Practice Questions
Concept Explanation
Algebra DS items test whether equations or inequalities yield a unique value for unknowns.
Standard Answer Choices
- A — Statement I alone is sufficient; Statement II alone is not.
- B — Statement II alone is sufficient; Statement I alone is not.
- C — Both together are sufficient, neither alone.
- D — Either statement alone is sufficient.
- E — Neither alone nor together is sufficient.
Algebraic DS Focus
Count independent equations vs unknowns. Watch for quadratics giving two roots unless extra constraints apply.
DS Decision Flow
- State exactly what must be determined (number, ratio, yes/no, or comparison).
- Test Statement I alone—sufficient or insufficient?
- Test Statement II alone—sufficient or insufficient?
- If neither alone works, combine both statements.
- Choose A–E based on sufficiency; never pick a value when data do not fix it uniquely.
Common Traps in Algebra Problems
- Assuming x² = 4 gives unique x (x = ±2).
- Treating dependent equations as independent.
- Ignoring domain restrictions (positive integers, etc.).
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Q1 EasyIf 2x + 3 = 11, then x =Explanation2x = 8 ⇒ x = 4. Hence the answer is 4.
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Q2 EasyIf x + y = 10 and x − y = 2, then x =ExplanationAdding: 2x = 12 ⇒ x = 6. Hence the answer is 6.
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Q3 EasyIf 3x − 7 = 20, x =Explanation3x = 27 ⇒ x = 9. Hence the answer is 9.
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Q4 EasyProduct (x − 3)(x + 2) = 0 gives x =ExplanationEither factor zero. Hence the answer is 3 or −2.
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Q5 EasyFor “Is x > 5?” — I: x = 7; II: x − 2 = 5. DS answer?ExplanationEach gives x = 7 > 5. Hence the answer is D.
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Q6 EasyFor “What is x + y?” — I: x = 8; II: y = 12. DS answer?ExplanationNeed both values: x + y = 20. Hence the answer is C.
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Q7 MediumFor “What is x?” — I: x² = 16; II: x is positive. DS answer?ExplanationI alone: x = ±4. II alone: x > 0 but value unknown. Together: x = 4. Hence the answer is C.
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Q8 MediumFor “What is y?” — I: 2x + y = 14; II: x = 4. DS answer?Explanationy = 14 − 2x. Need x from II: y = 6. Hence the answer is C.
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Q9 MediumIf x/3 + x/6 = 5, then x =Explanationx/2 = 5 ⇒ x = 10. Hence the answer is 10.
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Q10 MediumSum of three consecutive integers is 42. Middle integer is:Explanation3n = 42 ⇒ n = 14. Hence the answer is 14.
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Q11 MediumIf 5a + 2b = 36 and a = 4, then b =Explanation20 + 2b = 36 ⇒ b = 8. Hence the answer is 8.
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Q12 MediumFor “What is x?” — I: x + y = 10; II: x − y = 2. DS answer?ExplanationTwo equations, two unknowns ⇒ x = 6. Need both. Hence the answer is C.
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Q13 HardFor “How many solutions?” — I: x² = 9; II: |x| = 3. DS answer?ExplanationEach gives x = ±3: two solutions. Hence the answer is D.
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Q14 HardIf 4x + 5y = 50 and x = y, then x =Explanation9x = 50 ⇒ x = 50/9. Hence the answer is 50/9.
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DS1 Easy
What is the value of x?
Statement I2x + 3 = 11.
Statement IIx is a positive integer less than 10.
ExplanationStatement I: x = 4. Statement II alone does not fix x. Answer: A. -
DS2 Easy
What is y?
Statement I2x + y = 14.
Statement IIx = 4.
ExplanationNeed x to find y = 6. Neither alone gives y. Answer: C.
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DS3 Easy
What is x + y?
Statement Ix = 8.
Statement IIy = 12.
ExplanationNeed both values: x + y = 20. Answer: C. -
DS4 Medium
What is the value of x?
Statement Ix² = 16.
Statement IIx is positive.
ExplanationStatement I: x = ±4. Together with II: x = 4. Answer: C.