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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