1. The perimeter of a equilateral triangle and regular hexagon are equal. Find out the ratio of their areas?

a. 3:2

Explanation:

Let the side of the equilateral triangle = aa units and side of the regular hexagon is bb units.

Given that, 3a=6b3a=6b ⇒ab=21⇒ab=21

Now ratio of the areas of equilateral triangle and hexagon = 3‾√4a2:33‾√2b234a2:332b2

⇒3‾√4(2)2:33‾√2(1)2⇒34(2)2:332(1)2

⇒2:3⇒2:3

2. What is the remainder of (32^31^301) when it is divided by 9?

Correct option: b

Explanation:

See solved example 6 here

3231301932313019 = 53130195313019

Euler totient theorem says that [aϕ(n)n]Rem=1[aϕ(n)n]Rem=1

ϕ(n)=n(1−1a)(1−1b)…ϕ(n)=n(1−1a)(1−1b)… here n=ap.bq…n=ap.bq…

Now ϕ(9)=9(1−13)=6ϕ(9)=9(1−13)=6

Therefore, 5656 when divided by 9 remainder 1.

Now 313016=1301=1313016=1301=1

So 3130131301 can be written as 6k + 1

⇒531301=(56)K.51⇒531301=(56)K.51

5313019=(56)K.519=1K.59=55313019=(56)K.519=1K.59=5

3. Which of the following numbers must be added to 5678 to give a reminder 35 when divided by 460?

a. 980

b. 797

c. 955

d. 618

Correct option: b

Explanation:

Let xx be the number to be added to 5678.

When you divide 5678 + xx by 460 the remainder = 35.

Therefore, 5678 + xx = 460k + 35 here kk is some quotient.

⇒⇒ 5643 + xx should exactly divisible by 460.

Now from the given options x = 797.

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4.

A girl entered a store and bought x flowers for y dollars (x and y are

integers). When she was about to leave, the clerk said, “If you buy 10

more flowers I will give you all for $$2, and you will save 80 cents a dozen”. The values of x and y are:

a. (15,1)

b. (10,1)

c. (5,1)

d. Cannot be determined from the given information.

Correct option: c

Explanation:

Given she bought xx flowers for yy dollars.

So 1 flower cost = yxyx

12 flowers or 1 dozen cost = 12yx12yx

Again, xx+10 cost = 2 dollars

1 flower cost = 210+x210+x

12 flowers or 1 dozen cost = 2×1210+x=2410+x2×1210+x=2410+x

Given that this new dozen cost is 80 cents or 4/5 dollar less than original cost.

⇒12yx−2410+x=45⇒12yx−2410+x=45

From the given options, c satisfies this.

### 5. If a number is divided by 357 the remainder is 5, what will be the remainder if the number is divided by 17?

a. 9

b. 3

c. 5

d. 7

Correct option: c

Explanation:

Let ′N′′N′ be the given number.

N=357k+5N=357k+5 = 17×21k+517×21k+5

If this number is divided by 17 remainder is 5 as 357k is exactly divided by 17.

### 6. In how many possible ways can write 3240 as a product of 3 positive integers a,b and c.

a. 450

b. 420

c. 350

d. 320

Correct option:

Explanation:

3450=23×34×51=a×b×c3450=23×34×51=a×b×c

We have to distribute three 2’s to a, b, c in 3+3−1C3−1=5C2=103+3−1C3−1=5C2=10 ways

We have to distribute four 3’s to a, b, c in 3+4−1C3−1=6C2=153+4−1C3−1=6C2=15 ways

We have to distribute one 5 to a, b, c in 3 ways.

Total ways = 10×15×3=45010×15×3=450 ways.

### 7. On door A – It leads to freedomOn door B – It leads to Ghost houseOn door C – door B leads to Ghost houseThe statement written on one of the doors is wrong.Identify which door leads to freedom.

a. A

b. B

c. C

d. None

Correct option: c

Explanation:

Case 1: A, B are true. In this case, Statement C also correct. So contradiction.

Case

2: B, C are true. In this case, B leads to ghost house and C confirms

it. Now A is wrong. So door A does not lead to freedom. So Door C leads

to freedom.

### 8. In the given figure, If the sum of the values along each side is equal. Find the possible values a, b, c, d, e, and f.

a. 9, 7, 20, 16, 6, 38

b. 4, 9, 10, 13, 16, 38

c. 4, 7, 20, 13, 6, 38

d. 4, 7, 20, 16, 6, 33

Correct option: c

Explanation:

From the above table, 42 + a + b = 47 + e. Therefore, a + b = 5 + e. Option a, b ruled out.

47 + e = 15 + f. Therefore, 32 + e = f. Option d ruled out.

4 men throw a die each simultaneously. Find the probability that at least 2 people get the same number

a. 5/18

b. 13/18

c. 1/36

d. 1/2

### 9. 70, 54, 45, 41……. What is the next number in the given series?

a. 35

b. 36

c. 38

d. 40

Correct option: d

Explanation:

Consecutive squares are subtracted from the numbers.

70 – 54 = 16

54 – 45 = 9

45 – 41 = 4

So next we have to subtract 1. So answer = 41 – 1 = 40

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10.

