VERITAS PREP OFFICIAL SOLUTION:

The question is based on rounding. We need to figure out the value of y given some rounding scenarios. Let’s look at them one by one.

Statement 1: When the cost is rounded to the nearest cent, it becomes $7.65.

When rounded to the nearest cent, the cost becomes 7 dollars and 65 cents. 6xy7 cents got rounded to 65 cents. When will .6xy7 get rounded to .65? When .6xy7 lies anywhere in the range .6457 to .6547. Note that in all these cases, when you round the number to 2 digits, it will become .65.

Say price is 7.6468. We need to drop 68 but since 6 is ‘5 or greater’, 4 gets rounded up to 5.

Similarly, say the price is 7.6543. We need to drop 43. Since 4 is ‘4 or smaller’, 5 stays as it is.

So x and y can take various different values. This statement alone is not sufficient.

Statement 2: When the cost is rounded to the nearest tenth of a cent, it becomes $7.65

Now the cost is rounded to the tenth of a cent which means 3 places after the decimal. But the cost is given to us as $7.65. Since we need 3 places, the cost must be $7.650 (which will be written as $7.65)

When will 7.6xy7 get rounded to 7.650? Now this is the tricky part of the question – from 7.6xy7, you need to drop the 7 and round up y. When you do that, you get 7.650. This means 7.6xy7 must have been 7.6497. Only in this case, when we drop the 7, we round up the 9 to make 10, carry the 1 over to 4 and make it 5. This is the only way to get 7.650 on rounding 7.6xy7 to the tenth of a cent. Hence x must be 4 and y must be 9. This statement alone is sufficient to answer the question.

Answer (B)
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The exact cost price to make each unit of a widget is $7.6xy7, where x and y represent single digits. What is the value of y?

(1) When the cost is rounded to the nearest cent, it becomes $7.65.
(2) When the cost is rounded to the nearest tenth of a cent, it becomes $7.65.

1) Tells us that 7.6xy7 becomes 7.65 when rounded to the nearest cent, x = 4 or 5. This can happen by y being 1,2,3,4 and x being 5, or by y being 5,6,7,8,9 and x being 4. Not sufficient.

2) Tells us that 7.6xy7 becomes 7.650, this can happen by x being 4 and y being 9 (since the 7 rounds the 10th of a cent to 0, this must be 49).

B?

For statement 2 can't we get the same result if x and y were 4 and 8? i.e. 7.6487?

Then we receive 7.649 because we need to round up to tenth of cent
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Hi,

Can someone explain the rounding up to the tenth of a cent concept with some examples?

regards,
karthik

Rounding up of 0.123 to the nearest tenth will be 0.1

Rounding up of 0.125 to the nearest tenth will be 0.1

Rounding up of 0.153 to the nearest tenth will be 0.2

Rounding up of 0.156 to the nearest tenth will be 0.2

Rounding up of 7.156 to the nearest tenth will be 7.2

For rounding to -ths (tenths or hundredths or thousandths etc) look at the digit to the right of the digit in question. If this "to the right" digit is <5, keep the same "digit in question". But if this "to the right" digit is \(\geq\) 5, then "digit in question" gets incremented by 1.

Read: http://www.veritasprep.com/blog/2014/06 ... or-a-five/

Hope this helps.
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My 2 cents:
I think following discussion from (https://www.veritasprep.com/blog/2014/0 ... or-a-five/) article from which this question is taken is VVVIMP...
When the cost is in dollars such as 34.10, it represents 34 dollars and 10 cents, right? 12.35 would be 12 dollars and 35 cents.

Say if the cost is 34.1083 and we need to round to a cent, it means we need to find the nearest cent it represents so we round to two places after the decimal and it becomes 34.11.
If we round to the tenth of a cent, it means we want to find the nearest (1/10th) of a cent which is given by the third decimal place. so we will round it to 34.108
Usually, the questions directly give you the number of places to which you need to round – rounded to two places after the decimal/three places after the decimal etc.

Hi Bunuel
Need a clarification as I am not very thorough with rounding off concept.
What if y=0 & x =5, 7.6507. Wouldn't this no. also be rounded to 7.65 ?

7.6507 rounded to the nearest tenth of a cent is 7.651.
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Hi Bunuel,

For Statement 1, what about 7.6547, will it belong to that group? If we look only until 4, then it'd become 7.65, but if we include 7, it'll become 7.655, which will become 7.66. So when x equals 5, shouldn't y only go to 3, not 4? Thanks!

That;s not true.

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.
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Hi Bunuel!
When statement 2 says round it to the nearest tenth of a cent is that different from round to the nearest tenth? If yes, how so? what does rounding to nearest tenth/hundredth of a cent mean?
Because if not, then don't both statements tell us the same info :S

Thanks

Rounding to the nearest tenth of a cent means we need to round up to 3 decimal places.
Can someone please confirm?
Thanks
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chetan2u, Bunuel, VeritasKarishma, GMATBusters, nick1816 -- why does rounding one tenth of a cent, mean 3 decimal places ?

i thought it meant the tenth digit in a number

34.869 -- i thought the tenth digit of a cent was right after the decimal (=8)

Please explain logically why tenth of a cent means 9.

Thank you !

Hi

The amount is in dollars, whereas we are talking about tenth of cents.
If the amount is $7.1234, then in cents is 712.34 cents and the tenth of cents here is 3 now.