**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 = a units and side of the regular hexagon is b units.

Given that, 3a=6b ⇒ab=21

Now ratio of the areas of equilateral triangle and hexagon = 34a2:332b2

⇒34(2)2:332(1)2

⇒2:3

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

Correct option: b

Explanation:

32313019 = 5313019

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

ϕ(n)=n(1−1a)(1−1b)… here n=ap.bq…

Now ϕ(9)=9(1−13)=6

Therefore, 56 when divided by 9 remainder 1.

Now 313016=1301=1

So 31301 can be written as 6k + 1

⇒531301=(56)K.51

5313019=(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 x be the number to be added to 5678.

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

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

⇒ 5643 + x should exactly divisible by 460.

Now from the given options x = 797.

**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 x flowers for y dollars.

So 1 flower cost = yx

12 flowers or 1 dozen cost = 12yx

Again, x+10 cost = 2 dollars

1 flower cost = 210+x

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

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

⇒12yx−2410+x=45

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′ be the given number.

N=357k+5 = 17×21k+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: a

Explanation:

3450=23×34×51=a×b×c

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

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

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

Total ways = 10×15×3=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

**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.