General Aptitude Test

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General Aptitude Test - 3

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Question 1
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If p > q >1 and 0 < a < 1 then which of the following is correct option?

A
log_a(p – a) > log_a(q – a)

B
log_a(p + a) > log_a(q + a)

C
log_a(p – a) < log_a(q – a)

D
log_a(p + a) < log_a(q – a)

Solution

Explanation:

For a log function with base a as 0 < a < 1, the graph of the function can be drawn as bellow

The above graph is valid for,

x > 0 and 0 < a < 1

Since the function y = log_ax is a decreasing function for base a ∈ (0, 1). So, while operating log_a on a given inequality, the sign of the inequality will change.

Calculation:

Given:

p > q > 1

As, 0 < a < 1

⇒ (p – a) > (q – a) > 0

This is satisfying the condition for the domain of log_a(p – a) and loga(q – a).

Operating log function on both sides,

⇒ log_a(p - a) < log_a(q - a)

⇒ Option 3 is correct.
Question 2
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Which of the following options is the closest in meaning to the sentence below?

She enjoyed herself immensely at the party.

A
She had a terrible time at the party.

B
She had a horrible time at the party.

C
She had a terrific time at the party.

D
She had a terrifying time at the party.

Solution

The given sentence uses the word 'enjoy' which has a positive connotation and is followed by the adverb ‘immensely’, which means to a large extent.

All of the options except option 3 use adjectives with negative connotations - terrible, horrible, terrifying - to describe the subject's experience and and are hence, incorrect.

Option 3 uses the word 'terrific' which has a positive connotation and is hence accurate.

Hence, option 3 is correct.
Question 3
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Given Set A = {2, 3, 4, 5} Set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15} B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals 16?

A
0.20

B
0.25

C
0.30

D
0.33

Solution
Question 4
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Identify the answer figure from which the pieces given in the question figure have been cut.

A

B

C

D

Solution
Question 5
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Azeem, Bala, and Rohan are the three typists who working simultaneously can type 360 pages in 5 hr. In 1 hr, Rohan can type as many pages more than Bala as Bala can type more than Azeem. During a period of 7 hrs, Rohan can type as many pages as Azeem can, for 5 hrs. Total pages that Azeem can type in 4 hrs are _________ pages

A
112

B
113

C
114

D
117

Solution

Concept:

The total number of pages typed by Azeem, Bala, and Rohan = 360 pages in 5 hours.

⇒ The total number of pages typed by Azeem, Bala, and Rohan all together = pages/hour = 72 pages/hour

Let, the total number of pages typed by Azeem, Bala, and Rohan working alone are x pages/hour; y pages/hour, and z pages/hour respectively.

⇒ x + y + z = 72 … (1)

In 1 hour, Rohan can type as many pages more than Bala as Bala can type more than Azeem, that means,

⇒ x - y = y – z ⇒ 2y = x + z … (2)

During a period of 7 hours, Rohan can type as many pages as Azeem can, for 5 hours,

⇒ 7z = 5x … (3)

Calculation:

By equation (1) and (2),

⇒ 2y + y = 72 ⇒ y = 24

By equation (1) and (3),

By equation (1),

⇒ x + 20 + 24 = 72 ⇒ x = 28

Total pages that Azeem can type in 4 hours = 4x = 4 × 28 = 112 pages
Question 6
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Three and quarter hours back, when seen in the mirror, the reflection in the wall clock without numbers seems to show 7: 45. What time that the watch will show after one and quarter hours of actual time?

A
8:45

B
8:30

C
7:14

D
7:45

Solution

Concept:

When the reflection of a wall clock without number markings seemed to show 7:45 in a mirror so, the actual time three and quarter hours back.was 4:15 as shown in the figure,

Calculation:

This 04:15 was a time three and a quarter-hour back of actual time.

⇒ The actual current time = 04:15 + 3:15 = 07:30

So, time that the watch will show after one and quarter-hour of actual time = 07:30 + 1:15 = 8:45

Alternative:

Concept:

If the reflection time of a wall watch without numbering is 7: 45 then the actual time of the wall will be calculated by subtracting it from 11: 60.

⇒ The actual time = 11:60 – 7:45 = 4:15

Calculation:

This 04:15 was a time three and a quarter-hour back of actual time.

⇒ The actual current time = 04:15 + 3:15 = 07:30

So, time that the watch will show after one and quarter hours of actual time = 07:30 + 1:15 = 8:45
Question 7
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Directions For Questions

In the question given below, two statements are followed by two conclusions A and B. You have to take the two given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows the two given statements disregarding commonly known facts.

...view full instructions

Statements:

All boys are girls.

No girl is a father.

Conclusions:

A: All girls are boys.

B: No boy is a father.

A
Only A follows.

B
Only B follows.

C
Both A and B follow

D
Neither A nor B follows

Solution

Least possible Venn diagram:

Conclusions:

A: All girls are boys. → It is possible but not definite

B: No boy is a father. → True

Hence, only conclusion B is true.
Question 8
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Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:

A
2

B
4

C
6

D
8

Solution

All the possible ways will be:

R Q S P → (possible)

P Q S R → (possible)

R Q P S → (possible)

P Q R S → (possible)

Q R S P → (possible)

Q P S R → (possible)

The total number of possible ways will be = 6
Question 9
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The pie chart below has the breakup of the number of students from different departments in an engineering college for the year 2012. The proportion of male to female students in each department is 5:4. There are 40 males in Electrical Engineering. What is the difference between the number of female students in the Civil department and the female students in the Mechanical department?

A
32

B
33

C
34

D
30

Solution

Answer: 32 to 32

Explanation:

From the pie-chart, we have

The proportion of male to female students in each department is 5:4. ( male ratio = 5/9 and female ratio = 4/9)

Hence 40 males in Electrical Department, So total students in Electrical Department = 40 *(9/5) = 72

Total electrical student percentage = 20%

Hence Total number of students in college = (72/20)*100 = 360

Hence number of females in Mechanical Department = 0.1*(4/9)*(360) = 16

and number of females in Civil Department = 0.3*(4/9)*360 = 48

Hence the Difference = 48-16 = 32
Question 10
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Pointing to a photograph, a woman tells a boy, ‘I am the only daughter of this man and his son is your maternal uncle’. How is the woman related to the boy’s father?

A
Sister-in-law

B
Niece

C
Mother

D
Wife

Solution

Following symbols are used:

Clearly, the woman is the wife of boy’s father because the woman is boy’s mother.