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shasadou
Joined: 12 Aug 2015
Last visit: 24 Nov 2022
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Concentration: General Management, Operations
Schools: Johnson '18 (WL) Duke '18 (M) Tuck '18 (D)
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE:Management Consulting (Consulting)
23 Jan 2016, 02:08
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?
(1) y=x−1
(2) x is a prime number
(1) y=x−1
(2) x is a prime number
23 Jan 2016, 02:23
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shasadou
For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?
(1) y=x−1
(2) x is a prime number
(1) y=x−1
(2) x is a prime number
Hi,
A Good Q..
the Q statement is "For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?"
What doe sthis mean..
It means the largest power of x that is there in y!..
formula is \(\frac{y}{x} + \frac{y}{x^2}..\) and so on till the fraction \(\frac{y}{x^z}\) becomes less than 1..
x is a prime number or the biggest prime in any integer..
lets see the sentences..
(1) y=x−1
this means \(x^m\) in (x-1)!..
\(\frac{y}{x} + \frac{y}{x^2}..\). and so on means \(\frac{(x-1)!}{x}\)..
if x is prime, answer is 0..
if not it will depend on x..
say x=6, so y=5..
check for 3s in 5! as 3 is the largest prime number in 6..
\(\frac{5}{3}\)=1 so m=1..
different answers
But we do not know if x is prime or what is the largest prime in the integer x..
insuff
(2) x is a prime number
since there is no corelation in y and x, we cannot answer ..
say y is 50 and prime is 5, then it is \(\frac{50}{5}+\frac{50}{25}=12.\).
and say 4 and prime is 3then 4/3=1..
insuff..
combined .
we know that x is prime and y is x-1..
from this it becomes clear that y! or (x-1)! will not have x..
so power of x will be 0, or m=0..
suff
C
28 Sep 2016, 00:33
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shasadou
For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?
(1) y=x−1
(2) x is a prime number
(1) y=x−1
(2) x is a prime number
We need the greatest value of m for which x^m is a factor of y!
We have no relative values of x, y and m given in the question stem.
(1) y=x−1
Think what this means. Say x = 8. Then y = 7
We need greatest m such that 8^m is a factor of 7!
7! has a 2, a 4 and a 6 so it has four 2s. So it can make one 8. So m = 1.
But what if x = 7? Then y = 6
We need greatest m such that 7^m is a factor of 6!. Can we make 7 out of first 6 numbers? No, because 7 is prime. So it means that you can never make 7 out of any other 2 factors. So m = 0
Not sufficient.
(2) x is a prime number
x could be 7 but y could be either 6 or 10 (or infinite other values). 6! will not have any 7s but 10! will.
Not sufficient.
Using both:
This is our second case above. If x = prime, y is prime - 1. All numbers till prime - 1 will not be able to make a single prime.
i.e. our second case above. If x = 7, then y = 6 and all positive integers till 6 will not be able to make a 7. So m will always be 0.
Answer (C)
