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Data Sufficiency Butler: July 2024
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Problem Solving Butler: July 2024
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Greetings everyone, please I need help with this question 🙏
Any attempt would be appreciated.

should be within within half standard deviation with respect to mean

The solution I thought is: 840 = 2*2*2*3*5*7
We are given 840 is not the LCM but a common multiple of A,B,C.
Therefore 840 is a multiple of the LCM.
As we need the maximum values for A,B,C we assume LCM to be 420.
If there was no condition of A,B,C being greater than 1, then we could simply assume
A=420, B=210, C=1 (satisfies the condition of HCF=1) giving us the sum of 631.
Here, I just put A the biggest, B second biggest and C as 1.
However as A,B,C are greater than 1, we need a prime number to be one of A,B,C.
okay so to maximize A,B,C, we can safely choose A = 420.
for B and C, one of them has to be prime and both of them have to such that they still satisfy our main constraint (LCM of A,B,C = 420), which means B,C have to be factors of 420.
so, to get factors of 420 that make the largest sum, we choose the smallest prime number (3) and 420/3 as our two numbers.
so finally we get A=420, B=140, C=3.
so, A+B+C=563

I know this isnt the best way to explain but i tried. thanks

we can’t take 420,210,2 as HCF wont be 1 anymore.

Data Sufficiency Butler: July 2024
July 3	DS 1	DS 2

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Problem Solving Butler: July 2024
July 3	PS 1	PS 2

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Someone help please 🙏

Try using this­ -
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Can you post the question again

what is the highest power of 3 available in the expression 58!-38!
1.17
2.18
3.19
4.none

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https://gmatclub.com/forum/what-is-the- ... l#p3417996

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­What is the highest power of 3 available in the expression 58! - 38!?

A. 16
B. 17
C. 18
D. 19
E. 20

­58! - 38! =

= 38!(58 * 57 * 56 * ... * 39 - 1)

58 * 57 * 56 * ... * 39 is a multiple of 3, thus 58 * 57 * 56 * ... * 39 - 1 is 1 less than a multiple of 3, so not a multiple of 3 and thus will not contribute any 3's to the entire product.

The highest integer power of 3 in 38! is 38/3 + 38/9 + 38/27 = 12 + 4 + 1 = 17 (remember we take only the quotients of the divisions, that is 38/3 would give 12, not 12 2/3).

Answer: A

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For theory on the topic discussed in the question check: Number Properties

For similar questions check the following topics from our Special Questions Directory:

12. Trailing Zeros
13. Power of a number in a factorial

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This method is true ??