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Logical Reasoningतार्किक क्षमता · आँकड़ा पर्याप्तता

Data Sufficiencyआँकड़ा पर्याप्तता questions and answersप्रश्न और उत्तर

Data sufficiency questions do not ask for the answer. They ask whether the information given is enough to find one. Bank and placement papers like them because a well-prepared candidate can settle each one in under a minute without doing the arithmetic.

  • Unlimitedअसीमित fresh questionsनए प्रश्न
  • Answersउत्तर always one tap awayहमेशा एक टैप दूर
  • 1 subtopicउप-टॉपिक
  • IBPS PO ~3
  • SSC CGL ~1
  • TCS NQT ~2

Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।

How data sufficiency worksआँकड़ा पर्याप्तता को समझिए

Always use the same order. Cover statement II and ask whether statement I alone leaves exactly one possible answer. Then cover statement I and test statement II. Combine the two only if neither works on its own; combining first is the most common way to pick “both together” when one statement was enough.

“Sufficient” means the answer is fixed, not that it is easy to compute. If a statement says a two-digit number is a perfect square divisible by 9, you can stop as soon as you see that only 36 fits; you do not need to write the number in the option.

Count unknowns and independent facts. Two people’s ages are two unknowns: a ratio is one fact, a difference is another, so each alone is insufficient but the pair together fixes both ages. Facts that repeat each other in different words do not count twice.

Tricks that save timeसमय बचाने वाली ट्रिक्स

All tricks →सभी ट्रिक्स →

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Option killerविकल्प-छँटनीRarely taughtकम सिखाई जाने वाली✓ Checked on 5 cases✓ 5 मामलों पर जाँची गई

One test kills two options

Use it when:कब इस्तेमाल करें: You have checked statement I alone and are short of time.

  1. If I alone is sufficient, the answer is “I alone” or “either”; three options are gone.
  2. If I alone is not sufficient, “I alone” and “either” are gone; test II alone next.
  3. Only if both fail alone do you combine them.
Exampleउदाहरण

Statement I alone fixes the answer. Which options remain?

→ Only “I alone is sufficient” and “either I or II is sufficient”.

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: “I alone” and “either” are exactly the two options in which statement I works by itself; the other three all say that I alone is not enough. So the result of the first test always splits the five options into two and three.

Limits:सीमाएँ: Works only with the standard five-option format. Some papers add a sixth option for “questions that need both but give contradictory data”; check the option list first.

Formulaसूत्र✓ Checked on 36 cases✓ 36 मामलों पर जाँची गई

Two ages need two independent facts

Use it when:कब इस्तेमाल करें: A data-sufficiency question asks for one person’s age and the statements talk about two people.

  1. Count unknowns: two people → two ages.
  2. A ratio alone, a sum alone or a difference alone is one fact: never sufficient.
  3. Ratio + difference, or ratio + sum, is two facts: sufficient.
Exampleउदाहरण

Age of Ravi? I: Ravi : Sita = 3 : 2. II: Ravi is 8 years older than Sita.

→ Neither alone; together 3k − 2k = 8, k = 8, Ravi is 24: “both together”.

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: Each fact is one equation in two unknowns. One equation leaves a whole line of solutions (many whole-number ages), while two different equations cross at a single point.

Limits:सीमाएँ: The two facts must be independent: “Ravi is 8 years older” and “Sita is 8 years younger” say the same thing. Very small ratios with a tiny age range can occasionally leave one whole-number answer by accident.

Exam strategyपरीक्षा रणनीति

Cover one statement with your hand

Use it when:कब इस्तेमाल करें: Every data-sufficiency question, before you start calculating.

  1. Cover statement II and judge statement I alone.
  2. Cover statement I and judge statement II alone.
  3. Only then read both together.
Exampleउदाहरण

What is the number? I: it is a two-digit multiple of 45. II: it is even.

→ I alone: only 45 or 90 — not sufficient. II alone: not sufficient. Together: 90 — “both together”.

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: Reading both statements together first makes the combined picture stick, and it becomes very hard to notice that one statement was enough on its own. Physically hiding one statement forces the fair test.

Limits:सीमाएँ: It costs a few seconds per question; with very easy statements you can do it mentally.

Solved examplesहल किए गए उदाहरण

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

  1. Example 1उदाहरण 1 · Data sufficiency (two statements, five fixed options) · Easyआसान

    Tenzin is thinking of a two-digit number. What is the number? I. It is even. II. The sum of its digits is 1.

    1. Statement I alone is sufficient, but statement II alone is not.
    2. Statement II alone is sufficient, but statement I alone is not.
    3. Either statement I alone or statement II alone is sufficient.
    4. Both statements together are sufficient, but neither alone is.
    5. Even both statements together are not sufficient.
    Answer:उत्तर: Statement II alone is sufficient, but statement I alone is not.
    1. Statement I alone still allows 10 or 12 (and more).
    2. Statement II alone fixes the answer at 10.
    3. Both together fix the answer at 10.
    4. So: Statement II alone is sufficient, but statement I alone is not.

