**Question 1 :**

In the sequence of numbers 1, 2, 2, 3, 3, 3,. . . [assume the pattern of one 1, two 2s, three 3s, four 4s, and so on continues], the number in the 40^{th} position will be

(A) 8 (B) 9 (C) 10 (D) 11 (E) 40

**Solution :**

By adding the numbers appearing in the sequence, we get the ending position of a particular number.

For example,

1 + 2 + 3 = 6 (3 ends at 6th place)

1 + 2 + 3 + 4 = 10 (4 ends up with 10th place)

Like this, by finding the sum of the series which gives the answer 40, we get the required number.

1 + 2 + 3 + 4 + ........... + 8

= n(n + 1)/2

= 8(8+1)/2

= 4(9) = 36

So, 8 will end up with 36th position. Next we will have 9 nines.

Hence in 40^{th} position, we will have 9.

**Question 2 :**

Each side of a square is an integral number of inches, and its area is 576 square inches. If each side of the square is increased by 1 foot, forming a new square, the area of the new square, in square inches, is

(A) 577 (B) 588 (C) 720 (D) 1,296

(E) not determined

**Solution :**

Area of square = 576 square inches

a^{2} = 576

a = 24 inches

Side length of square is 24 inches

Here the side length is increasing 1 foot.

1 foot = 12 inches

side length of new square = 24 + 12 = 36 inches

Area of new square = 36^{2} = 1296 square inches

**Question 3 :**

Let P = 18/25, Q = 5/7, and R = 3/4. Then

(A) P < Q < R (B) P < R < Q (C) Q < P < R

(D) Q < R < P (E) R < P < Q

**Solution :**

In order to compare the given fractions, we have to make the denominators same.

P = 18/25, Q = 5/7, and R = 3/4

L.C.M of 25, 7, 4 = 700

Since we dont have any common divisor, we multiply 25, 7 and 4.

P = (18/25) ⋅ (28/28) = 504/700

Q = (5/7) ⋅ (100/100) = 500/700

R = (3/4) ⋅ (175/175) = 525/700

Now, we have same denominators and we may compare the numerators.

By arranging from least to greatest, we get Q < P < R.

Hence option c is correct.

**Question 4 :**

A water container is 3/4 full. After 20 ounces of water is removed, the container is 1/4 full. How many ounces of water does a full container hold?

(A) 20 (B) 40 (C) 60 (D) 80 (E) 100

**Solution :**

Quantity of water at initial = 3/4

Quantity of water removed = 3/4 - (1/4)

= 2/4 ==> 1/2

There is 20 ounces in 1/2 of the water in the container.

So, the full container will have 40 ounces.

**Question 5 :**

For how many integer values of n will the expression (n-10) / (14-n) have a positive value?

(A) 0 (B) 1 (C) 3 (D) 4 (E) 5

**Solution :**

To get the positive value,

n - 10 > 0 and 14 - n > 0

n - 10 > 0 Adding 10 on both sides n > 10 |
14 - n > 0 Subtracting 14 on both sides -n > -14 Multiply by (-) on both sides n < 14 |

By combining the above statements, we get 10 < n < 14

Possible values of n are 11, 12, 13.

Hence there are 3 possible values.

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