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a. 729

b. 765

c. 784

d. 812

**Answer:** c. 784

**Explanation:**

Since X bags are there and each has X cartons, Total cartons = X * X = X^{2}

**Only options C and D are perfect squares.**

729 is a perfect square

But it cannot be answer as condition is that with 58 books in each bag, 13 bags are not sufficient.

58 x 13 = 754 > 729

So if 729 is the answer, 13 bags are sufficient.

So answer is **Option D = 784**

a. 132

b. 138

c. 141.2

d. 145.8

**Answer:** b. 138

**Explanation:**

Since it is a square matrix, no. of rows = No. of columns

Let number of pebbles in each row be P

∴ Number of rows = P

Total Pebbles = P x P = P^{2} = 17424

**∴ P = 132 = No. of rows**

Tip:

**To find square root of numbers -**

17424 = Last digit i.e. digit in unit's place is 4

So square root will have 2 or 8 at the end.

Now leave last 2 digits. We are left with 174.

Nearest square to 174 which is less than 174 is 169.

169 is square of 13

So the square root is 132 or 138.

Now add 13 to 169

∴ 169 + 13 = 182

174<182 so answer is 132 = smaller number

**Note -** If after addition, 174> addition,

Then answer would be the greater number i.e. 138

a. 2

b. 3

c. 6

d. 8

**Answer:** c. 6

**Explanation:**

Here, first we must find factors of 384 by simple division

----------------------

2 384

----------------------

2 192

2 96

2 48

2 24

2 12

2 6

3 3

1

----------------------

**Factors of 384 =** 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 **= 2 ^{2} x 2^{2} x 2^{2} x 2 x 3**

Here we can see that all factors are in form of squares except two factors

If we divide by extra 2 and extra 3, it will be 2

Since all factors are in form of squares, the number too will be a perfect square.

Find X.

a. 5

b. 56

c. 100

d. 131

e. None of the above

**Answer:** e. None of the above

**Explanation:**

In such scenarios, trial and error method is suitable

We know that 40^{2} = 1600

So we must start finding squares of numbers less than 40

Take 39 first

How to find 39^{2}?

Finding the square of 2 digit numbers

Example 39^{2}

Find nearest multiple of 10 from 39. Here it is 40

40 - 39 = 1

Now subtract this value i.e. 1 from 39

∴ 39 - 1 = 38

Now multiply 40 and 38

∴ 40 x 38 = 40(30 + 8) = 1200 + 320 = 1520

The value we found by subtraction earlier is 1

Add 1^{2} to 1520

∴ 39^{2} = 1520 + 1^{2} = 1521

40

39

38

Thus

So answer is

a. -38

b. -34

c. -28

d. -27

**Answer:** c. -28

**Explanation:**

(-21952)^{1/3} = ((-1)(21952))^{1/3} = (-1)^{1/3} x (21952)^{1/3} = - (21952)^{1/3}

Finding cube root of any number easily

(21952)^{1/3} = Last digit i.e. digit in unit's place is 2

Cube of 8 has 2 in unit's place.

So cube root will have 8 at the end.

Now leave last 3 digits. We are left with 21.

Nearest cube to 21 which is less than 21 is 8.

8 is cube of 2. (Cube of 3 is 27 and 27>21)

So cube root is 28.