  2. Example 2उदाहरण 2 · Data sufficiency (two statements, five fixed options) · Mediumमध्यम

    In a class in Kochi, the students are ranked by marks with no ties. How many students are in the class? I. Meera is 44th from the top. II. Meera is 9th from the bottom.

    1. Statement I alone is sufficient, but statement II alone is not.
    2. Statement II alone is sufficient, but statement I alone is not.
    3. Either statement I alone or statement II alone is sufficient.
    4. Both statements together are sufficient, but neither alone is.
    5. Even both statements together are not sufficient.
    Answer:उत्तर: Both statements together are sufficient, but neither alone is.
    1. Statement I alone still allows 44 students or 45 students (and more).
    2. Statement II alone still allows 9 students or 10 students (and more).
    3. Both together fix the answer at 52 students.
    4. So: Both statements together are sufficient, but neither alone is.

  3. Example 3उदाहरण 3 · Data sufficiency (two statements, five fixed options) · Hardकठिन

    Three villages, Chandpur, Sitapur and Madhopur, are different places. A straight road runs from Chandpur to Sitapur and another from Sitapur to Madhopur; each road runs due north–south or due east–west. In which direction is Madhopur from Chandpur? I. Going from Chandpur to Madhopur by road, you travel 4 km east and then 1 km west. II. Madhopur lies due west of Sitapur.

    1. Statement I alone is sufficient, but statement II alone is not.
    2. Statement II alone is sufficient, but statement I alone is not.
    3. Either statement I alone or statement II alone is sufficient.
    4. Both statements together are sufficient, but neither alone is.
    5. Even both statements together are not sufficient.
    Answer:उत्तर: Statement I alone is sufficient, but statement II alone is not.
    1. Statement I alone fixes the answer at east.
    2. Statement II alone still allows north-west or south-west (and more).
    3. Both together fix the answer at east.
    4. So: Statement I alone is sufficient, but statement II alone is not.

  4. Example 4उदाहरण 4 · Data sufficiency (two statements, five fixed options) · Mediumमध्यम

    Vihaan is thinking of a two-digit number. What is the number? I. Its units digit is 5 more than its tens digit. II. It lies between 25 and 32.

    1. Statement I alone is sufficient, but statement II alone is not.
    2. Statement II alone is sufficient, but statement I alone is not.
    3. Either statement I alone or statement II alone is sufficient.
    4. Both statements together are sufficient, but neither alone is.
    5. Even both statements together are not sufficient.
    Answer:उत्तर: Both statements together are sufficient, but neither alone is.
    1. Statement I alone still allows 16 or 27 (and more).
    2. Statement II alone still allows 26 or 27 (and more).
    3. Both together fix the answer at 27.
    4. So: Both statements together are sufficient, but neither alone is.

  5. Example 5उदाहरण 5 · Data sufficiency (two statements, five fixed options) · Mediumमध्यम

    Harpreet is thinking of a two-digit number. What is the number? I. Its units digit is 5 more than its tens digit. II. Its tens digit is 3.

    1. Statement I alone is sufficient, but statement II alone is not.
    2. Statement II alone is sufficient, but statement I alone is not.
    3. Either statement I alone or statement II alone is sufficient.
    4. Both statements together are sufficient, but neither alone is.
    5. Even both statements together are not sufficient.
    Answer:उत्तर: Both statements together are sufficient, but neither alone is.
    1. Statement I alone still allows 16 or 27 (and more).
    2. Statement II alone still allows 30 or 31 (and more).
    3. Both together fix the answer at 38.
    4. So: Both statements together are sufficient, but neither alone is.

  6. Example 6उदाहरण 6 · Data sufficiency (two statements, five fixed options) · Mediumमध्यम

    Tenzin is thinking of a two-digit number. What is the number? I. The product of its digits is 16. II. Its two digits are equal.

    1. Statement I alone is sufficient, but statement II alone is not.
    2. Statement II alone is sufficient, but statement I alone is not.
    3. Either statement I alone or statement II alone is sufficient.
    4. Both statements together are sufficient, but neither alone is.
    5. Even both statements together are not sufficient.
    Answer:उत्तर: Both statements together are sufficient, but neither alone is.
    1. Statement I alone still allows 28 or 44 (and more).
    2. Statement II alone still allows 11 or 22 (and more).
    3. Both together fix the answer at 44.
    4. So: Both statements together are sufficient, but neither alone is.

Common mistakesआम गलतियाँ

  • Solving the question with both statements before checking each one alone.
  • Using outside knowledge or a “typical” value that the statements do not give.
  • Treating a statement that narrows the answer to two values as sufficient.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न

What are the five standard options?

I alone is sufficient; II alone is sufficient; either one alone is sufficient; both together are needed; and even both together are not sufficient.

If statement I alone is sufficient, which options are still possible?

Only “I alone” and “either I or II”. Test statement II alone to decide between them.

Do I need to calculate the final answer?

No. You only need to know whether a single answer is forced. Stop as soon as you can see that it is (or that two answers remain).

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