How many positive integers less than 500 can be formed using the

numbers 1,2,3,and 5 for digits, each digit being used only once.

a. 52

b. 68

c. 66

d. 34

Correct option:

Explanation:

Single digit number = 4

Double digit number = 4××3 = 12

Three digit numbers = 3××3××2= 18 (∵∵ If Hundred’s place is 5, then the number is greater than 500)

Total = 34.

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1.

In particular language if A=0, B=1, C=2,…….. .. , Y=24, Z=25 then

what is the value of ONE+ONE (in the form of alphabets only)

a. BDAI

b. ABDI

c. DABI

d. CIDA

Answer: a

Explanation:

This

problem is based on Base 26 rather than regular base 10 (decimal

system) that we normally use. In base 10 there are 10 digits 0 to 9

exist. In base 26 there are 26 digits 0 to 25 exist. To convert any

number into base 26, we have to divide the number with 26 and find the

remainder. (Study this Base system chapter).

Here, ONE + ONE =

E has value of 4. So E + E = 8 which is equal to I.

Now N + N = 13 + 13 = 26. But in base 26, there is no 26. So (26)10=(10)26(26)10=(10)26

So we put 0 and 1 carry over. But 0 in this system is A.

Now O + O + 1 = 14 + 14 + 1 = 29

Therefore, (29)10=(13)26(29)10=(13)26

But 1 = B and 3 = D in that system. So ONE + ONE = BDAI

### 2. Find the number of perfect squares in the given series 2013, 2020, 2027,……………., 2300 (Hint 44^2=1936)

a. 1

b. 2

c. 3

d. Can’t be determined

Answer: a

Explanation:

The

given series is an AP with common difference of 7. So the terms in the

above series are in the form of 2013 + 7k. We have to find the perfect

squares in this format in the given series.

Given that 44^2 = 1936.

Shortcut: To find the next perfect square, add 45th odd number to 44^2.

So 45^2 = 1936 + (2 x 45 -1) = 2025

46^2 = 2025 + (2 x 46 – 1) = 2116

47^2 = 2116 + (2 x 47 – 1) = 2209

Now subtract 2013 from the above numbers and divide by 7. Only 2209 is in the format of 2013 + 7k. One number satisfies.

### 3. What is in the 200th position of 1234 12344 123444 1234444….?

Answer: 4

Explanation:

The given series is 1234, 12344, 123444, 1234444, …..

So the number of digits in each term are 4, 5, 6, … or (3 + 1), (3 + 2), (3 + 3), …..upto n terms = 3n+n(n+1)23n+n(n+1)2

So 3n+n(n+1)2≤2003n+n(n+1)2≤200

For

n = 16, We get 184 in the left hand side. So after 16 terms the number

of digits equal to 184. And 16 them contains 16 + 3 = 19 digits.

Now 17 term contains 20 digits and 123444……417times123444……4⏟17times. So last digit is 4 and last two digits are 44.

### 4. 2345 23455 234555 234555……….. what was last 2 numbers at 200th digit?

Answer: 55

Explanation:

Proceed as above. The last two digits in the 200th place is 55.

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5.

There are equal number of boys and girls in a class. If 12 girls

entered out, twice the boys as girls remain. What was the total number

of students in a class?

Answer: 48

Explanation:

Let the boys = b and girls = g

Given bg−12=21bg−12=21

Substitute b = g in the above equation. g = 24. So total students = 24 + 24 = 48

### 6. a bb ccc dddd eeeee ………What is the 120th letter?

Answer: O

Explanation:

Number of letters in each term are in AP. 1, 2, 3, …

So n(n+1)2≤120n(n+1)2≤120

For n = 15, we get LHS = 120. So 15th letter in the alphabet is O. So 15th term contains 15 O’s.

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7.

There are 120 male and 100 female in a society. Out of 25% male and 20%

female are rural. 20% of male and 25% of female rural people passed in

the exam. What % of rural students have passed the exam?

Answer: 22%

Explanation:

From the above data, Rural male = 25%(120) = 30, Rural female = 20%(100) = 20.

Passed students from rural: male = 20%(30) = 6, female = 25%(20) = 5

Required percentage = 1150×100=22%1150×100=22%

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8.

1/7 th of the tank contains fuel. If 22 litres of fuel is poured into

the tank the indicator rests at 1/5th mark. What is the quantity of the

tank?

Answer: 385

Explanation:

Let the tank capacity = vv liters.

Given, v7+22=v5v7+22=v5

v5−v7=22⇒v=385v5−v7=22⇒v=385

### 9. What is the probability of getting sum 3 or 4 when 2 dice are rolled

Answer: 5/36

Explanation:

Required number of ways = (2, 1), (1, 2), (1, 3), (3, 1), (2, 2) = 5

Total ways = 62=3662=36

Probability = 536536

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10.

On the fabled Island of Knights and Knaves, we meet three people, A, B,

and C, one of whom is a knight, one a knave, and one a spy. The knight

always tells the truth, the knave always lies, and the spy can either

lie or tell the truth.A says: “C is a knave.”B says: “A is a knight.”C says: “I am the spy.”Who is the knight, who the knave, and who the spy?

Answer:

Explanation: A= Knight, B= Spy, C = Knave

Let

us say A is Knight and speaks truth. So C is Knave and B is spy. So

C’s statement is false and B’s statement is true. This case is

possible.

Let us say B is Knight. This is not possible as A also becomes Knight as B speaks truth.

Let us say C is Knight. This is clearly contradicted by C’s statement itself.