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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. Kudos for a correct solution. _________________ Manager  Joined: 18 Dec 2014 Posts: 99 Re: The exact cost price to make each unit of a widget is$7.6xy7, where x  [#permalink]

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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? Math Expert V Joined: 02 Sep 2009 Posts: 61524 Re: The exact cost price to make each unit of a widget is$7.6xy7, where x  [#permalink]

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Bunuel wrote:
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. Kudos for a correct solution. 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.

_________________
Intern  Joined: 06 Apr 2015
Posts: 29
Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink] ### Show Tags Bunuel wrote: Bunuel wrote: 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.

Kudos for a correct solution.

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) For statement 2 can't we get the same result if x and y were 4 and 8? i.e. 7.6487? Retired Moderator Joined: 06 Jul 2014 Posts: 1209 Location: Ukraine Concentration: Entrepreneurship, Technology GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 The exact cost price to make each unit of a widget is$7.6xy7, where x  [#permalink]

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kelvind13 wrote:
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
_________________
Intern  Joined: 30 Oct 2010
Posts: 47

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iikarthik wrote:
Harley1980 wrote:
kelvind13 wrote:
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

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.

Hope this helps.
Manager  G
Joined: 14 Oct 2012
Posts: 157

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Bunuel wrote:
Bunuel wrote:
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. Kudos for a correct solution. 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.

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 ?
Math Expert V
Joined: 02 Sep 2009
Posts: 61524
Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink] ### Show Tags AKY13 wrote: Bunuel wrote: Bunuel wrote: 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.

Kudos for a correct solution.

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) 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. _________________ Manager  B Joined: 11 Aug 2019 Posts: 83 Re: The exact cost price to make each unit of a widget is$7.6xy7, where x  [#permalink]

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Bunuel wrote:
Bunuel wrote:
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. Kudos for a correct solution. 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.

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!
Math Expert V
Joined: 02 Sep 2009
Posts: 61524
Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink] ### Show Tags shabuzen102 wrote: Bunuel wrote: Bunuel wrote: 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.

Kudos for a correct solution.

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) 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. _________________ Manager  B Joined: 21 Feb 2017 Posts: 151 Re: The exact cost price to make each unit of a widget is$7.6xy7, where x  [#permalink]

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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
Intern  S
Joined: 13 Jun 2019
Posts: 40
Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink] ### Show Tags Bunuel wrote: 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.

Kudos for a correct solution.

Rounding to the nearest tenth of a cent means we need to round up to 3 decimal places.
Thanks
_________________
Make YOUR Life a Masterpiece!! Remember that Winter ALWAYS turns to Spring... Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink] 04 Feb 2020, 02:19 Display posts from previous: Sort by # The exact cost price to make each unit of a widget is$7.6xy7, where x  