Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The total distance of a road trip is 3,000 miles. Ahmad drove $\frac{3}{4}$ of the total distance and Ali drove the remainder. How many miles did Ali drive?
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Step-by-Step Explanation & Concept Rationale
The fraction of the distance driven by Ali is: \[1 - \frac{3}{4} = \frac{1}{4}\] \[\text{Ali's Distance} = \frac{1}{4} \times 3000 = 750\text{ miles}\] Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The ratio of the weight of an object on the Moon to its weight on Earth is $1 : 6$. If an astronaut weighs 180 lbs on Earth, what is his weight on the Moon?
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Step-by-Step Explanation & Concept Rationale
Using the given ratio: \[\text{Weight on Moon} = \frac{1}{6} \times \text{Weight on Earth} = \frac{1}{6} \times 180 = 30\text{ lbs}\] Thus, the correct option is (D).
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If $a : b = 6 : 7$ and $b : c = 8 : 9$, find the compound ratio $a : b : c$.
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Step-by-Step Explanation & Concept Rationale
To combine the ratios, make the term for $b$ common ($\text{LCM}(7, 8) = 56$): \[a : b = (6 \times 8) : (7 \times 8) = 48 : 56\] \[b : c = (8 \times 7) : (9 \times 7) = 56 : 63\] Therefore: \[a : b : c = 48 : 56 : 63\] Thus, the correct option is (A).
Q. 4
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The ratio of books sold by shop A to shop B is $7 : 4$, and the ratio of books sold by shop B to shop C is $5 : 3$. If shop C sold 36 books, how many books did shop A sell?
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Step-by-Step Explanation & Concept Rationale
Express the continuous ratio $A : B : C$: \[A : B = 7 : 4 = 35 : 20\] \[B : C = 5 : 3 = 20 : 12\] Thus: \[A : B : C = 35 : 20 : 12\] Given that shop C sold 36 books ($12x = 36 \implies x = 3$): \[A = 35 \times 3 = 105\] Thus, shop A sold 105 books. Thus, the correct option is (C).
Q. 5
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The subscriber counts of three channels A, B, and C are in the ratio $2 : 5 : 6$. If the total number of subscribers across all three channels is 65,000, find the combined number of subscribers for channels A and C.
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Step-by-Step Explanation & Concept Rationale
The sum of the ratio parts is: \[2 + 5 + 6 = 13\text{ parts}\] Value of one ratio part: \[\frac{65000}{13} = 5000\] The combined ratio parts for channels A and C is $2 + 6 = 8\text{ parts}$. \[\text{Combined Subscribers} = 8 \times 5000 = 40,000\] Thus, the correct option is (C).
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