[Math Revolution GMAT math practice question]
If x and y are prime numbers, how many factors has x^2y^2?
1) xy=10
2) x+y is odd
If x and y are prime numbers, how many factors has x^2y^2?
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
<p>
More than that, each statement alone is sufficient to guarantee that x and y are different. (Why?)
Conclusion: 2 <= x < y , both primes (in each statement alone).
This is enough to guarantee the answer is unique (and the same) in each statement alone (*), hence the answer is D.
(*) It is (2+1)*(2+1) if only positive factors are considered, twice this value in reality (therefore 18).
(Some people consider "factor" as a "positive divisor". This is wrong in math in general, and also in GMAT in particular, as a careful look at the Official Guide shows.)
Kudos to the proposer of this problem: He/She did not violate an important "Data Sufficiency rule": you cannot find a unique answer with the question stem pre-statements (only).
In fact, before the given statements, the primes x and y COULD be equal and, in this case, the answer would be 10 (= 2*(4+1)). In other words, pre-statements, we have 10 and 18 as "potential answers".
We may assume without loss of generality that x is not greater than y (due to the symmetries in the question stem and in our focus).</p>
If x and y are prime numbers, how many factors has x^2y^2?
1) xy=10
2) x+y is odd
More than that, each statement alone is sufficient to guarantee that x and y are different. (Why?)
Conclusion: 2 <= x < y , both primes (in each statement alone).
This is enough to guarantee the answer is unique (and the same) in each statement alone (*), hence the answer is D.
(*) It is (2+1)*(2+1) if only positive factors are considered, twice this value in reality (therefore 18).
(Some people consider "factor" as a "positive divisor". This is wrong in math in general, and also in GMAT in particular, as a careful look at the Official Guide shows.)
Kudos to the proposer of this problem: He/She did not violate an important "Data Sufficiency rule": you cannot find a unique answer with the question stem pre-statements (only).
In fact, before the given statements, the primes x and y COULD be equal and, in this case, the answer would be 10 (= 2*(4+1)). In other words, pre-statements, we have 10 and 18 as "potential answers".
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
To count the positive factors of a positive integer:
1. Prime-factorize the integer
2. Write the prime-factorization in the form (a^p)(b^q)(c^r)...
3. The number of factors = (p+1)(q+1)(r+1)...
Generally, GMAT problems about factors are constrained to POSITIVE factors.
On the GMAT, the posted problem would probably appear as follows:
Case 1: x≠y
Here, to determine the number of factors for x²y², we add 1 to each exponent and multiply:
(2+1)(2+1) = 9 factors
Case 2: x=y, with the result that x²y² = x²x ²= x�
Here, to determine the number of factors for x�, we add 1 to the exponent:
4+1 = 5 factors
Implication:
To determine the number of factors, we need to know whether x=y.
Question stem, rephrased:
Does x=y?
Statement 1:
Only one pair of prime numbers has a product of 10:
2 and 5.
Thus, x≠y.
SUFFICIENT.
Statement 2:
Since x+y = odd, either x or y is ODD, while the other value is EVEN.
Thus, x≠y.
SUFFICIENT.
The correct answer is D.
1. Prime-factorize the integer
2. Write the prime-factorization in the form (a^p)(b^q)(c^r)...
3. The number of factors = (p+1)(q+1)(r+1)...
Generally, GMAT problems about factors are constrained to POSITIVE factors.
On the GMAT, the posted problem would probably appear as follows:
Only two cases are possible:Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If x and y are prime numbers, how many POSITIVE factors has x^2y^2?
1) xy=10
2) x+y is odd
Case 1: x≠y
Here, to determine the number of factors for x²y², we add 1 to each exponent and multiply:
(2+1)(2+1) = 9 factors
Case 2: x=y, with the result that x²y² = x²x ²= x�
Here, to determine the number of factors for x�, we add 1 to the exponent:
4+1 = 5 factors
Implication:
To determine the number of factors, we need to know whether x=y.
Question stem, rephrased:
Does x=y?
Statement 1:
Only one pair of prime numbers has a product of 10:
2 and 5.
Thus, x≠y.
SUFFICIENT.
Statement 2:
Since x+y = odd, either x or y is ODD, while the other value is EVEN.
Thus, x≠y.
SUFFICIENT.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
If x and y are different prime numbers, then xy has (2+1)(2+1) = 9 factors.
If x and y are the same prime number, then xy has 4+1 = 5 factors.
Condition 1)
Since x and y are prime numbers and xy = 10, either x = 2 and y = 5, or x = 5 and y = 2.
So, x and y are different prime numbers. Thus, condition 1) is sufficient.
Condition 2)
Since x and y are prime numbers and x + y is odd, one of them is even and the other one is odd.
So, x and y are different prime numbers. Thus, condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
If x and y are different prime numbers, then xy has (2+1)(2+1) = 9 factors.
If x and y are the same prime number, then xy has 4+1 = 5 factors.
Condition 1)
Since x and y are prime numbers and xy = 10, either x = 2 and y = 5, or x = 5 and y = 2.
So, x and y are different prime numbers. Thus, condition 1) is sufficient.
Condition 2)
Since x and y are prime numbers and x + y is odd, one of them is even and the other one is odd.
So, x and y are different prime numbers. Thus, condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]