of X must be ≤4
but we still don't have a unique value for X 
hence this statement is not sufficient.
Statement 2
When we will round Y to nearest hundredths the result can be either 3.2X or it can be 3.2  where X+1 is a single digit number.
Given the answer is 3.24 
hence X can either be 4 (for Y≤4)
or X can be 3 (for Y>5)
Hence X can be 3 or 4 
Clearly this statement is still insufficient.
Combining the two statements we see that both values of X i.e 3 and 4 will make both the statements true.
Hence X may be 3 or 4
So we still don't have a unique value of X
Hence combination statement is insufficient too. 
Hence E

PerseveranceWins · Answer

Statement 1 - Rounded to nearest tenth = 3.2
This means that X can be 0,1,2,3 or4 - any of these - because rounding up with these digits next to 2 would lead to 3.2 as the answer. -- not sufficient

Statement 2 - Rounded to 100ths - 3.24 - This means that X can be either 3 or 4.

Case when X is 3:-
3.23Y6 - If Y is 5,6,7,8 or 9 , then rounding up this number would give result - 3.24

Case when X is 4:-
3.24Y6 - If Y is 0,1,2,3 or 4, then rounding up the number would give - 3.24
So, we can see that in case of statement 2 as well, X can have 2 values - 3,4 - so not sufficient.

Combining both statements - still X can be either 3 or 4.
So Answer - E

kokus · Answer

3.2XY6

1) 3.2 -> X<5 -> Insufficient (if x was >5, then rounding to the nearest tenth will result in 3.3)
2) 3.24 -> X was rounded to 4, therefore if rounded up, x is 3 or if rounded down it was 4.
Rounded Up:3.2386 = 3.239 = 3.24
Rounded Down: 3.2416 = 3.242 = 3.24

Insufficient X can be either 3 or 4

1+2) Statement 1 is already included in 2, as we now that x<5 (3 or 4) -> Insufficient -> E

Basshead · Answer

(1) This statement tells us that the number was rounded down; the square can be 0, 1, 2, 3, or 4. INSUFFICIENT

(2) If the triangle is 5, 6, 7, 8, or 9, then the square can be 3. If the triangle is 0, 1, 2, 3, or 4, then the square can be 4. INSUFFICIENT.

(1&2) Combining the two statements, the square can be 3 or 4. INSUFFICIENT.

Answer is E.

siddhantvarma · Answer

Statement (1): When the decimal is rounded to the nearest tenth, 3.2 is the result.

When rounding to the nearest tenth, we look at the hundredths digit (X) to determine whether to round up or down.

If X < 5, we round down to 3.2
If X ≥ 5, we round up to 3.3
Since the result is 3.2, we must have X < 5
So X must be 0, 1, 2, 3, or 4 => Insufficient

Statement (2): When the decimal is rounded to the nearest hundredth, 3.24 is the result.

When rounding to the nearest hundredth, we look at the thousandths digit (Y) to determine rounding.

If Y < 5, we round down to 3.2X
If Y ≥ 5, we round up to 3.2(X+1) or possibly 3.3 if X = 9
Since the result is 3.24, either:
X = 4 and Y < 5, or
X = 3 and Y ≥ 5 (rounding up to 3.24)
=> Insufficient

From statement (2) alone, X could be either 3 or 4, so it's insufficient.

Using both statements together:
From (1), X must be 0, 1, 2, 3, or 4
From (2), X must be either 3 or 4
Combining these, X is either 3 or 4

However, this still doesn't uniquely determine X, so both statements together are insufficient => Answer is (E)

If X and Y each represent single digits in the decimal above

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Units	Decimal	Tenths	Hundredths	Thousandths	Ten Thousandths
3	.	2	4	1	6

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If X and Y each represent single digits in the decimal above

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