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SNAP Linear Equations and Polynomials Questions 2026
Linear Equations and Polynomials make up most of the Algebra questions in the SNAP Quantitative, DI & DS section, which has 20 of the paper's 60 questions in a 60-minute test. Expect 2 to 3 questions from these topics, and remember that each wrong answer costs 0.25 marks.
Linear Equations questions rest on one idea: you need as many independent equations as unknowns. Polynomials questions add another: roots and coefficients are linked, so you can often reach the answer without solving. Practise 10 to 15 questions daily, mixing word problems, root-coefficient questions, remainder theorem questions and Data Sufficiency.
SNAP Linear Equations and Polynomials Questions PDF
This PDF covers two- and three-variable equations, word problems on ages, digits and money, conditions for unique, no and infinite solutions, quadratic equations, nature of roots, sum and product of roots, the remainder and factor theorems, and a SNAP-style Data Sufficiency question, each with a step-by-step solution. Solve it timed at about one minute per question, then review where a shortcut could have saved time and which questions you should have skipped.
Download SNAP Linear Equations and Polynomials Questions PDF
How to Solve SNAP Linear Equations and Polynomials Questions
Linear Equations and Polynomials questions in SNAP rarely need heavy calculation. Most can be solved in under a minute once you spot the pattern: equations with swapped coefficients, a quadratic whose coefficients add up to zero, or a question that needs only the sum of the roots. The key is to choose the method before you start writing.
Since SNAP deducts 0.25 marks for every wrong answer, checking your answer by substituting it back into the equation is worth the few extra seconds. Here are some methods that can help you solve SNAP Linear Equations and Polynomials questions quickly and accurately:
Count equations against unknowns: If they don't match, the question usually wants a combination such as x + y, not the individual values.
Add or subtract equations: For 3x + 2y = 17 and 2x + 3y = 18, adding gives x + y = 7 and subtracting gives x − y = −1, so x = 3 and y = 4.
Plug in the options: Start with a middle option; if it is too large or too small, strike out the options on that side.
Use roots and coefficients: For α² + β² or 1/α + 1/β, find the sum and product of the roots from the coefficients instead of solving for the roots.
Check the sum of coefficients: If a + b + c = 0, one root is 1 and the other is c/a. For 3x² − 5x + 2 = 0, the roots are 1 and 2/3.
Translate word problems with care: Write each sentence as an equation before calculating. If five years ago A was three times as old as B, and in five years A will be twice as old as B, then A − 5 = 3(B − 5) and A + 5 = 2(B + 5). This gives B = 15 and A = 35. Remember that "five years ago" changes every person's age, not just one.
Use the remainder theorem for division questions: To find the remainder when x³ − 4x² + 2x + 5 is divided by (x − 2), put x = 2: 8 − 16 + 4 + 5 = 1. No long division is needed.
Substitute for a repeated expression: In (x² + x)² − 8(x² + x) + 12 = 0, let t = x² + x. The equation becomes t² − 8t + 12 = 0, so t = 2 or 6, and each value gives a simple quadratic in x.
Learn the key results by heart:
- For a₁x + b₁y = c₁ and a₂x + b₂y = c₂: unique solution if a₁/a₂ ≠ b₁/b₂; no solution if a₁/a₂ = b₁/b₂ ≠ c₁/c₂; infinitely many if all three ratios are equal
- Roots of ax² + bx + c = 0 are [−b ± √(b² − 4ac)] ÷ 2a; D = b² − 4ac > 0, = 0 or < 0 gives distinct, equal or no real roots
- Sum of roots = −b/a; product of roots = c/a
- Equation with roots α and β: x² − (α + β)x + αβ = 0
- α² + β² = (α + β)² − 2αβ; (α − β)² = (α + β)² − 4αβ; 1/α + 1/β = (α + β) ÷ αβ
- Roots are reciprocals of each other if c = a; roots are equal in size but opposite in sign if b = 0
- For ax³ + bx² + cx + d = 0: sum of roots = −b/a, sum of products taken two at a time = c/a, product of roots = −d/a
- Remainder when f(x) is divided by (x − a) is f(a); (x − a) is a factor if f(a) = 0
- ax² + bx + c has its minimum (a > 0) or maximum (a < 0) at x = −b/2a, and that value is c − b²/4a
- A two-digit number minus its reverse = 9(a − b); a two-digit number plus its reverse = 11(a + b)
Use the minimum-value shortcut: For 2x² − 8x + 3, the minimum occurs at x = 8 ÷ 4 = 2, and the minimum value is 3 − 64 ÷ 8 = −5. This is faster than completing the square.
