1. For |2x − 5| = 3, what is the sum of all solutions?
Solve 2x − 5 = 3 ⇒ x = 4 and 2x − 5 = −3 ⇒ 2x = 2 ⇒ x = 1. Sum of solutions = 4 + 1 = 5.
x=4 or x=1 ⇒ sum=5
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Aptitude & Reasoning · Question Set
Algebra & Linear Equations interview questions for placements and exams.
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Aptitude & Reasoning
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Solve 2x − 5 = 3 ⇒ x = 4 and 2x − 5 = −3 ⇒ 2x = 2 ⇒ x = 1. Sum of solutions = 4 + 1 = 5.
x=4 or x=1 ⇒ sum=5
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From x − y = 1, we have x = y + 1. Substitute into 2x + 3y = 13: 2(y+1) + 3y = 13 ⇒ 5y + 2 = 13 ⇒ 5y = 11 ⇒ y = 11/5. Then x = y + 1 = 11/5 + 5/5 = 16/5.
x=y+1 ⇒ 2(y+1)+3y=13 ⇒ y=11/5 ⇒ x=16/5
aₙ = a₁ + (n−1)d = 7 + 19×3 = 7 + 57 = 64.
a20 = 7 + 19*3 = 64
From 5x − y = 7 ⇒ multiply by 2: 10x − 2y = 14. Add with 3x + 2y = 12 ⇒ 13x = 26 ⇒ x = 2.
2*(5x−y)=10x−2y; add ⇒ (3x+2y)+(10x−2y)=12+14
Add 7 to both sides to isolate the variable term: 3x = 18. Divide by 3: x = 6.
3x−7=11 ⇒ 3x=18 ⇒ x=6
Bring x-terms to one side: 3x − 2x = 3 + 5 ⇒ x = 8.
2x+3=3x−5 ⇒ x=8
Work rates add linearly. A’s rate = 1/6 job/hour; B’s rate = 1/3 job/hour. Together, 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 job per hour, so they take 2 hours for one job.
together rate = 1/6 + 1/3 = 1/2 ⇒ time = 1 ÷ (1/2) = 2 h
Total parts = 3 + 5 = 8. Larger share corresponds to 5 parts: (5/8)×560 = 350.
560 × (5/8) = 350
Expand: 6x − 15 ≤ 9 ⇒ 6x ≤ 24 ⇒ x ≤ 4.
6x−15 ≤ 9 ⇒ 6x ≤ 24 ⇒ x ≤ 4
Slope m = (y₂ − y₁)/(x₂ − x₁) = (15 − 3)/(6 − 2) = 12/4 = 3.
m = (15−3)/(6−2) = 12/4 = 3
Set y = 0 ⇒ 4x = 20 ⇒ x-intercept = 5. Set x = 0 ⇒ 5y = 20 ⇒ y-intercept = 4. Sum = 5 + 4 = 9.
x-int: (5,0); y-int: (0,4); 5+4=9
Distribute first: 3(x + 4) = 3x + 12. Distribute second: −2(x − 5) = −2x + 10. Combine like terms: (3x − 2x) + (12 + 10) = x + 22.
3x+12 − 2x+10 = (3x−2x) + (12+10) = x + 22
Use SI = (P×R×T)/100. So 600 = (P×5×3)/100 ⇒ 600 = 15P/100 ⇒ P = 600×100/15 = 4000.
P = (SI×100)/(R×T) = 600×100/(5×3) = 4000
Take LCM 12: (4x + 3x)/12 = 7 ⇒ 7x/12 = 7 ⇒ 7x = 84 ⇒ x = 12.
(x/3)+(x/4)=7 ⇒ (4x+3x)/12=7 ⇒ x=12
Translate: 2x − 7 = 11 ⇒ 2x = 18 ⇒ x = 9.
2x−7=11 ⇒ x=9
Let the numbers be x (larger) and y (smaller). Then x + y = 26 and x − y = 4. Add the equations: 2x = 30 ⇒ x = 15.
x+y=26, x−y=4 ⇒ 2x=30 ⇒ x=15
Point–slope: y − y₁ = m(x − x₁) ⇒ y − 5 = −2(x − 4) ⇒ y = −2x + 13.
y−5 = −2(x−4) ⇒ y = −2x + 13