Algebra
10 solved SSC CGL Quantitative Aptitude previous year questions on Algebra, each with the correct answer and a full explanation.
Q1
The sum of three numbers is 252 . If the first number is thrice the second and third number is two-third of the first, then the second number is
✓ Correct answer: c) 42
ExplanationAssume that the three numbers be a, b and c a+b+c=252 ..............................(i) Now, a=3b and using (i) & (ii), we get 3b + b + 2b = 252 6b = 252 b = 42
Q2
If the expression px3-2x2-qx+18 is completely divisible by (x2-9), then what is the ratio between p and q respectively?
✓ Correct answer: a) 1 : 9
ExplanationGiven, is completely divisible by So, is a factor of Then, x = 3, – 3 If we put values of x in given expression, we get Hence, Hence, Option A is the correct answer.
Q3
If the expression px3-qx2-7x-6 is completely divisible by x2-x-6, then what is the value of p and q respectively?
✓ Correct answer: b) 1,0
ExplanationGiven, is completely divisible by then, is a factor of So, will roots of will also be the roots of now, So, x = –2 , 3 are the roots of ….(A) If we put the value of x in Eq.(A) …..(i) and, ………(ii) on solving eq.(i) & (ii), we get Hence, Option B is the correct answer.
Q4
The difference between the cubes of two given natural numbers is 6272 , while the positive difference between the two given numbers is 8 . What is the sum of the cubes of the two given numbers?
✓ Correct answer: a) 9728
ExplanationLet, the two natural numbers are and . | | SSC As per the question, - = 6272 (x - y) ( + + xy) = 6272 x - y = 8 Taking square both sides, + - 2xy = 64 + = 64 + 2xy Put the value in equation (1) we get, (8) (64 + 2xy + xy) = 6272 512 + 24xy = 6272 24xy = 6272 - 512 xy = = 240 We know that, = = 64 + 2xy + 2xy ( from equation 3) = 64 + 4xy = 64 + 960 = 1024 x + y = 32.........(4) On solving equation (2) and (4) we get, x = 20 and y = 12 + = = 8000 + 1728= 9,728 Hence, the correct answer is (A).
Q5
The sum of the two numbers is 98 .The difference between the two numbers is 28 .Find one of the two numbers.
✓ Correct answer: d) 35
ExplanationLet, the two numbers are and where .The sum of the two numbers is 98 .(i) The difference between the two numbers is 28 .(ii) From (i) and (ii) we get, 98 63=35 One of the two numbers is35. Hence, the correct answer is (D).
Q6
The difference between the cubes of two given natural numbers is 6272 , while the positive difference between the two given numbers is 8 . What is the product of the two given numbers?
✓ Correct answer: b) 240
ExplanationLet's denote the two natural numbers as a and b, where a>b.The difference between the cubes of the two numbers is 6272: a³ - b³ = 6272 (i) The positive difference between the two numbers is 8: a - b = 8 (ii) a = b + 8 Substitute this value of a into the first equation: (b+8)³ - b³ = 6272 b³ + 24b² + 192b + 512 - b³ = 6272 24b² + 192b + 512 = 6272 24b² + 192b = 5760 b² + 8b = 240 b² + 8b + 16 = 240 + 16 (b + 4)² = 256 b + 4 = 16 b = 12 b = -20 (which is not possible as we are dealing with natural numbers) Since we are looking for positive difference, we consider b = 12, which leads to ab = 12 x 20 = 240 So, the product of the two given natural numbers is 240. Hence, option B is correct
Q7
The sum of the cubes of two given natural numbers is 9728 , while the sum of the two given numbers is32. What is the positive difference between the cubes of the two given numbers?
✓ Correct answer: a) 7272
ExplanationThe sum of the cubes of two given natural numbers is 9728 , while the sum of the two given numbers is 32 . .........(1) x + y = 32 x = 32 - y Put the value of x in equation (1) 32768 - y - 3×y×32(32 - y) + y = 9728 -3072y + 96y = - 23040 y - 32y + 240 = 0 (y - 12) (y - 20) = 20 y = 12, 20 So, x = 32 -12 = 30 Now, x - y = 9000 -1728 = 7272 Hence, the correct option is A.
Q8
For what value of m will the system of equations 17x+my+102=0 and 23x+299y+138=0 have infinite number of solutions?
✓ Correct answer: a) 221
ExplanationWe know that, When Ax+By=C and Px+Qy=R form a system of liner equation, then it has infinitely many solution if, Since the given system of linear equation is said to have an infinite number of solutions. so, According to the concept, Hence, Hence, Option A is the correct answer.
Q9
The sum of the cubes of two given natural numbers is 9728 , while the sum of the two given numbers is 32 . What is the product of the two given numbers?
✓ Correct answer: c) 240
ExplanationWe have, The sum of the cubes of two numbers (a3 + b3) is 9728 .The sum of the numbers (a + b) is32. We know that, Hence, the correct answer is (C).
Q10
The square of 72 is equal to the product of 216 and a number. Find the number.
✓ Correct answer: c) 24
ExplanationGiven that.The square of 72 is equal to the product of 216 and a number.Let, the number be .As per the question, x = Hence, the correct answer is (C).
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