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Choose the correct statement.

Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give K cookies to each one of her 24 students, with none left over. Mr. Betancourt was also able to give S cookies to each one of his 18 students, with none left over. If N > 0, what is the value of N?

(1) N < 100

(2) N > 50

Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. Each statement ALONE is sufficient to answer the question. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

Title

Common Multiple Cookies

Your Result

Correct

Difficulty

Hard

Your Pace

0:09

Others' Pace

2:16

Video Explanation

Text Explanation

*Note: The text of the question in the video explanation is from an older version of the question. However, the explanation is still accurate.

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. Betancourt'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 of 18 and 24 are the 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)

Related Lessons

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