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Intern  Joined: 24 Apr 2010
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In the decimal above, ♣ and x represent single digits. What  [#permalink]

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8 00:00

Difficulty:   95% (hard)

Question Stats: 35% (01:40) correct 65% (02:06) wrong based on 207 sessions

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\$7.9♣x7

In the decimal above, ♣ and x represent single digits. What is the value of x ?

(1) When the sum is rounded to the nearest cent, its cash value is \$7.94.

(2) When the sum is rounded to the nearest tenth of a cent, its cash value is \$7.95.

Originally posted by perseverant on 28 May 2010, 15:32.
Last edited by Bunuel on 03 Mar 2014, 14:07, edited 2 times in total.
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GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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5
3
perseverant wrote:
You are right! B is the answer, I understand why statement 1 is insufficient, but I still dont understand why statement 2 is sufficient (2) When the sum is rounded to the nearest tenth of a cent, its cash value is \$7.95.

\$7.9♣x7, when this is rounded to the nearest of tenth of a cent it should have 7._ _ _ three places of decimal.

so effectively 7.95 is 7.950 and for the \$7.9♣x7 to be 7.950 x must be 9 and ♣ must be 4.

\$7.9497 -> just round this to nearest tenth of a cent you will get 7.950
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##### General Discussion
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GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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1
perseverant wrote:
\$7.9♣x7

In the decimal above, ♣ and x represent single digits. What is the value of x ?

(1) When the sum is rounded to the nearest cent, its cash value is \$7.94.

(2) When the sum is rounded to the nearest tenth of a cent, its cash value is \$7.95.

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

Could someone explain in detail how to solve this? I will post the answer later.

Thanks!

IMO B

\$7.9♣x7

In the decimal above, ♣ and x represent single digits. What is the value of x ?

(1) When the sum is rounded to the nearest cent, its cash value is \$7.94.
When rounded to the nearest cent,the value is 7.94 which means it could be 7.9417 or 7.9367 etc

(2) When the sum is rounded to the nearest tenth of a cent, its cash value is \$7.95.
it is 7.9497 and x =9

as we are here rounding till \$7.9♣x and the last 7 will increment x as 7>5 which will in turn increment ♣ by 1
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Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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You are right! B is the answer, I understand why statement 1 is insufficient, but I still dont understand why statement 2 is sufficient Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
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Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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Let us write the number as 7.9ab7
From 2)
This has been rounded to 7.950
In that case if the value of "a" is 5 then b is 0-4. But if the value of "a" is 4 then b is 9. There is no way to determine a single value of b. Hence 2) alone is insufficient.

Pls correct if the reasoning is wrong.

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Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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What is the meaning of "nearest tenth of a cent" (as given in (2) ) ?
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Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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subhashghosh wrote:
What is the meaning of "nearest tenth of a cent" (as given in (2) ) ?

Nearest cent means "nearest tenth' AND nearest tenth of a cent means 'nearest hundredths'.
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Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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1
gmat1220 wrote:
Let us write the number as 7.9ab7
From 2)
This has been rounded to 7.950
In that case if the value of "a" is 5 then b is 0-4. But if the value of "a" is 4 then b is 9. There is no way to determine a single value of b. Hence 2) alone is insufficient.

Pls correct if the reasoning is wrong.

Posted from my mobile device

In the scenario highlighted above, the rounded value would be 7.951 to 7.955 depending on b being 0-4, whereas the stem tells us that value has to be 7.950 which can happen only when a is 4 and b is 9.
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Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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Yup I realized it. Thanks for undeceiving me. For the very first time the OA given by Kaplan is wrong.
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Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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it can also happen when b is 8.
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Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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kamalkicks wrote:
it can also happen when b is 8.

+1, it can be 6,7 and 8, why only 9??
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Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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2
prekelen wrote:
C
x=4 I guess what they mean by "cash value" is the exact value only.

If cash value is \$7.95 and this is rounded to 3 digits after decimal, the rounded value must be 7.950 i.e. the same as the cash value.

How will you get 7.950 as the value rounded to the thousandth digit?
Only when the number you rounded was 7.9497 (there needs to be a 7 in the ten thousandth position)
When you round this to reduce one digit, you increase the rightmost 9 by one to account for the rightmost 7. When you do this, 49 becomes 50 so you get 7.950.

