number systems Model Questions & Answers, Practice Test for ibps so prelims
Find the total number of prime factors in $2^17 × 6^31 × 7^5 × 10^11 × 11^10 × (323)^23$
Answer: (c)
$2^17 × 6^31 × 7^5 × 10^11 × 11^10 × (323)^23$
= $2^17 × 2^31 × 3^31 ×7^5 × 2^11 × 5^11 × 11^10 × 17^23 × 19^23$
= $2^59 × 3^31 × 5^11 × 7^5 × 11^10 × 17^23 × 19^23$
∴ Total number of prime factors
= 59 + 31 + 11 + 5 + 10 + 23 + 23 = 162
Farah got married 8 years ago. Today her age is 1$2/7$ times her age at the time of her marriage. At present her daughter's age is one-sixth of her age. What was her daughter's age 3 years ago?
Answer: (b)
Let Farah's age at the time of her marriage be x.
Then, $(x + 8) = x × 9/7$
${9x}/7 - x = 8$
$x = {8 × 7}/2 = 28$ years
∴ Farah's present age = 28 + 8 = 36 years
∴ Daughter's age 3 years ago
= $36 × 1/6 - 3$= 3 years
Two different two-digit natural numbers are written beside each other such that the larger number is written on the left. When the absolute difference of the two numbers is subtracted from the four-digit number so formed, the number obtained is 5481. What is the sum of the two two digit numbers?
Answer: (d)
As the larger number is written on the left, the larger number is either 54 or 55.
Let the smaller number be x.
Case I: The larger number is 54.
5400 + x = 5481 + 54 – x
2x = 5535 – 5400 = 135
(In this case x will not be a natural number.)
Case II: The larger number is 55.
5500 + x = 5481 + 55 – x
2x = 5536 – 5500 = 36
⇒ x = 18
Hence, the required sum = 73.
The number $log_2{7}$ is
Answer: (a)
Suppose, possible, $log_2{7}$ is rational, say p/q where p and q are integers, prime to each other.
Then, $p/q = log_2{7} ⇒ 7 = 2^{p/q} ⇒ 2^p = 7^q$
which is false since L.H.S. is even and R.H.S. is odd.
Obviously $log_2{7}$ is not an integer and hence not a prime number.
Farah got married 8 years ago. Today her age is 1$2/7$ times her age at the time of her marriage. At present her daughter's age is one-sixth of her age. What was her daughter's age 3 years ago?
Answer: (a)
Let Farah's age at the time of her marriage be x.
Then, $(x + 8) = x × 9/7$
${9x}/7 - x = 8$
$x = {8 × 7}/2 = 28$ years
Farah's present age = 28 + 8 = 36 years
Daughter's age 3 years ago
= $36 × 1/6 - 3$ = 3 years
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