Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Am

Question

Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give the same number of cookies to each one of her 24 students, with none left over. Mr. Betancourt also able to give the same number of cookies to each one of his 18 students, with none left over. What is the value of N?

(1) N < 100

(2) N > 50

Kudos for a correct solution.

(1) N < 100

(2) N > 50

Lucky2783 · Answer

24n = N in Ms. Ames 's Case.
18k= N in Mr. Betancourt's case

so N=72*X(where X +ive integer)

(1) N < 100
 N=72
 sufficient.

(2) N > 50
 N=72,144 ... 
 Not Sufficient.

LaxAvenger · Answer

A for me:

LCM of both equations will be 3^2 * 2^3 = 72.

(1) N < 100 : Correct

(2) N > 50: Incorrect as N can be more than 1 value

Harley1980 · Answer

LCM(a, b) = \frac{(a*b)}{GCD(a*b)}

GCD (24, 18) = 6

LCM (24, 18) = \frac{(24*18)}{6} = 72

So first possible number of N is 72 and next number will be equal 72 + 72 = 144

1) N < 100 so it's 72
Sufficient

2) N > 50 and we have at least two variants 72 and 144
Insufficient

Answer is A

rachitsinha · Answer

Since N is divisible by both 24 and 18, it will be the LCM of the two numbers

N = LCM(18,24) = 72

1) N <100

then only 1 possibility for N=72

Sufficient

2) N> 50

N can be 72,144,....

Not Sufficient

Hence answer should be A

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

This question is really about common multiples and the LCM. If Ms. Ames can give each of her 24 students k cookies, so that they all get the same and none are left over, then 24k = N. Similarly, in Mr. Betencourt’s class, 18s = N.

What are the common multiples of 18 and 24?

18 = 2*9 = 2*3*3 = 6*3

24 = 3*8 = 2*2*2*3 = 6*4

From the prime factorizations, we see that GCF = 6, so the LCM is

LCM = 6*3*4 = 72

and all other common multiples are multiples of 72: {72, 144, 216, 288, 360, …}

Statement #1: if N < 100, the only possibility is N = 72. This statement, alone and by itself, is sufficient.

Statement #2: if N > 50, then N could be 72, or 144, or 216, or etc. Many possibilities. This statement, alone and by itself, is not sufficient.

Answer = (A)

ScottTargetTestPrep · Answer

We are given that when a teacher gives N cookies to her class of 24 students such that each student receives the same number of cookies, and when another teacher gives his 18 students N cookies such that each student receives the same number of cookies, neither teacher has any cookies left. Thus:

N/24 = integer and N/18 = integer

Thus, N must be a multiple of 18 and 24. In that case, N must be also a multiple of the LCM of 18 and 24, which is 72.

In other words, the number of cookies is a multiple of 72.

Statement One Alone:

N < 100

Since the only multiple of 72 less than 100 is 72, N must be 72. Statement one alone is sufficient to answer the question.

Statement Two Alone:

Since there are an infinite number of multiples of 72 greater than 50, we cannot determine a value for N. Statement two alone is not sufficient to answer the question.

Answer: A

Nightmare007 · Answer

Just a hunch. What if they both had 0 cookies. And they gave each of all students 0 cookies?  Bunuel .

abhimahna · Answer

Hey  Nightmare007  ,

You need to understand that in such type of questions, whenever we are saying N things are distributed, N should always be taken as a positive integer.

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Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Am

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