Scholarship Test Practice

Answer- C

Tax = 9%

Cost inclusive of tax = Rs. 1417

Let cost of the handbag excluding the tax be x 1.09x = 1417

x = 1300

Reduction in price = (1417 – 1300) = 117

Answer- B

Difference of 75 and 57 is 18

This results in a change of average by 3

Hence number of people in the group is 18/3 = 6

Answer- C

It is to be filled with minimum number of possible tiles,

Hence, we have to find the largest square tile that helps us fill the floor We thus find the HCF

HCF (140cm, 525cm) = 35cm

Hence the side of the square tile must be 35 cm

Answer- B

Finally there was 81 litres of milk Initially there was 192 litres of milk

Let the percentage milk withdrawn each time be x % So 81 = 192 (1 – x/100) ³

Solving for which we get x = 25

Answer- C

Let us say Robin scores x runs his first 5 innings Then he scores x + 35 in his last five inning

Minimum runs scores in 6 th innings is when he scored 0 in first innings Hence minimum score in 6 th innings is 35

Answer- D

Based on the information given in the question,

The ratio of First person : Second person : Third person = 2 : 1 :3 And hence the share of third person = 4680 x 3/6 = 2340

Share of third person is Rs. 2340

Answer- A

A empties tank in 45 min and B empties entire tank in 36 min Together they empty it in 1/36 + 1/45 = 1/20 ie 20 min Quarter tank will be emptied in 5 min

Answer- C

Meaning: The use of too many words to express an idea.
Synonyms: Circumlocution, Diffuseness, Verbiage
Antonyms: Brevity, Briefness, Terseness

Answer- D

Explanation:

Meaning: Magniloquent is using high-flown or bombastic language.
Synonyms: Grandiloquent, High-sounding, Lofty
Antonyms: Terse, Crisp

Answer- B

Explanation:

Meaning: Yokel is an uneducated or simple-minded person from the countryside.
Synonyms: Bumpkin, Rustic, Hillbilly
Antonyms: Cosmopolitan, Sophisticate

Answer- C

Explanation:

Meaning: To vindicate is to free from a charge of wrongdoing.
Synonyms: Acquit, Clear, Exonerate
Antonyms: Criminate, Incriminate, Accuse

Answer- C

Let his marks be 10, 9, 8, 7, and 6 in the five subjects. Hence, he has scored 40 marks. This constitutes only 60% of the total marks. Hence, total marks 40/0.6 = 66.7 or 67 approx. , which is the maximum mark in all 5 subjects.

Since the total marks in each subject is the same, hence maximum marks in each subject will be 67/5 = 13 approx. Out of this 50% is the passing marks. In other words to pass in a subject, he needs to score 6.5 marks. We can see that only in 1 subject, he scored less than this viz. 6. Hence, he passed in 4 subjects.

Answer- A

The number of apples = 8, so the amount eaten by each of the three is 8/3 apples therefore first friend should be paid for 5 – (8/3) and second friend should be paid for 3–(8/3) apples. They should distribute  the sum of Rs.8 in ratio 7/3 : 1/3, i.e., 7 : 1

Answer- B

A’s saving = 100 – 75 = 25% of his salary. B’s saving = 100 – 80 = 20% of his salary C’s saving = 100 – 56 = 44% of his salary 25/100 of A’s salary : 20/100 of B’s salary : 44/100 of C’s salary = 10 : 12 : 33

or 25 × A’s salary : 20 × B’s salary : 44 × C’s salary = 10 : 12 : 33

or 25 × A’s salary / 20 × B’s salary = 10/12

or A’s salary : B’s salary = 2 : 3,

B’s salary : C’s salary = 4 : 5

Thus A : B = 2 : 3, B : C = 4 : 5 Now making B common we have

A : B = 8 : 12, B : C = 12 : 15, or A : B : C = 8 : 12 : 15

Total salary = 350 Þ A’s salary = 8 / (8 + 12 + 15) × 350 = 80

B’s salary = 12 / (8 + 12 + 15) = 120, and C’s Salary = 150

Answer- A

For this question, its imperative to note the overall tone of the sentence, there are adjectives used to talk about the appearance of the old man.

Hence from the options we need to choose a word that is in sync with this, ‘mottled’ means something that is marked with spots and hence fits here perfectly.

Answer- D

Work backwards from the options. If the cylinder has a capacity of 1200 litre, then the conical vessel shall have a capacity of 700 litres. Once 200 litres have been taken out from the same, the remaining holding of each of them shall be 1000 & 500.

Alternate: Let the cylinder has a capacity of X litre, then the conical vessel shall have a capacity of

(x – 500) litres.

(x – 200) = 2 (x – 700) = x = 1200.

Answer- B

Answer- C

Method of solving this CAT Question from Number Theory - HCF and LCM: Given two numbers, finding HCF, and LCM is very easy. Finding the numbers is much tougher given some property about HCF and the numbers.

We need to find ordered pairs (x, y) such that xy * HCF(x, y) = 1080.

Let x = ha and y = hb where h = HCF(x, y) => HCF(a, b) = 1.

So h3(ab) = 1080 = (23)(33)(5).

We need to write 1080 as a product of a perfect cube and another number.

Four cases:

1. h = 1, ab = 1080 and b are co-prime. We have 4 pairs of 8 ordered pairs (1, 1080), (8, 135), (27, 40) and (5, 216). (Essentially we are finding co-prime a,b such that a*b = 1080).

2. h = 2, We need to find the number of ways of writing (33) * (5) as a product of two co-prime numbers. This can be done in two ways - 1 and (33) * (5) , (33) and (5)

number of pairs = 2, number of ordered pairs = 4

3. h = 3, number of pairs = 2, number of ordered pairs = 4

4. h = 6, number of pairs = 1, number of ordered pairs = 2

Hence total pairs of (x, y) = 9, total number of ordered pairs = 18.

The pairs are (1, 1080), (8, 135), (27, 40), (5, 216), (2, 270), (10, 54), (3, 120), (24, 15) and (6, 30).

Answer- A

Method of solving this CAT Question from Number Theory - HCF and LCM: When a number is divided by 8, a remainder of 7 can be thought of as a remainder of -1. This idea is very useful in a bunch of questions.

Note: When a number is divided by 8, a remainder of 7 can be thought of as a remainder of -1. This idea is very useful in a bunch of questions. So, N = 5a - 1 or N + 1 = 5a

N = 6b - 1 or N + 1 = 6b

N = 7c - 1 or N + 1 = 7c

N = 8d - 1 or N + 1 = 8d

N = 9e - 1 or N + 1 = 9e

N + 1 can be expressed as a multiple of (5, 6, 7, 8, 9)

N + 1 = 5a*6b*7c*8d*9e

Or N = (5a*6b*7c*8d*9e) - 1

Smallest value of N will be when we find the smallest common multiple of (5, 6, 7, 8, 9)

or LCM of (5, 6, 7, 8, 9)

N = LCM (5, 6, 7, 8, 9) - 1 = 2520 - 1 = 2519.

The question is "Find the smallest number that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9?"

Hence the answer is "2519"

Case I:

Case II:

Statement I certainly true.

Statement II can be true but is not definitely true. Hence, statement I is a conclusion.

Hence, option (a) is the correct option.