Events & Promotions
|
|
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.
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
26 Sep 2018, 05:36
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
54% (02:11) correct
46%
(02:08)
wrong
based on 106
sessions
History
Date
Time
Result
Not Attempted Yet
If the product of the digits of the two-digit positive integer n is 12, what is the value of n?
(1) n can be expressed as the sum of two perfect squares in exactly one way.
(2) n is smaller than 40.
(1) n can be expressed as the sum of two perfect squares in exactly one way.
(2) n is smaller than 40.
26 Sep 2018, 06:46
Kudos
Bookmarks
lets start by listing the factors of 12
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
since it's a 2-digit integer the 1-12 combination is out. (twelve cannot be 'a digit')
next list the numbers that can be formed with the remaining factors
26
34
43
62
now lets look at 1)
sum of perfect squares in 1 way
26
--> 1 & 5 => 1 & 25 = 26
2 results in 4 and 22 which is not a perfect square
3 results in 9 and 17 which is prime
4 results in 16 and 10, which is not a perfect square
5 puts us back in the first situations
SO: 26 matches, however, we are looking for a single number so none of the others should be possible to be represented as a sum of perfect squares, or should be possible to be represented as different summs of perfect squares
-->looking at 34
1 gives 1 and 33 --> not a perf square
2 gives 4 and 30 --> not a perf square
3 gives 9 and 24 --> not a perf square
4 gives 16 and 18 --> not a perf square
5 gives 25 and 9 --> 2 perfect squares
6 gives 36 which is larger than 34
we found 2 possible n values
1 is not sufficient
2)n is smaller than 40
straight out we can have 26 and 34 --> multiple values = not sufficient
1+2) since the 2 values smaller than 40 are also the values that we found complied to 1), this means we still have 2 possible values
Not sufficient --> E
kudos if it helped
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
since it's a 2-digit integer the 1-12 combination is out. (twelve cannot be 'a digit')
next list the numbers that can be formed with the remaining factors
26
34
43
62
now lets look at 1)
sum of perfect squares in 1 way
26
--> 1 & 5 => 1 & 25 = 26
2 results in 4 and 22 which is not a perfect square
3 results in 9 and 17 which is prime
4 results in 16 and 10, which is not a perfect square
5 puts us back in the first situations
SO: 26 matches, however, we are looking for a single number so none of the others should be possible to be represented as a sum of perfect squares, or should be possible to be represented as different summs of perfect squares
-->looking at 34
1 gives 1 and 33 --> not a perf square
2 gives 4 and 30 --> not a perf square
3 gives 9 and 24 --> not a perf square
4 gives 16 and 18 --> not a perf square
5 gives 25 and 9 --> 2 perfect squares
6 gives 36 which is larger than 34
we found 2 possible n values
1 is not sufficient
2)n is smaller than 40
straight out we can have 26 and 34 --> multiple values = not sufficient
1+2) since the 2 values smaller than 40 are also the values that we found complied to 1), this means we still have 2 possible values
Not sufficient --> E
kudos if it helped
15 Oct 2018, 06:13
Kudos
Bookmarks
We are given that the product of the digits of a two digit positive integer is 12.
That is say x and y are the digits of two digit positive integer (n = xy), then x*y = 12.
now let us check the no. of factors of 12 = 3*2^2 => 2*3 = 6 factors.
The 6 factors are 1, 2, 3, 4, 6, 12.
So 12 could be obtained by the multiplication of the two single digits in the following ways:
1. 2*6
2. 6*2
3. 3*4
4. 4*3
so, we have 4 ways.
Keeping the above information in mind, let us proceed to the statements.
Statement 1 says that n can be expressed as the sum of two perfect squares in exactly one way.
That is, 2^2 + 3^2 = 13, 3^2+4^2 = 25, so on... this does not conclusively give an answer. Insufficient.
Statement 2 says that the no. n is less than 40. So, n<40, from the stimulus data we get 26, 34 as the possible values, still we do not get a unique value. Insufficient.
Combining both statements give us a lot many values starting from 13 until 40, so, since the combination of the statements is also inconclusive.
Answer is E.
That is say x and y are the digits of two digit positive integer (n = xy), then x*y = 12.
now let us check the no. of factors of 12 = 3*2^2 => 2*3 = 6 factors.
The 6 factors are 1, 2, 3, 4, 6, 12.
So 12 could be obtained by the multiplication of the two single digits in the following ways:
1. 2*6
2. 6*2
3. 3*4
4. 4*3
so, we have 4 ways.
Keeping the above information in mind, let us proceed to the statements.
Statement 1 says that n can be expressed as the sum of two perfect squares in exactly one way.
That is, 2^2 + 3^2 = 13, 3^2+4^2 = 25, so on... this does not conclusively give an answer. Insufficient.
Statement 2 says that the no. n is less than 40. So, n<40, from the stimulus data we get 26, 34 as the possible values, still we do not get a unique value. Insufficient.
Combining both statements give us a lot many values starting from 13 until 40, so, since the combination of the statements is also inconclusive.
Answer is E.
