12 Days of Christmas GMAT Competition - Day 3: If k is a positive

Question

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If k is a positive integer less than or equal to 200, what is the greatest prime factor of k?

(1) k is a multiple of 40.
(2) 50 is a factor of k.

Bunuel · Accepted Answer

GMAT Club Official Explanation:

If k is a positive integer less than or equal to 200, what is the greatest prime factor of k?

(1) k is a multiple of 40.

The multiples of 40 less than or equal to 200 are 40, 2*40, 3*40, 4*40, and 5*40. Since 40 = 2^3*5, the greatest prime factor of k, whatever it might be, is 5. Sufficient.

(2) 50 is a factor of k.

The multiples of 50 less than or equal to 200 are 50, 2*50, 3*50, and 5*50. Since 50 = 25^2, the greatest prime factor of k, whatever it might be, is 5. Sufficient.

Answer: D.

Schinchan_bh · Answer

k<=200 given
(1)k=40x
40 80 120 160 200 all of this number greatest prime factor is 5.
(2)k=50x
50 100 150 200 all of this here also 5 so (d) is correct.

umangshah · Answer

Statement 1: k multiple of 40. Thus, prime factorization of 40 would be 2*2*2*5 and if Maximum value of k is 200 then it is 40*5 . From this we can say that greatest Prime factor of K would be 5. Sufficient.

Statement 2: Since 50 is a factor of K. Thus values of K can be 50,100,150 and 200. Again same as Statement 1, we can conclude that greatest prime will be 5. Sufficient.

Option D is correct.

missionmba2025 · Answer

(1) k is a multiple of 40.

k can be 40, 80, 120, or 160

All the numbers have 5 has the greatest prime factor. Hence, the statement is sufficient.

(2) 50 is a factor of k

k can be 50*1, 50*2, or 50*3

All the numbers have 5 has the greatest prime factor. Hence, the statement is sufficient.

IMO D

sanjitscorps18 · Answer

Given k <=200 (1) k is a multiple of 40. => k = 40 * n => k = 2^3 * 5 * n Now if k <= 200 then n <= 5 => k can be 40, 80, 120, 160 or 200 => n can be 1, 2, 3, 2^2, 5 Hence the highest prime factor remains 5 for all combinations Sufficient (2) 50 is a factor of k. => k = 50 * n => k = 5^2 * 2 * n Now if k <= 200 then n <= 4 => k can be 50, 100, 150 and 200 => n can be 1, 2, 3, 2^2 hence the highest prime factor remains 5 Sufficient Option D

12 Days of Christmas GMAT Competition - Day 3: If k is a positive

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12 Days of Christmas GMAT Competition - Day 3: If k is a positive

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