Jaime earned enough money by selling seashells at 25 cents each to buy

Question

Jaime earned enough money by selling seashells at 25 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?

(A) 5
(B) 11
(C) 17
(D) 25
(E) 30

(A) 5 
(B) 11 
(C) 17 
(D) 25 
(E) 30

GMATinsight · Accepted Answer

His payment is in Multiples of 25 cents

Payment Required is in Multiples of 55 cents

No left over means, Payment Done = Payment Required

i.e. 25x = 55y
i.e. 5x = 11y

i.e.  Minimum  value of x = 11 (co-efficient of y)
and  Minimum  value of y = 5 (co-efficient of x)

i.e. Minimum Value of x = 11

Answer: option B

Skywalker18 · Answer

Let the number of seashells sold by Jamie = x
and the number of paperback books sold = y
Selling price of seashells = 25 cents
Buying price of seashells = 55 cents

Now since all the money earned selling seashells is used to buy the books
25x = 55 y

Prime fatorization of 
25 = 5*5
55 = 11* 5

We need to find the LCM of the 2 numbers
LCM = 5^2 * 11
 = 25 * 11 
 = 275

Least number of seashells sold , x = 275/ 25 = 11

Answer B

CounterSniper · Answer

25*11=275 , which is exactly divisible by 55 
Thus 11 is the minimum

EMPOWERgmatRichC · Answer

Hi All,

Since we're asked for the LEAST number of seashells that could have been sold, and the answer choices are numbers, we can TEST THE ANSWERS.

We're given a number of facts to work with:
1) Jamie sells seashells at 25 cents each.
2) Jamie buys books at 55 cents each.
3) Jamie spent ALL the money he earned selling seashells on books.

We're asked for the LEAST number of seashells that Jamie could have sold...

Let's TEST Answer A: 5 seashells...

With 5 seashells, Jamie would have 5(25) = 125 cents. This would allow him to buy 2 books for 110 cents total, but he would then have 15 cents left over. We're told that he spent ALL of his money on books, so this cannot be the correct answer.

Answer B: 11 seashells....

With 11 seashells, Jamie would have 11(25) = 275 cents. This would allow him to buy 5 books for 275 cents total, with no money left over. This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:  B

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

vijayjha · Answer

LCM of 25 and 55, that is 275,
There fore least number will be 275/25 =11

Sent from my ONEPLUS A3003 using  GMAT Club Forum mobile app

ScottTargetTestPrep · Answer

Solution:
 
Since Jaime spent all the money he earned selling seashells to buy the books (assuming he had no money left over), the least number of seashells he could have sold must occur when the money he earned, in cents, is the least common multiple (LCM) of 25 and 55. Since the LCM of 25 and 55 is 5 x 5 x 11 = 275, the least number of seashells he could have sold is 275/25 = 11.

Answer: B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Jaime earned enough money by selling seashells at 25 cents each to buy

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Jaime earned enough money by selling seashells at 25 cents each to buy

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards