1. If the fractions [latex]\frac {2}{5}, \frac {4}{7}, \frac {5}{9}, \frac {8}{11} and \frac {10}{13} [/latex] are arranged in descending order of their values, which one will be the fourth?

A. [latex] \frac {8}{11} [/latex] B. [latex] \frac {5}{9} [/latex] C. [latex] \frac {4}{7} [/latex] D. [latex] \frac {10}{13} [/latex]

Answer: Option B
Explanation: We will convert these given fractions into their corresponding decimal values.
[latex] \frac {2}{5} = 0.4, \frac {4}{7} = 0.57, \frac {5}{9} = 0.55 \frac {8}{11} = 0.72, \frac {10}{13} = 0.76 [/latex]
Descending order means greatesst value will come first followed by second greatest value and so....on...smallest value will come at last.
So, Descending order = 0.76, 0.72, 0.57, 0.55, 0.40
[latex]\frac {10}{13} > \frac {8}{11} > \frac {4}{7} > \frac {5}{9} > \frac {2}{5}[/latex]
2. Number obtained by interchanging the digits of a two-digit number is more than the original number by 27 and the sum of the digits is 13. What is the original number?

A. 58 B. 67 C. 76 D. 85

Answer: Option A
Explanation: Let's say the 2 digit number is xy. So in expanded form we can write this number as [latex]10x + y [/latex].
Number obtained by interchanging the digits of original.number will be [latex]10y + x [/latex]
([latex]10y + x [/latex]) = ([latex]10x + y [/latex]) + 27
[latex]\Rightarrow[/latex] [latex]10y - y [/latex] = [latex]10x - x [/latex] + 27
[latex]\Rightarrow 9y = 9x + 27[/latex]
[latex]x + 3 = y[/latex] ............1
Now sum of the digits of the number is 13 so,
[latex] x + y [/latex] = 13 ........2
on solving we get,
[latex]x = 5, y = 8[/latex]
therefore, the original number was 58, which when reversed became85
3. If the product of two successive positive integers is 3192, which is the smaller integer?
<ul>A. 52 B. 58 C. 54 D. 56
Answer: Option D
Explanation: Let the first integer be n and second one be n + 1
[latex]\Rightarrow[/latex] n(n + 1) = 3192
[latex]\Rightarrow {n}^{2}[/latex] + n - 3192 = 0
[latex]\Rightarrow {n}^{2}[/latex] + 57n - 56n - 3192 = 0
[latex]\Rightarrow[/latex] n(n + 57) - 56 (n + 57) = 0
[latex]\Rightarrow[/latex] (n + 57)(n - 56) = 0
Hence n= 56, n= - 57 is not acceptable because it is negative integer.
4. Difference between the digits of a two digit number is 5 and the digit in the unit’s place is six times the digit in the ten’s place. What is the number?

A. 27 B. 72 C. 16 D. 61

Answer: Option C
Explanation: First Condition (difference between the digits is 5) is satisfying in all the options but clearly only in 16 unit digit is 6 times the digit in the ten's place.
Alternatively,
Let the two - digit number be 'xy'.
Therefore, The digit is unit's place is six times the digit in tne ten's place [latex]\Rightarrow[/latex] y = 6x .........1
Difference between the digit is 5 [latex]\Rightarrow[/latex] y - x = 5 ..........2
Substitute equation 1 and 2
[latex]\Rightarrow[/latex] 6x - x = 5
[latex]\Rightarrow[/latex] x = 1
[latex]\Rightarrow[/latex] y = 6
therefore, Number = 16
5. Two third of three- fourth of one-fifth of a number is 15. What is 30 percent of that number?

A. 35 B. 45 C. 65 D. 30

Answer: Option B
Explanation: Let the number be a.
therefore a [latex] \times (\frac {1}{5} \times \frac {3}{4} \times \frac {2}{3}) = 15 [/latex]
[latex]\Rightarrow[/latex] a = 150
therefore, 30 % of 150 = [latex]\frac {(150 \times 30)} {100}[/latex] = 45

1. 32, ?, 1024, 2048, 2048

A. 324 B. 256 C. 224 D. 326

Answer: Option B
Explanation: [latex] 32 \times 8 [/latex] = 256
[latex] 256 \times 4 [/latex] = 1024
[latex] 1024 \times 2 [/latex] = 2048
2. 9, 5, 6, 10.5, 23 ?

