Numbers problems
- 1. n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4?
Options- A. 3
- B. 2
- C. 1
- D. 0 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 2
Explanation:
Let n = 4 q + 3. Then 2 n = 8 q + 6 = 4(2 q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
- 2. The product of a number and its multiplicative inverse is
Options- A. 1
- B. 0
- C. -1
- D. Infinity Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 1
Explanation:
The mutiplicative inverse of a number is nothing but a reciprocal of a number.
Now, the product of a number and its multiplicative inverse is always equal to 1.
For example :
Let the number be 15
Multiplicative inverse of 15 = 1/15
The product of a number and its multiplicative inverse is = 15 x 1/15 = 1.
- 3. If a2 = 12, then a4 =?
Options- A. 144
- B. 72
- C. 36
- D. 24 Also asked in: Bank Exams, AIEEE, CAT, GATE, Bank Clerk, Analyst, Bank PO, IT Trainer
Correct Answer: 144
Explanation:
Given a x a = 12
asked to find a x a x a x a = (a x a) x (a x a)
a4 = a2 x a2
= 12 x 12
= 144.
- 4. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
Options- A. 10 & 12
- B. 10 & 18
- C. 12 & -18
- D. -12 & 18 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, IT Trainer
Correct Answer: -12 & 18
Explanation:
Given, difference of the squares of two numbers is 180.
= k2 - l2 - 180
Also, square of the smaller number is 8 times the larger.
= l2 = 8k
Thus, k2 - 8a - 180 = 0
k2 ? 18k + 10k - 180 = 0
? k(k - 18) + 10(k ? 18) = 0
= (k + 10)(k ? 18) = 0
? k = -10, 18
Thus, the other number is
324 - 180 = l2
? Numbers are 12, 18 or -12, 18.
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