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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 SVP Joined: 16 Nov 2010 Posts: 1673 Location: United States (IN) Concentration: Strategy, Technology Followers: 34 Kudos [?]: 464 [3] , given: 36 Re: Price Percentage Increase, Find Original Price. [#permalink] ### Show Tags 11 Mar 2012, 00:17 3 This post received KUDOS 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. _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Math Expert Joined: 02 Sep 2009 Posts: 33997 Followers: 6076 Kudos [?]: 76270 [2] , given: 9969 Re: A store owner decided to raise the price of a particular [#permalink] ### Show Tags 11 Mar 2012, 00:39 2 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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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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
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]

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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 Current Student Joined: 21 Oct 2013 Posts: 194 Location: Germany GMAT 1: 660 Q45 V36 GPA: 3.51 Followers: 1 Kudos [?]: 29 [0], given: 19 Re: A store owner decided to raise the price of a particular [#permalink] ### Show Tags 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.

greetings
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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

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....

[Reveal] Spoiler:
D

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** GMAT Club Legend Joined: 09 Sep 2013 Posts: 10563 Followers: 495 Kudos [?]: 129 [0], given: 0 Re: A store owner decided to raise the price of a particular [#permalink] ### Show Tags 24 Feb 2016, 18:02 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Director Joined: 12 Aug 2015 Posts: 706 Followers: 10 Kudos [?]: 84 [0], given: 167 Re: A store owner decided to raise the price of a particular [#permalink] ### Show Tags 14 Apr 2016, 04:45 Hey EMPOWERgmatRichC You are assuming here that the price is an INteger.. What if its NOT... My Guess is => THIS IS A WRONG QUESTION AS ALL OPTIONS ARE POSSIBLE.. _________________ Give me a hell yeah ...!!!!! Math Forum Moderator Status: Moving Towards Perfection Now Joined: 11 Jun 2011 Posts: 1157 Location: India Concentration: International Business, Finance Schools: ISB '18 WE: Corporate Finance (Commercial Banking) Followers: 31 Kudos [?]: 271 [0], given: 197 Re: A store owner decided to raise the price of a particular [#permalink] ### Show Tags 14 Apr 2016, 10:52 stonecold wrote: Hey EMPOWERgmatRichC You are assuming here that the price is an INteger.. What if its NOT... My Guess is => THIS IS A WRONG QUESTION AS ALL OPTIONS ARE POSSIBLE.. Let price be$ 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

Hence this is our answer.

E. $78.10 Further inspection is not required since we have already found out the answer at (D) stonecold No question of treating the number as integers / not take it as it is given in the question stem. _________________ Abhishek.... Director Joined: 12 Aug 2015 Posts: 706 Followers: 10 Kudos [?]: 84 [0], given: 167 Re: A store owner decided to raise the price of a particular [#permalink] ### Show Tags 14 Apr 2016, 10:56 Abhishek009 wrote: stonecold wrote: Hey EMPOWERgmatRichC You are assuming here that the price is an INteger.. What if its NOT... My Guess is => THIS IS A WRONG QUESTION AS ALL OPTIONS ARE POSSIBLE.. Let price be$ 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

Hence this is our answer.

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.. _________________ Give me a hell yeah ...!!!!! Math Forum Moderator Status: Moving Towards Perfection Now Joined: 11 Jun 2011 Posts: 1157 Location: India Concentration: International Business, Finance Schools: ISB '18 WE: Corporate Finance (Commercial Banking) Followers: 31 Kudos [?]: 271 [0], given: 197 Re: A store owner decided to raise the price of a particular [#permalink] ### Show Tags 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. _________________ Abhishek.... Director Joined: 12 Aug 2015 Posts: 706 Followers: 10 Kudos [?]: 84 [0], given: 167 A store owner decided to raise the price of a particular [#permalink] ### Show Tags 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 .. _________________ Give me a hell yeah ...!!!!! Math Forum Moderator Status: Moving Towards Perfection Now Joined: 11 Jun 2011 Posts: 1157 Location: India Concentration: International Business, Finance Schools: ISB '18 WE: Corporate Finance (Commercial Banking) Followers: 31 Kudos [?]: 271 [1] , given: 197 A store owner decided to raise the price of a particular [#permalink] ### Show Tags 14 Apr 2016, 11:16 1 This post received KUDOS 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 .. Ok taking your way - 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.... _________________ Abhishek.... Director Joined: 12 Aug 2015 Posts: 706 Followers: 10 Kudos [?]: 84 [0], given: 167 A store owner decided to raise the price of a particular [#permalink] ### Show Tags 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 _________________ Give me a hell yeah ...!!!!! Math Forum Moderator Joined: 13 Apr 2015 Posts: 932 Location: India Concentration: Strategy, General Management WE: Information Technology (Consulting) Followers: 28 Kudos [?]: 353 [1] , given: 499 A store owner decided to raise the price of a particular [#permalink] ### Show Tags 14 Apr 2016, 11:44 1 This post received KUDOS 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......................... EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 6878 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 299 Kudos [?]: 2038 [1] , given: 161 Re: A store owner decided to raise the price of a particular [#permalink] ### Show Tags 14 Apr 2016, 12:07 1 This post received KUDOS Expert's post 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. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: A store owner decided to raise the price of a particular   [#permalink] 14 Apr 2016, 12:07
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