A. 50 B. 65 C. 70 D. 60

Answer: Option D
Explanation: [latex] 9 \times 0.5 + 0.5 [/latex] = 5
[latex] 5 \times 1 + 1 [/latex] = 6
[latex] 6 \times 1.5 + 1.5 [/latex] = 10.5
[latex] 10.5 \times 2 + 2 [/latex] = 23
[latex] 23 \times 2.5 + 2.5 [/latex] = 60
3. 17, 98, 26, ?, 35, 80

A. 79 B. 69 C. 89 D. 59

Answer: Option C
Explanation: 26 - 17 = 9; 35 – 26 = 9
98 – 9 = 89
4. 2, 17, 89, 359, 1079, ?

A. 2143 B. 2152 C. 2169 D. 2159

Answer: Option D
Explanation: [latex] 2 \times 6 + 5 [/latex] = 17
[latex] 17 \times 5 + 4 [/latex] = 89
[latex] 89 \times 4 + 3 [/latex] = 359
[latex] 359 \times 3 + 2 [/latex] = 1079
[latex] 1079 \times 2 + 1 [/latex] = 2159
5. 7, 4.5 ,5.5, 12, 49,?

A. 393 B. 351 C. 362 D. 375

Answer: Option A
Explanation: [latex] 7 \times 0.5 + 1 [/latex] = 4.5.
[latex] 4.5 \times 1 + 1 [/latex] = 5.5.
[latex] 5.5 \times 2 + 1 [/latex] = 12.
[latex] 12 \times 4 + 1 [/latex] = 49.
[latex] 49 \times 8 + 1 [/latex] = 393.

Directions for Questions (1 - 5): Study the following arrangement carefully and answer the question given below:
A, B, >, &, 1, 3, 5, Q, P, #, ?, C, 2, 4, E, Z, U, V, 6, *, !, 8, F, +, -, 7, J, K, 9, /, @, 0, O, L, R
1. How many such numbers are there in the above arrangement each of which is immediately preceded by a number and also immediately followed by a number?

A. 1 B. 2 C. 4 D. 3 E. 5

Answer: Option A
Explanation:
The pattern is:-
Number – Number – Number
A, B, >, &, 1, 3, 5, Q, P, #, ?, C, 2, 4, E, Z, U, V, 6, *, !, 8, F, +, -, 7, J, K, 9, /, @, 0, O, L, R
Total pairs = 1 (135)
2. Which of the following is tenth to the right of tenth from the left end?

A. * B. V C. 6 D. ! E. 8

Answer: Option A
Explanation:
Required character = 10 + 10 = 20th
* is 20th from the left end.
3. How many such vowels are there in the above arrangement each of which is immediately preceded by a number and also immediately followed by a consonant?

A. 4 B. 1 C. 2 D. 3 E. 5

Answer: Option C
Explanation:
The pattern is:-
Number ---- Vowel ---- Consonant
A, B, >, &, 1, 3, 5, Q, P, #, ?, C, 2, 4, E, Z, U, V, 6, *, !, 8, F, +, -, 7, J, K, 9, /, @, 0, O, L, R Total pairs = 2 (4EZ, 0OL)
4. Which of the following is ninth to the right of twenty-fifth from the right end?

A. ! B. 8 C. * D. 6 E. V

Answer: Option C
Explanation:
Required character = 25 - 9 = 16th
* is 16th from the right end.
5. If all numbers are dropped from the above arrangement, which of the following will be seventh from the left end?

A. B B. # C. ? D. C E. E

Answer: Option B
Explanation:
After dropping numbers, the pattern observed is;
P, Q, >, &, A, B, #
# is seventh from the left end.