1. M is the father of N who is the son of V. In order to know the relation of M to P, which of the statement/statements is/are necessary?
1. P is the brother of V.
2. The daughter of N is the granddaughter of V.
A. Only (1)
B. Only (2)
C. Either (1) or (2)
D. (1) and (2) both
Answer - Option A
Explanation -
M is the father of N and N is the son of V.
Hence, V is the mother of N.
From (1), P is the brother of V
Therefore, M is the brother-in-law of P because V is the wife of M.
From (2), the daughter of N, is the granddaughter of V. From this we do not get any relation of M to P.
2. A is the son of C; C and Q are sisters; Z is the mother of Q and P is the son of Z. Which of the following statements is true?
A. P and A are cousins
B. P is the maternal uncle of A
C. Q is the maternal grandfather of A
D. C and P are sisters
Answer - Option B
Explanation -
C and Q are sisters and A is the son of C. Hence, C is the mother of A or Z is the mother Q.
Hence, Z is the maternal grandmother of A. P is the son of Z. Hence, P is the maternal uncle of A.
3. The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
A. 240
B. 270
C. 295
D. 360
Answer - Option B
Explanation -
Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
4. [latex] {12}^{2} \times {6}^{2} \div 432 = ?[/latex]
A. 5184
B. 5060
C. 5148
D. None of these
Answer - Option A
Explanation -
[latex]\frac{{12}^{3} \times {6}^{4}}{432} = \frac{{12}^{3} \times {6}^{4}}{12 \times {6}^{2}} = {12}^{2} \times {6}^{2} = {72}^{2} = 5184[/latex]
5. A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:
A. [latex]59 \frac {7}{12}[/latex] min. past 3
B. 4 p.m.
C. [latex]58 \frac {7}{11}[/latex] min. past 3
D. [latex]2 \frac {3}{11}[/latex] min. past 4
Answer - Option B
Explanation -
Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = [latex]\frac {37}{4} [/latex] hrs.
3 min. 5 sec. of this clock = 3 min. of the correct clock.
[latex]\Rightarrow \frac {37}{720}[/latex] hrs of this clock = [latex]\frac {1}{20}[/latex] hrs of the correct clock.
[latex]\Rightarrow \frac {37}{4}[/latex] hrs of this clock = ([latex]\frac {1}{20} \times \frac {720}{37} \times\frac {37}{4} [/latex]) hrs of the correct clock.
= 9 hrs of the correct clock.
i.e, The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.