If the value was 7.9487, rounded to 3 decimal places, it would be 7.949. This is not the same as 7.95
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Re: 9 x7 In the decimal above, and x represent single digits.  [#permalink]

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1
In this question first of all it is very important to understand the terms " rounded to the nearest cent" and "rounded to the nearest tenth of a cent"

Without pre knowledge it is difficult to touch this question, here concept of rounding is not same as general concept of rounding at 10th or 100th place after decimal.

I did some googling to understand this concept Cents represents two digits after decimal such as
2.43 >> 2 dollar 43 cents
2.57 >> 2 dollar 57 cents.

Sum rounded to the nearest cents means rounding at second digit after decimal.
E.g 2.345 = 2.35
E.g 4.553 = 4.55
E.g 5.561 = 5.56

Sum rounded to the nearest tenth of a cents means rounding at digit after cents that is third digit after decimal.
3.34xy round of x as per value of y (here y is 100th place of cent and x is 10th place)
E.g 3.5678 = 3.568 7 become 8
E.g 3.5622 = 3.562 truncated last digit bcz it was less than 5.

Now back to the question.

Statement 2: Rounding to the nearest tenth of the cent is 7.95_ one digit is missing and that should be zero which is not mentioned in question but expected.

So we have 7.950 <--- \$7.9♣x7

As 100th digit of the cent is 7 definitely it will add 1 to 10th digit that is x, thus only one digit can yield zero after addition of 1 that is 9.

Thus x = 9 and ♣x should be 49 to have final result as 7.950.
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Re: In the decimal above, ♣ and x represent single digits...  [#permalink]

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So the key here is "cash value" which limits rounding possibilities. Thanks for highlighting it Karishma.

VeritasPrepKarishma wrote:
prekelen wrote:
C
x=4 I guess what they mean by "cash value" is the exact value only.

If cash value is \$7.95 and this is rounded to 3 digits after decimal, the rounded value must be 7.950 i.e. the same as the cash value.

How will you get 7.950 as the value rounded to the thousandth digit?
Only when the number you rounded was 7.9497 (there needs to be a 7 in the ten thousandth position)
When you round this to reduce one digit, you increase the rightmost 9 by one to account for the rightmost 7. When you do this, 49 becomes 50 so you get 7.950.

If the value was 7.9487, rounded to 3 decimal places, it would be 7.949. This is not the same as 7.95
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In the decimal above, x andy represent single digits. What i  [#permalink]

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This question is from the KAPLAN quiz bank.

\$7.9xy7

In the decimal above, x and y represent single digits. What is the value of y ?

(1) When the sum is rounded to the nearest cent, its cash value is \$7.94.

(2) When the sum is rounded to the nearest tenth of a cent, its cash value is \$7.95.

Please have a look at the first image below for the 'official' solution.

I'm having my doubts for the following reasons: statement 2 says that when rounding to the nearest tenth of cent, the cash value is 7.95. Since we know the hundredth of a cent is 7, we know that when rounding to the nearest tenth of a cent we must add +1 to y. since the new cash value is 7.95 or 7.950, the only value for y that would make it 0 after rounding is 9. Why isn't this so?

thanks for explaining Max
Attachments Kaplan_rounding.jpg [ 351.57 KiB | Viewed 3608 times ]

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Re: In the decimal above, ♣ and x represent single digits. What  [#permalink]

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So my answer (B) was correct afterall.. Perhaps someone from KAPLAN would care to elaborate on why they would include wrong answers in their 199\$ Quiz Bank?! I got really nervous after I read the KAPLAN description because I was convinced I had it right..
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Re: 9 x7 In the decimal above, and x represent single digits.  [#permalink]

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PiyushK wrote:
In this question first of all it is very important to understand the terms " rounded to the nearest cent" and "rounded to the nearest tenth of a cent"

Without pre knowledge it is difficult to touch this question, here concept of rounding is not same as general concept of rounding at 10th or 100th place after decimal.

