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# A store owner decided to raise the price of a particular

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A store owner decided to raise the price of a particular [#permalink]

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11 Mar 2012, 00:04
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I could figure this one out in about two seconds if I had a calculator, but I hear that's not allowed on the GMAT, so I need to know how to get this answer quick by hand. Thanks!

A store owner decided to raise the price of a particular item by exactly 10%. Of the following which is NOT the new price?

A. \$1.10
B. \$8.80
C. \$11.00
D. \$57.30
E. \$78.10
[Reveal] Spoiler: OA

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Re: Price Percentage Increase, Find Original Price. [#permalink]

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11 Mar 2012, 00:17
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The new price should be divisible by 11 , because new price = 1.1 * old price. Answer is D, because it's not divisible by 11.
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Re: A store owner decided to raise the price of a particular [#permalink]

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11 Mar 2012, 00:39
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Stoneface wrote:
I could figure this one out in about two seconds if I had a calculator, but I hear that's not allowed on the GMAT, so I need to know how to get this answer quick by hand. Thanks!

A store owner decided to raise the price of a particular item by exactly 10%. Of the following which is NOT the new price?

A. \$1.10
B. \$8.80
C. \$11.00
D. \$57.30
E. \$78.10

Old Price * 1.1 = New Price -> Old Price * 11 = New Price *10 --> the new price in cents must be a multiple of 11 (assuming that the new price in cents is an integer);

To check which price is a multiple of 11 and which is not you should use divisibility rule for 11: if you sum every second digit of a number and then subtract the sum of all other digits and the answer is divisible by 11, then the number is divisible by 11. Only answer choice D, 5730 cents, is not divisible by 11: (7+0)-(5+3)=-1, which is not divisible by 11

Check for more divisibility rules here: math-number-theory-88376.html

Hope it helps.
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A store owner decided to raise the price of a particular [#permalink]

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14 Apr 2016, 11:16
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stonecold wrote:
Abhishek009 wrote:
stonecold wrote:
Completely DISAGREE
For non integers every answer works..

Is it so ? I never bothered to check that please provide us with your explanation..

Lets check again.

see
Every answer is valid Except D (as you put it) ..
D will be valid if => x= 573/11
Hence D will be valid too

Remember No one told us that x needs be an integer ..

Let price be x { we do not know whether it is even / odd/ integer / whole number}

The store owner decided to raise the price of a particular item by exactly 10%, so the new price must be x *110 /100 =>1.1x

So, The new number must be 1.1 times the original price.

Now, check option (D)

1.1x = 57.30
So, x = 57.30/1.1 ~ 52.09 (Approximately)

But the Same is not with option (E)

1.1x = 78.10
x = 71

So IMHO (D) does not fall into the group....

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A store owner decided to raise the price of a particular [#permalink]

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14 Apr 2016, 11:44
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Hi stonecold,

Abhishek is right. Option D is correct.

When 573 is divided by 11 we get a remainder 1.
1/11 is non terminating and the question states that the increase is exactly 10%.

Since the value is non terminating, original price cannot be accurately determined. The original value can be 52.0909090909.........................

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Re: A store owner decided to raise the price of a particular [#permalink]

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14 Apr 2016, 12:07
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Hi stonecold,

This question is still 'restricted' to the reality of 'dollars and cents.' While Answer D could be divided by 1.1, you would end up with a repeating decimal in the original price of that item. Regardless of how hard you look, you will never find a store that charges you a price that includes a repeating decimal.

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Re: A store owner decided to raise the price of a particular [#permalink]

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11 Mar 2012, 00:50
But (8+0)-(7+1)=0, and zero isn't divisble by 11, either. Is zero exempt from the rule?

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Re: A store owner decided to raise the price of a particular [#permalink]

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11 Mar 2012, 00:53
Stoneface wrote:
But (8+0)-(7+1)=0, and zero isn't divisble by 11, either. Is zero exempt from the rule?

Zero is divisible by EVERY integer except zero itself, since 0/integer=integer.

Check for more number properties hints/tips/rules the link in my previous topic.
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Re: A store owner decided to raise the price of a particular [#permalink]

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25 Nov 2013, 11:33
Stoneface wrote:
I could figure this one out in about two seconds if I had a calculator, but I hear that's not allowed on the GMAT, so I need to know how to get this answer quick by hand. Thanks!

A store owner decided to raise the price of a particular item by exactly 10%. Of the following which is NOT the new price?

A. \$1.10
B. \$8.80
C. \$11.00
D. \$57.30
E. \$78.10

10% increase = 1.1x where x is the original amount.
1.1 = 11/10. So the answer must be a multiple of 11.
Only answer choice that is not a multiple of 11 is D.

Hence D

Hope it helps!
Cheers
J

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Re: A store owner decided to raise the price of a particular [#permalink]

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18 Dec 2013, 04:55
jlgdr wrote:
Stoneface wrote:
I could figure this one out in about two seconds if I had a calculator, but I hear that's not allowed on the GMAT, so I need to know how to get this answer quick by hand. Thanks!

A store owner decided to raise the price of a particular item by exactly 10%. Of the following which is NOT the new price?

A. \$1.10
B. \$8.80
C. \$11.00
D. \$57.30
E. \$78.10

10% increase = 1.1x where x is the original amount.
1.1 = 11/10. So the answer must be a multiple of 11.
Only answer choice that is not a multiple of 11 is D.

