Let P = 36000. Let Q equal the sum of all the factors of 36000, not including 36000 itself. Let R be the sum of all the prime numbers less than 36000. Rank the numbers P, Q, and R in numerical order from smallest to biggest.
(A) P, Q, R
(B) P, R, Q
(C) Q, P, R
(D) R, P, Q
(E) R, Q, P
The OA is A.
The calculus are so long. Experts, how can I solve this one in a shorter way?
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Let P = 36000. Let Q equal the sum of all the factors of
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Hi VJesus12,
This question asks us to consider 3 values:
P = 36000
Q = the sum of all the factors of 36000, not including 36000
R = the sum of all the prime numbers less than 36000.
We're asked to order the numbers P, Q, and R from least to greatest.
To start, the GMAT would never expect you to add up the values that this question asks us to think about, so you have to think more in terms of number patterns and how the three values relate to one another.
Let's compare Q and P. With Q, there are plenty of 'big' factors that we could list: 18,000.... 12,000..... 9,000, etc. so that sum would clearly be larger than P. Eliminate Answer C and E.
Now, let's compare R and P. There's no practical way to list out all of the primes that are less than 36,000... but think about all of the primes that exist between 1 and 100.... There are clearly a lot of prime numbers in that small range, so if we're dealing with the primes from 1 to 36,000, then there will likely be LOTS of prime numbers, including some really BIG ones. That sum would have to be a really big number. Thus, R is also greater than P. Eliminate Answer D.
Between Q and R, it helps to think about what the largest value in each group would be... The largest value in Q is 18,000, but there are almost certainly a LOT of prime numbers that are between 18,000 and 36,000... and it's likely that the sum of just those primes alone would be greater than the value of Q. When you include the primes from 1 to 18,000, the value of R gets even bigger. Logically, R would have to be greater than Q.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This question asks us to consider 3 values:
P = 36000
Q = the sum of all the factors of 36000, not including 36000
R = the sum of all the prime numbers less than 36000.
We're asked to order the numbers P, Q, and R from least to greatest.
To start, the GMAT would never expect you to add up the values that this question asks us to think about, so you have to think more in terms of number patterns and how the three values relate to one another.
Let's compare Q and P. With Q, there are plenty of 'big' factors that we could list: 18,000.... 12,000..... 9,000, etc. so that sum would clearly be larger than P. Eliminate Answer C and E.
Now, let's compare R and P. There's no practical way to list out all of the primes that are less than 36,000... but think about all of the primes that exist between 1 and 100.... There are clearly a lot of prime numbers in that small range, so if we're dealing with the primes from 1 to 36,000, then there will likely be LOTS of prime numbers, including some really BIG ones. That sum would have to be a really big number. Thus, R is also greater than P. Eliminate Answer D.
Between Q and R, it helps to think about what the largest value in each group would be... The largest value in Q is 18,000, but there are almost certainly a LOT of prime numbers that are between 18,000 and 36,000... and it's likely that the sum of just those primes alone would be greater than the value of Q. When you include the primes from 1 to 18,000, the value of R gets even bigger. Logically, R would have to be greater than Q.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
