A store owner decided to raise the price of a particular

Question

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

Bunuel · Accepted Answer

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.

subhashghosh · Answer

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.

Stoneface · Answer

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

Bunuel · Answer

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.

jlgdr · Answer

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

unceldolan · Answer

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

jlgdr · Answer

No, it doesn't and thats why the question is somewhat flawed Cheers J

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EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made,
Rich

stonecold · Answer

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..

Abhishek009 · Answer

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. :-D

stonecold · Answer

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 Completely DISAGREE For non integers every answer works..

Abhishek009 · Answer

Is it so ? I never bothered to check that please provide us with your explanation.. Lets check again. :-D

stonecold · Answer

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 ..

Abhishek009 · Answer

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....

stonecold · Answer

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

Kurtosis · Answer

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.........................

EMPOWERgmatRichC · Answer

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

piyush945 · Answer

In this question, we need to determine the new price. The price must be 1.1 times of the old price. 
However, there is one assumption in this question : The old price is a whole number. 
With this assumption in mind, you will realise that the OA is D

bumpbot · Answer

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A store owner decided to raise the price of a particular

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