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26 May 2021, 16:39
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
47% (01:15) correct
53%
(01:14)
wrong
based on 15
sessions
History
Date
Time
Result
Not Attempted Yet
What is the number of factors of a number x?
(1) x = y*z where y and z have exactly one common factor between them.
(2) The number of factors of X is equal to twice the number of factors of Y.
(1) x = y*z where y and z have exactly one common factor between them.
(2) The number of factors of X is equal to twice the number of factors of Y.
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sherxon
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05 Jun 2021, 01:47
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S1: x= y*z = A*B*t^2 whare t is common factor of y and z. But we have no info about other factors of y*z.
Insufficient
S2: again we don't have information about z.
Insufficient
S1&2: again not sufficient as info about z is missing from both statements.
Answer is E
Posted from my mobile device
Insufficient
S2: again we don't have information about z.
Insufficient
S1&2: again not sufficient as info about z is missing from both statements.
Answer is E
Posted from my mobile device
05 Jun 2021, 09:52
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AkhilAggarwal
Solution:
Step 1: Analyse Question Stem
We need to find the number of factors of x.
- • To calculate the total number of factors of a number, the number has to be in the prime factorized form.
• Then, the total factors are calculated using the formula:
- o (a + 1)(b + 1)(c + 1) where a, b, c,…… are the powers of the primes.
Statement 1:x = y*z where y and z have exactly one common factor between them.
- • If y = 6 and z = 8 such that they have exactly one common factor i.e., 2
- o Then, x = y*z = 6*8 = 48 = \(2^{4}\) * 3
- o In this case, the total number of factors of x = (4+1)(1+1) = 10
- o Then, x = y*z = 6*10 = 60 = \(2^{2}\) * 3 * 5
- o In this case, the total number of factors of x = (2+1)(1+1)(1+1) = 12
Hence, statement 1 is not sufficient and we can eliminate the answer options A and D.
Statement 2: The number of factors of X is equal to twice the number of factors of Y.
- • If the number of factors of y = 2, then the number of factors of x = 4
• If the number of factors of y = 3, then the number of factors of x = 6
Hence, statement 2 is not sufficient and we can eliminate the answer option B.
Step 3: Analyse Statements by Combining
On combining, we do not have any sufficient information to determine x or its total number of factors.
Thus, both the statements combined are insufficient and we can eliminate the answer option C.
Hence, the correct answer is Option E.
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