by Rich Cohen Rich.C@empowergmat.com www.EMPOWERgmat.com
This series of emails and PMs focuses on situations that many Test Takers face during their studies. The names of the original posters have been changed to protect their identities.
“Re-writing” DS Questions
Hi Rich,
I was working through a practice DS question, but had trouble understanding part of the explanation. The question says:
"If k is an integer greater than 1, and S is the sum of all positive divisors of k, is S>k+1?"
The rephrase in the explanation was "Is k not prime?" Can you help explain what this means?
Jacques
Hi Jacques,
This DS question (like many DS questions) is based on a Number Property.
The term "prime number" refers to a positive integer that is divisible by just 2 things: itself and the number 1.
Here are some primes: 2, 3, 5, 7, 11….
Since most numbers are NOT prime, they have additional factors.
For example, the factors of 8 are 1, 2, 4 and 8
This means that when you sum up all the factors (divisors) of a number, you'd get a total that is GREATER than that number + 1. With prime numbers however, you would get a sum that was EQUAL to that number + 1.
In this question, if K = 8, then S = 1+2+4+8 = 15 and the answer to the question would be YES
In this question, if K = 2, then S = 1+2 = 3 and the answer to the question would be NO.
In effect, it's asking whether K is a prime number or not.
Comparison Rules in SC Questions
Dear Rich,
Why is Answer A not correct here?
Like Austen, the characters of Forster are concerned largely with achieving economic security in a world riddled with class distinctions.
a) Like Austen, the characters of Forster
b) Like Austen, Forster's characters
c) Like Austen's, Forster's characters
d) As with Austen, Forster's characters
e) As are Austen's Forster's characters
Kellen
Hi Kellen,
This SC is based on Comparison rules, meaning that we have to compare LIKE things.
Here, we can compare Austen to Forster or we can compare Austen's characters to Forster's characters.
Answer A compares Austen to the characters of Forster, which is an invalid comparison.
With that insight, which answer would you choose?
Be THOROUGH When Dealing With DS Questions
Rich,
I’ve attempted this DS question, but I get answer A and the correct answer is answer C. What am I missing here (sorry the question did not have an explanation with it)?
1. How many integers x exist such that a < x < b?
(1) b - a = 7
(2) a and b are integers
Lucille
Hi Lucille,
This DS question is built around a test of your thoroughness. Notice how you are NOT told anything about A and B….?
We're asked how many integers are between A and B. This is a perfect question for TESTing Values
Fact 1: B - A = 7
If B = 8 and A = 1, then the integers between them are 2, 3, 4, 5, 6, and 7 (a total of 6 integers)
If B = 8.5 and A = 1.5, then the integers between them are 2, 3, 4, 5, 6, 7 and 8 (a total of 7 integers)
Fact 1 is INSUFFICIENT.
Fact 2: A and B are integers.
Since we don't know what A and B are, there's really no way to answer this question…..but if you're looking for proof….
If B = 8 and A = 1, then the answer to the question is 6 integers
If B = 2 and A = 1, then the answer to the question is 0 integers.
Fact 2 is INSUFFICIENT
Combined, we know that B - A = 7 AND A and B are integers. This means that there must be exactly 6 integers between them. You can TEST any set of values that fit these rules and you'll get the same answer every time.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
