1. Which of the following number is divisible by 24 ?

A. 35718 B. 63810 C. 537804 D. 3125736 E. 537805

2. [latex]\frac {753 \times 753 + 247 \times 247 - 753 \times 247}{753 \times 753 \times 753 + 247 \times 247 \times 247} = ?[/latex]

A. [latex]\frac {1}{1000}[/latex] B. [latex]\frac {1}{506}[/latex] C. [latex]\frac {253}{500}[/latex] D. [latex]\frac {450} {500}[/latex] E. None of these

3. (?) + 3699 + 1985 - 2047 = 31111

A. 34748 B. 27474 C. 30154 D. 27574 E. None of these

4. At 3:40, the hour hand and the minute hand of a clock form an angle of:

A. 120° B. 125° C. 130° D. 135° E. None of these

5. How many times are the hands of a clock at right angle in a day?

A. 22 B. 24 C. 44 D. 48 E. 50

Answers and Explanations
1. Answer - Option D
Explanation -
24 = 3 x 8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Consider option (D),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
i.e, 3125736 is divisible by (3 x 8), i.e., 24.
2. Answer - Option A
Explanation -
[latex]\frac {{a}^{2} + {b}^{2} - ab}{{a}^{3} + {b}^{3}}= \frac {1}{a + b} = \frac {1}{753 + 247} = \frac {1}{1000}[/latex]
3. Answer - Option B
Explanation -
x + 3699 + 1985 - 2047 = 31111
[latex]\Rightarrow [/latex] x + 3699 + 1985 = 31111 + 2047
[latex]\Rightarrow [/latex] x + 5684 = 33158
[latex]\Rightarrow [/latex] x = 33158 - 5684 = 27474.
4. Answer - Option C
Explanation -
Angle traced by hour hand in 12 hrs. = 360°.
Angle traced by it in [latex]\frac {11}{3} hrs = (\frac {360}{12} \times \frac {11}{3})° = 110° [/latex]
Angle traced by minute hand in 60 min. = 360°.
Angle traced by it in 40 min. = [latex](\frac {360}{60} \times 40)° = 240°[latex]
i.e, Required angle (240 - 110)° = 130°
5. Answer - Option C
Explanation -
In 12 hours, they are at right angles 22 times.
i.e, In 24 hours, they are at right angles 44 times.

1. Pointing to a photograph of a boy Suresh said, "He is the son of the only son of my mother." How is Suresh related to that boy?

A. Brother B. Uncle C. Cousin D. Father E. Grandfather

2. If A + B means A is the mother of B; A - B means A is the brother B; A % B means A is the father of B and A x B means A is the sister of B, which of the following shows that P is the maternal uncle of Q?

A. Q - N + M x P B. P + S x N - Q C. P - M + N x Q D. Q - S % P E. Q - S % N

3. If A is the brother of B; B is the sister of C; and C is the father of D, how D is related to A?

A. Brother B. Sister C. Nephew D. Mother E. Cannot be determined

Direction(4-5): Dev, Kumar, Nilesh, Ankur and Pintu are standing facing to the North in a playground such as given below:

• Kumar is at 40 m to the right of Ankur.
• Dev is are 60 m in the south of Kumar.
• Nilesh is at a distance of 25 m in the west of Ankur.
• Pintu is at a distance of 90 m in the North of Dev.

4. Which one is in the North-East of the person who is to the left of Kumar?

A. Dev B. Nilesh C. Ankur D. Pintu E. None of these

5. If a boy starting from Nilesh, met to Ankur and then to Kumar and after this he to Dev and then to Pintu and whole the time he walked in a straight line, then how much total distance did he cover?

A. 215 m B. 155 m C. 245 m D. 185 m E. None of these

Answers and Explanations
1. Answer - Option D
Explanation -
The boy in the photograph is the only son of the son of Suresh's mother i.e., the son of Suresh. Hence, Suresh is the father of boy.
2. Answer - Option C
Explanation -
P - M → P is the brother of M
M + N → M is the mother of N
N x Q → N is the sister of Q
Therefore, P is the maternal uncle of Q.
3. Answer - Option E
Explanation -
If D is Male, the answer is Nephew.
If D is Female, the answer is Niece.
As the sex of D is not known, hence, the relation between D and A cannot be determined.
Note: Niece - A daughter of one's brother or sister, or of one's brother-in-law or sister-in-law. Nephew - A son of one's brother or sister, or of one's brother-in-law or sister-in-law.
4. Answer - Option D
Explanation [4-5]-

Ankur is in the left of Kumar. Hence Pintu is in North-East of Ankur.
5. Answer - Option A
Explanation -
Required distance = 25 m + 40 m + 60 m + 90 m
Required distance = 215 m

Direction (1 – 4): Study the following information carefully and answer the given questions.
P, Q, R, S, T, U, V and W are sitting round the circle and are facing the centre: 1. P is second to the right of T who is the neighbour of R and V. 2. S is not the neighbour of P. 3. V is the neighbour of U. 4. Q is not between S and W. W is not between U and S.
1. Which two of the following are not neighbours ?

A. RV B. UV C. RP D. QW E. WV

2. Which one is immediate right to the V ?

A. P B. U C. R D. T E. W

3. Which of the following is correct ?

A. P is to the immediate right of Q B. R is between U and V C. Q is to the immediate left of W D. U is between W and S E. None of these

4. What is the position of S ?

A. Between U and V B. Second to the right of P C. To the immediate right of W D. Data inadequate. E. Between U and w

5. One morning after sunrise, Vimal started to walk. During this walking he met Stephen who was coming from opposite direction. Vimal watch that the shadow of Stephen to the right of him (Vimal). To Which direction Vimal was facing?

A. East B. West C. South D. Data inadequate E. North

Answers and Explanations
Explanation [1-4]-

1. Answer - Option A
2. Answer - Option D
3. Answer - Option C
4. Answer - Option C
5. Answer - Option C
Explanation -
Sun rises in the east. So the shadow of a man will always falls towards the west. Since the shadow of Stephen is to the right of Vimal. Hence Vimal is facing towards South.