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The exact cost price to make each unit of a widget is $7.6xy7, where x

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The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink]

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New post 10 Apr 2015, 04:40
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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.

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Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink]

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New post 10 Apr 2015, 06:40
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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).

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Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink]

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New post 13 Apr 2015, 04:22
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)
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink]

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New post 19 Apr 2015, 09:39
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?
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The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink]

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New post 19 Apr 2015, 10:06
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
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Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink]

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New post 17 Nov 2015, 15:53
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
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Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink]

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New post 17 Nov 2015, 16:18
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.

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

Hope this helps.
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Re: The exact cost price to make each unit of a widget is $7.6xy7, where x [#permalink]

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New post 20 Apr 2017, 22:50
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.
Re: The exact cost price to make each unit of a widget is $7.6xy7, where x   [#permalink] 20 Apr 2017, 22:50
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