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Bunuel
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If x is a product of all integers from 2 to 24, inclusive, what is the 30 Nov 2021, 03:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

Question Stats:

75% (01:17) correct 25% (01:37) wrong based on 155 sessions

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If x is a product of all integers from 2 to 24, inclusive, what is the greatest integer y for which 35^y is a factor of x?

(A) 2
(B) 3
(C) 5
(D) 7
(E) 9
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B
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If x is a product of all integers from 2 to 24, inclusive, what is the 10 Dec 2021, 14:12
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Asked: If x is a product of all integers from 2 to 24, inclusive, what is the greatest integer y for which 35^y is a factor of x?

35 = 5*7
x = 24!

Greatest power of 7 in 24! = 3
Greatest power of 5 in 24! = 4
Greatest power of 35 in x = min (3,4) = 3

IMO B

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If x is a product of all integers from 2 to 24, inclusive, what is the 15 Aug 2026, 08:23
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x = 2 x 3 x 4 x ..... 24

35^y = (7 x 5)^y

how many factors of 7 and 5 are there to max of 24
7, 14, 21 7 has 3
5,10,15,20. 5 has 4

therefor max for 35 is 3
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If x is a product of all integers from 2 to 24, inclusive, what is the 14 Sep 2026, 11:22
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Product of all integers from 2-24 is basically 24!

In order to find the max y for which 35^y is a factor of 24! we need to find max y for 5^y and 7^y

Therefore 24/5 = max 3 for power of 5
and 24/7 = max 3 for the power of 7

There fore max power of y for 35^y is 3
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If x is a product of all integers from 2 to 24, inclusive, what is the 16 Sep 2026, 01:16
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Hey, on my end each reply above is showing text of the post will remain hidden until OA is released. How can I see the replies? My soln was -

24/5 = 4
4/5 = 0 so highest exponent would be 4, where am I going wrong? Bunuel
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If x is a product of all integers from 2 to 24, inclusive, what is the 16 Sep 2026, 04:08
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If x is a product of all integers from 2 to 24, inclusive, what is the greatest integer y for which 35^y is a factor of x?

(A) 2
(B) 3
(C) 5
(D) 7
(E) 9

35^y = 5^y * 7^y, so we need to count how many factors of 5 and 7 are contained in 2 * 3 * ... * 24.

Factors of 5:
5, 10, 15, 20

So there are 4 factors of 5.

Factors of 7:
7, 14, 21

So there are 3 factors of 7.

We can therefore form only 3 complete pairs of 5 * 7 = 35.

Thus, y = 3.

Answer: B.

architkap
Hey, on my end each reply above is showing text of the post will remain hidden until OA is released. How can I see the replies? My soln was -

24/5 = 4
4/5 = 0 so highest exponent would be 4, where am I going wrong? Bunuel
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The issue is that 35 = 5 * 7, so we need both factors.

There are 4 factors of 5, but only 3 factors of 7:

24/7 = 3

So we can form only 3 complete factors of 35. Therefore, y = 3.

Hope it's clear.

P.S. The replies are no longer hidden. Fixed that.
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