Guess only when you can eliminate: With −0.25 for a wrong answer, guess only after ruling out at least one option.
For Data Sufficiency, do not solve fully: Check only whether a unique answer exists. A quadratic gives two values unless a statement rules one out.
Data Sufficiency example: What is the value of x? Statement 1: x² − 5x + 6 = 0. Statement 2: x > 2. Statement 1 gives x = 2 or 3, and Statement 2 gives only a range, so neither is sufficient alone. Together they fix x = 3, so both statements are needed.
Question 1
A man buys 2 apples and 3 kiwi fruits for $$₹ 37$$. If he buys 4 apples and 5 kiwi fruits for $$₹ 67$$, then what will be the total cost of 1 apple and 1 kiwi fruit?
correct answer:- 3
Question 2
The electricity bill of a certain establishment is partly fixed and partly varies with the number of units of electricity consumed. When in a certain month 540 units are consumed, the bill is ₹1800. In another month, 620 units are consumed, and the bill is ₹2040. In yet another month, 500 units are consumed. The bill for that month would be ..........
correct answer:- 1
Question 3
A multiple choice examination consists of 20 questions. The scoring is +5 for each correct answer, —2 for each incorrect answer, and 0 for each unanswered question. A student's score on the examination is 48. The maximum number of questions he could have answered correctly is
correct answer:- 2
Question 4
Three different numbers are chosen such that when each of the numbers is added to the average of the remaining two, the number 65, 69 and 76 are obtained. The average of the three original numbers is
correct answer:- 1
Question 5
On a particular day of a trade fair, 35000 visitors had visited the fair. The amount collected at the entrance counter was Rs. 9,50,000. The entrance fee was at the rate of Rs. 40 for an adult and Rs.20 for a child. If 10% of the visitors had used free passes, the number of children who visited the fair is
correct answer:- 2
Question 6
Four natural numbers, when added three at a time, give the sums 180, 197 and 208 and 222. Smallest of the four numbers is
correct answer:- 2
Question 7
If $$ a =\sqrt{8}-\sqrt{7} $$ and $$ a=\frac{1}{b} $$ then $$ \frac{a^{2}+b^{2}-3ab}{a^{2}+b^{2}+ab} $$ is equal to
correct answer:- 4
Question 8
If x+y =12 and xy = 27, x > y, then the value of $$(x^3 - y^3)$$ is:
correct answer:- 2
Question 9
The pair of linear equations 3x + y = 1 and px + 2y = 5 has no finite solution if
correct answer:- 2
Question 10
Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?
correct answer:- 2
Question 11
If$$\ x^{2}$$- 3x + 1 = 0, then the value of $$\ x^{5}+\frac{1}{x^{5}}\ $$is equal to
correct answer:- 2
Question 12
If $$x = 5 - \frac{1}{x} $$, then what is the value of $$x^{5} + \frac{1}{x^{5}}$$?
correct answer:- 3
Question 13
If $$x^{3} - y^{3} = 112$$ and $$x - y = 4$$, then what is the value of $$x^{2} + y^{2}$$?
correct answer:- 3
Question 14
If $$3x - \frac{1}{3x} = 9$$, then what is the value of $$x^{2} + \frac{x^2}{81}$$?
correct answer:- 2
Question 15
If $$x^{2} -7x + 1 = 0$$, then what is the value of $$x + \frac{1}{x}$$?
correct answer:- 1
Question 16
If $$\ \sqrt{7x+12}+\sqrt{7x-12}=3+\sqrt{33}\ $$, then what is the value of x?
correct answer:- 3
Question 17
If $$\frac{x+\sqrt{x^{2}-1}}{x-\sqrt{x^{2}-1}}+\frac{x-\sqrt{x^{2}-1}}{x+\sqrt{x^{2}-1}}$$= 62, then what is the value of $$x$$ ($$x < 0$$) ?
correct answer:- 1
Question 18
If x + y + z = 0, then what is the value of $$\frac{x^{2}}{yz}+\frac{y^{2}}{xz}+\frac{z^{2}}{xy}$$?
correct answer:- 4
Question 19
If $$\frac{a}{b}+\frac{b}{a}=2$$, then the value of a-b is:
correct answer:- 3
Question 20
If x=a(b-c), y=b(c-a), z=c(a-b), then the value of $$(\frac{x}{a})^3\ +\ (\frac{y}{b})^3\ +\ (\frac{z}{c})^3\ $$is:
correct answer:- 3