I did some googling to understand this concept Cents represents two digits after decimal such as
2.43 >> 2 dollar 43 cents
2.57 >> 2 dollar 57 cents.

Sum rounded to the nearest cents means rounding at second digit after decimal.
E.g 2.345 = 2.35
E.g 4.553 = 4.55
E.g 5.561 = 5.56

Sum rounded to the nearest tenth of a cents means rounding at digit after cents that is third digit after decimal.
3.34xy round of x as per value of y (here y is 100th place of cent and x is 10th place)
E.g 3.5678 = 3.568 7 become 8
E.g 3.5622 = 3.562 truncated last digit bcz it was less than 5.

Now back to the question.

Statement 2: Rounding to the nearest tenth of the cent is 7.95_ one digit is missing and that should be zero which is not mentioned in question but expected.

So we have 7.950 <--- \$7.9♣x7

As 100th digit of the cent is 7 definitely it will add 1 to 10th digit that is x, thus only one digit can yield zero after addition of 1 that is 9.

Thus x = 9 and ♣x should be 49 to have final result as 7.950.

I am trying to go back to statement 1 if it makes sense. So if we say the number is \$7.9497 (as per statement 2) then how do we get \$7.94 in statement 1? If \$7.9497 is rounded to nearest cents then it should be 7.95 also. Shouldn't it? Feels like statement 1 and 2 are contradicting each other...
Bunuel please clarify when you get a chance.
Thank you.
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Re: 9 x7 In the decimal above, and x represent single digits.  [#permalink]

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khanym wrote:

I am trying to go back to statement 1 if it makes sense. So if we say the number is \$7.9497 (as per statement 2) then how do we get \$7.94 in statement 1? If \$7.9497 is rounded to nearest cents then it should be 7.95 also. Shouldn't it? Feels like statement 1 and 2 are contradicting each other...
Bunuel please clarify when you get a chance.
Thank you.

This question is flawed. If you look at their explanation, what they mean by "When the sum is rounded to the nearest tenth of a cent, its cash value is \$7.95" is not correct. In the explanation, they say that "when we round to x and then round to ♣" for stmnt 2. This is not correct. When we round to third digit after decimal, we do not then round to second digit. If we want to round to second digit, we must do it in one step.

Let me give you an example:

Say you have 2.48
If you want to round it to the closest integer, will it be 2 or 3? Note that 2.48 is less than 2.50 which is in the middle so it should be rounded to 2. But if you start applying rounding from the rightmost digit 2.48 will becomes 2.5 and that will become 3 (round up). But that is not correct. 2.48 is not closer to 3. Hence, when rounding, only the digit immediately to the right is considered.

Therefore, their analysis of statement 2 is incorrect. That is why it clashes with stmnt 1. Actually stmnt 2 is sufficient alone and \$7.9497 is the only way to get 7.950 upon rounding to tenths of a cent (i.e. the third digit to the right of the decimal)
If, by cash value they mean the value that can be represented in cash (there are 1 cent/2 cent coins but no tenth of a cent coin) which is essentially 2 digits after the decimal, then they cannot round to the tenth of a cent.
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GRE 1: Q169 V154 Re: In the decimal above, ♣ and x represent single digits. What  [#permalink]

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Hi Vyshak
I am not able to understand this question.
What is cash value?
What is rounding to nearest cent?
what is rounding to tenths of a cent?

can you please explain this in the easiest way possible.

Regards
Stone Cold
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Re: In the decimal above, ♣ and x represent single digits. What  [#permalink]

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stonecold wrote:
Hi Vyshak
I am not able to understand this question.
What is cash value?
What is rounding to nearest cent?
what is rounding to tenths of a cent?

can you please explain this in the easiest way possible.

Regards
Stone Cold

Hi stonecold,

Even I was not aware of the phrase 'tenths of a cent' but the above discussions helped.
What is cash value? - Original value of cash
What is rounding to nearest cent? - Approximated value of cash to two decimal places (nearest hundredth).
what is rounding to tenths of a cent? - Approximated value of cash to three decimal places (nearest thousandth).

Hope it helps. Re: In the decimal above, ♣ and x represent single digits. What   [#permalink] 19 Nov 2016, 04:07

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