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Manager  Status: I will not stop until i realise my goal which is my dream too
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If X and Y each represent single digits in the decimal above  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 75% (01:27) correct 25% (01:25) wrong based on 320 sessions

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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.

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Originally posted by harshavmrg on 25 Jun 2011, 23:28.
Last edited by Bunuel on 31 Jul 2014, 03:49, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If X and Y each represent single digits in the decimal above  [#permalink]

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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?
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Re: If X and Y each represent single digits in the decimal above  [#permalink]

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harshavmrg wrote:
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?

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.
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Re: If X and Y each represent single digits in the decimal above  [#permalink]

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thanks for the answer Jami
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Re: If X and Y each represent single digits in the decimal above  [#permalink]

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Hey I have stumbled across this question and still confused.

Dont you think 3.2416 should be 3.23 when rounded to 100?
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Re: If X and Y each represent single digits in the decimal above  [#permalink]

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1
suraabhi wrote:
Hey I have stumbled across this question and still confused.

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

It is hundreDTHs, not hundreds;

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)
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GRE 1: Q169 V154 Re: If X and Y each represent single digits in the decimal above  [#permalink]

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clearly x=3,4 satisfy both and hence no unique value => E
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Re: If X and Y each represent single digits in the decimal above  [#permalink]

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4
Here is a visual that should help.
Attachments Screen Shot 2016-03-28 at 6.01.19 PM.png [ 128.44 KiB | Viewed 6360 times ]

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Re: If X and Y each represent single digits in the decimal above  [#permalink]

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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)
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GRE 1: Q169 V154 Re: If X and Y each represent single digits in the decimal above  [#permalink]

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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[X+1] 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
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Re: If X and Y each represent single digits in the decimal above  [#permalink]

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harshavmrg wrote:
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.

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
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Re: If X and Y each represent single digits in the decimal above  [#permalink]

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_________________ Re: If X and Y each represent single digits in the decimal above   [#permalink] 04 Mar 2019, 19:37
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