|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
21 May 2018, 21:47
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
47% (02:38) correct
53%
(02:32)
wrong
based on 93
sessions
History
Date
Time
Result
Not Attempted Yet
Sarah and Angela are playing a game where Angela gives a random positive integer 'N' to Sarah, such that N>1, and the job of Sarah is to find whether the product of all consecutive integers from 1 to N-1 is divisible by N or not. If the product of consecutive integers from 1 to N-1 turns out to be divisible by N, then such an integer N would be called a 'winning number' for Sarah. If Angela gave 10 distinct positive integers to Sarah, how many of those 10 turned out to 'winning numbers' for Sarah?
(1) Out of the 10 integers given by Angela, exactly 5 have less than 3 positive factors.
(2) Out of the 10 integers given by Angela, only 1 integer is even.
(1) Out of the 10 integers given by Angela, exactly 5 have less than 3 positive factors.
(2) Out of the 10 integers given by Angela, only 1 integer is even.
22 May 2018, 03:14
Kudos
Bookmarks
amanvermagmat
Observation : Primes are the only numbers N for which 1*2*3*......*N-1 is not divided by N , as prime N does not have any other factor(s) ( of course other than 1 ) that is less than N.The a prime number N has only 2 factors; namely, 1 & N.
(1) Out of the 10 integers given by Angela, exactly 5 have less than 3 positive factors.
5 have less than 3 positive factors ==> 5 have 2 positive factors (note1) == > 5 numbers are prime ==> Those 5 can not be the winning numbers
Hence the other five could be ..... unless one of them is not 4.
For 4 : 1*2*3 / 4 = 1.5 ....... not divisible
Hence if 4 is included , Sarah have 4 winning number , otherwise 5.......................................Hence not sufficient.
(2) Out of the 10 integers given by Angela, only 1 integer is even.
Clearly not sufficient as this property depends on Prime&Non-Prime .......................................Hence not sufficient.
(1) +(2) ====>
exactly 5 have less than 3 positive factors, exactly 5 have eual or more than 3 positive factors & only 1 integer is even
Case 1: 5 prime ( incl 2), 5 non prime = winning # 5
Case 2: 5 prime ( excl 2), 5 non prime (incl 4)) = winning # 4 .......................................Hence not sufficient.
we can go on further but not required.
Hence I would go for option E.
30 Aug 2024, 23:21
Kudos
Bookmarks
The concept underlying this problem is introduction of primes in this series
Whenever a prime is introduced in this series it is a new number (since primes doesn't have any other factors)
So if we know no.of primes we can eliminate them as magical numbers
from statement 1) we can eliminate primes (5) & the rest we can analyze
Before concluding the answer to be 5, there is one more exception which is 4.
if 4 needs to be a magical number it must divide 3! = 6, but obviously 4 cannot divide 6.
Since we don't have information on 4, we cannot conclude if the answer is 5 or it is 4 => Insufficient
from statement 2) we get to know that only one integer in the series is even
Here,
a) we don't have info on primes to eliminate
b) we don't have info whether 4 is in the distinct numbers provided or not => Insufficient
Combining statement 1) and statement 2)
we eliminate 5 primes, we still have 5 numbers. But again we arrive at the road block if 4 is in the set of numbers or not
if 4 is in the set of numbers then answer is 4, else 5 => Insufficient
Whenever a prime is introduced in this series it is a new number (since primes doesn't have any other factors)
So if we know no.of primes we can eliminate them as magical numbers
from statement 1) we can eliminate primes (5) & the rest we can analyze
Before concluding the answer to be 5, there is one more exception which is 4.
if 4 needs to be a magical number it must divide 3! = 6, but obviously 4 cannot divide 6.
Since we don't have information on 4, we cannot conclude if the answer is 5 or it is 4 => Insufficient
from statement 2) we get to know that only one integer in the series is even
Here,
a) we don't have info on primes to eliminate
b) we don't have info whether 4 is in the distinct numbers provided or not => Insufficient
Combining statement 1) and statement 2)
we eliminate 5 primes, we still have 5 numbers. But again we arrive at the road block if 4 is in the set of numbers or not
if 4 is in the set of numbers then answer is 4, else 5 => Insufficient