Hence D

Hope it helps!
Cheers
J

A 1 * 1.1 = 1.10 \$
B 8 * 1.1 = 8.80 \$
C 10* 1.1 = 11 \$
D - strange Number
E 71 * 1.1 = 78.1 \$

since D is the only answer, where I couldn't calculate the percents right away, I chose D.

BUT if the store owner had strange prices like 52.09 \$ the new price would be 57.30 \$. Is this a real GMAT question? Because it says nowhere that the original price has to be integer.

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Re: A store owner decided to raise the price of a particular [#permalink]

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18 Dec 2013, 05:11
No, it doesn't and thats why the question is somewhat flawed

Cheers
J

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Re: A store owner decided to raise the price of a particular [#permalink]

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12 Jan 2015, 14:12
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Re: A store owner decided to raise the price of a particular [#permalink]

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12 Jan 2015, 14:39
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Hi All,

This question has a great "pattern-matching" shortcut built into it, but you'll have to pay attention to the answer choices to see it.

We're told that a store owner raises the price of an item by 10%. We're asked which of the 5 answers could NOT possibly be the new price.

In this scenario, it's real easy to come up with a simple example of what the store owner did.

IF....
price = \$1, then new price = \$1.10

Answer B is just 8 times \$1.10, which makes sense because 10% of 8 is 0.80...

IF...
price = \$8, then new price = \$8.80

So the shortcut is just to find the answers that are multiples of \$1.10

Answer C is another quick "find" - it's 10 times \$1.10

Between D and E, you have to do a little work, but if you "break down" E, you get....

78.10 = 77.00 + 1.10

77.00 = 70 + 7 (which is 10% of 70)
1.10 = 1 + 0.1 (which is 10% of 1)
So E is another multiple of \$1.10

[Reveal] Spoiler:
D

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Re: A store owner decided to raise the price of a particular [#permalink]

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Re: A store owner decided to raise the price of a particular [#permalink]

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14 Apr 2016, 04:45
Hey EMPOWERgmatRichC You are assuming here that the price is an INteger..
What if its NOT...
My Guess is => THIS IS A WRONG QUESTION AS ALL OPTIONS ARE POSSIBLE..
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Re: A store owner decided to raise the price of a particular [#permalink]

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14 Apr 2016, 10:52
stonecold wrote:
Hey EMPOWERgmatRichC You are assuming here that the price is an INteger..
What if its NOT...
My Guess is => THIS IS A WRONG QUESTION AS ALL OPTIONS ARE POSSIBLE..

Let price be \$ 10
The store owner decided to raise the price of a particular item by exactly 10%, so the new price must be 110 *10 /100 =>11

So, The new price must be a multiple of 11

From the given options check for all the multiples of 11

Test of divisibility of 11 is

 " if the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11."

A. \$1.10
B. \$8.80
C. \$11.00

By a quick glance even a 2nd grader can eliminate options A,B and C , because they are all divisible by 11 , let with only 2 options check for the divisibility rule for options D and E

D. \$57.30

Sum of even digits is 5+3 = 8
Sum of odd digits is 7 +0 = 7

Difference of the even and odd digits is 8 - 7 = 1 ; not divisible by 11

E. \$78.10

Further inspection is not required since we have already found out the answer at (D)

stonecold No question of treating the number as integers / not take it as it is given in the question stem.
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Re: A store owner decided to raise the price of a particular [#permalink]

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14 Apr 2016, 10:56
Abhishek009 wrote:
stonecold wrote:
Hey EMPOWERgmatRichC You are assuming here that the price is an INteger..
What if its NOT...
My Guess is => THIS IS A WRONG QUESTION AS ALL OPTIONS ARE POSSIBLE..

Let price be \$ 10
The store owner decided to raise the price of a particular item by exactly 10%, so the new price must be 110 *10 /100 =>11

So, The new price must be a multiple of 11

From the given options check for all the multiples of 11

Test of divisibility of 11 is

 " if the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11."

A. \$1.10
B. \$8.80
C. \$11.00

By a quick glance even a 2nd grader can eliminate options A,B and C , because they are all divisible by 11 , let with only 2 options check for the divisibility rule for options D and E

D. \$57.30

Sum of even digits is 5+3 = 8
Sum of odd digits is 7 +0 = 7

Difference of the even and odd digits is 8 - 7 = 1 ; not divisible by 11

E. \$78.10

Further inspection is not required since we have already found out the answer at (D)

stonecold No question of treating the number as integers / not take it as it is given in the question stem.

Completely DISAGREE
For non integers every answer works..

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Re: A store owner decided to raise the price of a particular [#permalink]

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14 Apr 2016, 11:02
stonecold wrote:
Completely DISAGREE
For non integers every answer works..

Is it so ? I never bothered to check that please provide us with your explanation..

Lets check again.
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A store owner decided to raise the price of a particular [#permalink]

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14 Apr 2016, 11:07
Abhishek009 wrote:
stonecold wrote:
Completely DISAGREE
For non integers every answer works..

Is it so ? I never bothered to check that please provide us with your explanation..

Lets check again.

see
Every answer is valid Except D (as you put it) ..
D will be valid if => x= 573/11
Hence D will be valid too

Remember No one told us that x needs be an integer ..
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A store owner decided to raise the price of a particular [#permalink]

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14 Apr 2016, 11:20
Yes..Abhishek009
But the Question is Which of the following Cannot be the value of x
hence we cannot say which one.
x needs to be an integer here
P.S - We can play along all day .. Every value is valid unless stated otherwise
CC :- Vyshak
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A store owner decided to raise the price of a particular   [#permalink] 14 Apr 2016, 11:20

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