150 Questions • 135 Minutes • PYQ Mock Test in Hindi and English
Let the number be x.
51% of x = 714 → x = 714 × 100/51 = 1400
39% of 1400 = 0.39 × 1400 = 546
Alternative shortcut:
714 × (39 / 51) = 546
• Key trick: Find the whole number first or use direct unitary method ratios.
• This is a straightforward percentage problem frequently asked in competitive exams.
Convert fractions to decimals for easy comparison:
5/7 ≈ 0.7143
9/11 ≈ 0.8181
7/8 = 0.875
Comparing the decimal values: 0.7143 < 0.8181 < 0.875
Thus, the ascending order is: 5/7, 9/11, 7/8
Convert boundaries to a common denominator (LCM of 4 and 6 is 12, or use 60 for clean integers):
3/4 = 45/60 (0.75)
5/6 = 50/60 (0.833)
Check the option values:
1/2 = 30/60 (0.50) → Less than 3/4
2/3 = 40/60 (0.666) → Less than 3/4
4/5 = 48/60 (0.80) → Correct! Liesa exactly between 45/60 and 50/60
9/10 = 54/60 (0.90) → Greater than 5/6
Method 1: Find 20% of 80 and add it.
20% of 80 = (20 / 100) × 80 = 16
Required number = 80 + 16 = 96
Method 2: Multiplier trick:
80 × 1.20 = 96
Find the prime factorization of 675:
675 = 5 × 135 = 5 × 5 × 27 = 3 × 3 × 3 × 5 × 5
675 = 3³ × 5²
For a perfect cube, the powers of all prime factors must be multiples of 3.
3³ is already a complete triplet cube.
5² lacks one factor of 5 to become 5³.
Therefore, we must multiply by 5.
Let the three consecutive odd numbers be (n - 2), n, and (n + 2).
Sum = (n - 2) + n + (n + 2) = 15
3n = 15 → n = 5
The three numbers are 3, 5, and 7.
Their product = 3 × 5 × 7 = 105.
Let the weight of each of the initial 50 boxes be x kg.
Total weight of first group = 50x
Total weight of additional 5 boxes = 5 × 105 = 525 kg
Total combined weight equation:
50x + 525 = 55 × 95
50x + 525 = 5225
50x = 5225 - 525 = 4700
x = 4700 / 50 = 94 kg.
Let the two numbers be a and b.
Average = (a + b) / 2 = 7.5 → a + b = 15
Square root of product = √(ab) = 6 → ab = 36
We need two numbers whose sum is 15 and product is 36.
Testing options:
For 12 and 3: 12 + 3 = 15 and 12 × 3 = 36.
Matches perfectly.
Divide 75070 by 65 to find the remainder:
75070 ÷ 65 = 1154 with a remainder of 60.
To find the closest divisible multiples:
Lower multiple = 75070 - 60 = 75010 (Distance = 60)
Higher multiple = 75070 + (65 - 60) = 75070 + 5 = 75075 (Distance = 5)
Since 5 is less than 60, 75075 is the nearest number.
Annie Besant presided over the Calcutta session of the Indian National Congress in 1917, becoming its first woman president.
• Note: Sarojini Naidu was the first Indian woman president (Kanpur Session, 1925).
• Annie Besant was a prominent British socialist, theosophist, and Home Rule campaigner in India.
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