In the decimal above, ♣ and x represent single digits. What

(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

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

You are right! B is the answer, I understand why statement 1 is insufficient, but I still dont understand why statement 2 is sufficient

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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What is the meaning of "nearest tenth of a cent" (as given in (2) ) ?
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Nearest cent means "nearest tenth' AND nearest tenth of a cent means 'nearest hundredths'.

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.

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

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.

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

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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