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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] New post 10 Mar 2012, 23:04
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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] New post 10 Mar 2012, 23:17
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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] New post 10 Mar 2012, 23:39
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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

Answer: D.

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

Hope it helps.
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Re: A store owner decided to raise the price of a particular [#permalink] New post 10 Mar 2012, 23:50
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] New post 10 Mar 2012, 23:53
Expert's post
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] New post 25 Nov 2013, 10:33
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!
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Re: A store owner decided to raise the price of a particular [#permalink] New post 18 Dec 2013, 03:55
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] New post 18 Dec 2013, 04:11
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] New post 12 Jan 2015, 13:12
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Re: A store owner decided to raise the price of a particular [#permalink] New post 12 Jan 2015, 13:39
Expert's post
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

You'll notice that answer is Answer A.

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

That leaves just one answer....

Final Answer:
[Reveal] Spoiler:
D


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Re: A store owner decided to raise the price of a particular   [#permalink] 12 Jan 2015, 13:39
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