Aptitude - Number
11.
Find the number of factors of 1728.
Answer
Prime factorization of 1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 = 26 x 33
Add 1 to each exponent and mulitply them to get the number of factors.
∴ No. of factors of 1728 = (6 + 1) x (3 + 1) = 7 x 4 = 28.
Answer :
Option CExplanation :
Prime factorization of 1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 = 26 x 33
Add 1 to each exponent and mulitply them to get the number of factors.
∴ No. of factors of 1728 = (6 + 1) x (3 + 1) = 7 x 4 = 28.
12.
Find the number of zeroes in 8 x 15 x 23 x 17 x 25 x 22.
Answer
8 x 15 x 23 x 17 x 25 x 22 = (23 x 3 x 5 x 23 x 17 x 52 x 11 x 2)
Zeroes are formed only by the combination of 2 x 5
In this case only 3 pairs of 2 x 5 are formed, so there will be 3 zeroes
Answer :
Option CExplanation :
8 x 15 x 23 x 17 x 25 x 22 = (23 x 3 x 5 x 23 x 17 x 52 x 11 x 2)
Zeroes are formed only by the combination of 2 x 5
In this case only 3 pairs of 2 x 5 are formed, so there will be 3 zeroes
13.
Find the unit digit in 67 x 37 x 43 x 91 x 42 x 33 x 4.
Answer
Just multiply unit digits to get the unit digit.
7 x 7 x 3 x 1 x 2 x 3 x 4 = 3528
∴ Unit digit is 8
Answer :
Option DExplanation :
Just multiply unit digits to get the unit digit.
7 x 7 x 3 x 1 x 2 x 3 x 4 = 3528
∴ Unit digit is 8
14.
186 x 186 x 136 x 136 − 2 x 186 x 136 = ?
Answer
Given expression = (186)2 + (136)2 − 2 x 186 x 136
(186 - 136)2 = 502 = 2500
Answer :
Option AExplanation :
Given expression = (186)2 + (136)2 − 2 x 186 x 136
(186 - 136)2 = 502 = 2500
15.
A common factor of (4743 + 4343) and (4747 + 4347) is :
Answer
When n is odd, (xn + an) is divisible by (x + a)
∴ Each one is divisible by (47 + 43).
Hence, the common factor is (47 + 43).
Answer :
Option BExplanation :
When n is odd, (xn + an) is divisible by (x + a)
∴ Each one is divisible by (47 + 43).
Hence, the common factor is (47 + 43).
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