Quantitative Aptitude & Reasoning
Q. Solve for x: x^2 + 6x + 9 = 0.
-
A.
x = -3
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B.
x = 3
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C.
x = 0
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D.
x = -9
Solution
This factors to (x + 3)(x + 3) = 0, so x = -3.
Correct Answer: A — x = -3
Q. Solve for y: 3y + 4 = 19.
Solution
Subtract 4 from both sides: 3y = 15. Divide by 3: y = 5.
Correct Answer: C — 5
Q. What are the roots of the equation x^2 - 5x + 6 = 0?
-
A.
1 and 6
-
B.
2 and 3
-
C.
3 and 4
-
D.
0 and 6
Solution
Factoring gives (x - 2)(x - 3) = 0, so x = 2 and x = 3.
Correct Answer: B — 2 and 3
Q. What are the solutions to the equation x^2 + 2x - 8 = 0?
-
A.
x = 2, -4
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B.
x = -2, 4
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C.
x = 4, -2
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D.
x = -4, 2
Solution
Factoring gives (x + 4)(x - 2) = 0, so x = -4 and x = 2.
Correct Answer: C — x = 4, -2
Q. What are the solutions to the equation x^2 + 4x + 4 = 0?
-
A.
x = -2
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B.
x = 2
-
C.
x = 0
-
D.
x = -4
Solution
This factors to (x + 2)(x + 2) = 0, so the double root is x = -2.
Correct Answer: A — x = -2
Solution
12 divided by 7 is 1 with a remainder of 5, so 12 mod 7 = 5.
Correct Answer: A — 5
Q. What is 15 divided by 4?
Solution
15 divided by 4 equals 3.75.
Correct Answer: A — 3.75
Solution
15 divided by 4 is 3 with a remainder of 3.
Correct Answer: C — 3
Solution
7 divided by 3 gives a remainder of 1.
Correct Answer: B — 2
Q. What is the 10th term of the arithmetic sequence 2, 5, 8, ...?
Solution
The nth term is given by 2 + (n-1) * 3. For n=10, it is 2 + 27 = 29.
Correct Answer: A — 29
Q. What is the 5th term in the arithmetic sequence 2, 5, 8, ...?
Solution
The common difference is 3. The 5th term is 2 + 4*3 = 14.
Correct Answer: A — 14
Q. What is the 5th term of the arithmetic sequence 2, 5, 8, ...?
Solution
The common difference is 3; the 5th term is 2 + 4*3 = 14.
Correct Answer: B — 14
Q. What is the 5th term of the arithmetic sequence 3, 7, 11, ...?
Solution
The common difference is 4; thus, the 5th term is 3 + 4*4 = 19.
Correct Answer: B — 19
Q. What is the 5th term of the arithmetic sequence where the first term is 2 and the common difference is 3?
Solution
The nth term is given by a_n = a_1 + (n-1)d. Here, a_5 = 2 + 4*3 = 14.
Correct Answer: B — 14
Q. What is the discriminant of the equation 2x^2 + 3x + 1 = 0?
Solution
The discriminant is b^2 - 4ac = 3^2 - 4(2)(1) = 9 - 8 = 1.
Correct Answer: A — 1
Q. What is the discriminant of the equation 2x^2 - 4x + 2 = 0?
Solution
Discriminant D = b² - 4ac = (-4)² - 4(2)(2) = 16 - 16 = 0.
Correct Answer: A — 0
Q. What is the discriminant of the equation 3x^2 + 6x + 2 = 0?
Solution
The discriminant is b^2 - 4ac = 6^2 - 4*3*2 = 36 - 24 = 12.
Correct Answer: A — 0
Q. What is the greatest common divisor (GCD) of 12 and 15?
Solution
The GCD of 12 and 15 is 3, as it is the largest number that divides both.
Correct Answer: B — 3
Q. What is the greatest common divisor (GCD) of 36 and 60?
Solution
The GCD of 36 and 60 is 12.
Correct Answer: B — 12
Q. What is the greatest common divisor (GCD) of 48 and 180?
Solution
The GCD of 48 and 180 is 12.
Correct Answer: B — 12
Q. What is the greatest common divisor (GCD) of 48 and 18?
Solution
GCD(48, 18) = 6.
Correct Answer: A — 6
Q. What is the HCF of 100 and 250?
Solution
The HCF of 100 and 250 is 50, as it is the largest number that divides both.
Correct Answer: A — 50
Q. What is the HCF of 14, 28, and 42?
Solution
The HCF of 14, 28, and 42 is 14, as it is the largest number that divides all three.
Correct Answer: A — 14
Q. What is the HCF of 24 and 36?
Solution
The HCF of 24 and 36 is 6, as it is the largest number that divides both.
Correct Answer: A — 6
Q. What is the HCF of 56, 98, and 42?
Solution
The HCF of 56, 98, and 42 is 14, as it is the largest number that divides all three.
Correct Answer: A — 14
Q. What is the HCF of 81 and 27?
Solution
The HCF of 81 and 27 is 27, as it is the largest number that divides both.
Correct Answer: A — 27
Q. What is the LCM of 12, 15, and 20?
-
A.
60
-
B.
120
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C.
180
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D.
240
Solution
The LCM of 12, 15, and 20 is 60, as it is the smallest number that is a multiple of all three.
Correct Answer: B — 120
Q. What is the LCM of 4 and 5?
Solution
The LCM of 4 and 5 is 20, as it is the smallest number that is a multiple of both.
Correct Answer: A — 10
Q. What is the LCM of 6 and 8?
Solution
The LCM of 6 and 8 is 24, as it is the smallest number that is a multiple of both.
Correct Answer: B — 24
Q. What is the LCM of 6, 8, and 12?
Solution
The LCM of 6, 8, and 12 is 24, as it is the smallest number that is a multiple of all three.
Correct Answer: A — 24
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