Source: Compiled by ALLEN Career Institute

What is the least number which when doubled will be exactly divisible by 12, 14, 18 and 22?

Explanation:
LCM of 12, 14, 18 and 22 = 2772
Hence the least number which will be exactly divisible by 12, 14, 18 and 22 = 2772
2772 ÷ 2 = 1386
1386 is the number which when doubled, we get 2772
Hence, 1386 is the least number which when doubled will be exactly divisible by 12, 14, 18 and 22.

X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?

Explanation:
Ratio of the investment
=21000:17500=210:175=21000:17500=210:175 =42:35=6:5=42:35=6:5
Share of X in the profit
=26400×611=2400×6=14400

If A is coded as -, B is coded as +, C is coded as * and D is coded as / then evaluate 8 A 1 B 11 C 12 D 4 C 5?

Explanation:
Given, A is coded as -,
B is coded as +,
C is coded as * and
D is coded as /
and the given expression:8 A 1 B 11 C 12 D 4 C 5
By using correct symbols, we get,
8 - 1 + 11 * 12 / 4 * 5 = 172

Pointing out to a lady, a girl said, "She is the daughter-in-law of the grandmother of my father's only son." How is the lady related to the girl?

Explanation:
My father's only son - My brother; Grandmother of my brother - My grandmother.
Daughter-in-law of my grandmother - My mother.
So, the lady is girl's mother.

What is the two-digit number?
I. The difference between the two digits is 9.
II. The sum of the digits is equal to the difference between the two digits.

Explanation:
Let the tens and unit digits be x and y respectively. Then,
From Statement I. x-y= 9.
From Statement II. x+y=x-y.
From I and II, we get x-y= 9 and x+y= 9.
On solving, we get x= 9 and y= 0.
Therefore, Required number is 90.
Thus, both Statements and II are necessary to answer.

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