Data sufficiency for RRB Group D

A data sufficiency question gives you a question and two statements. Your job is not to find the answer. Your job is to decide whether the statements give enough information to find it. That one change in the task catches people: they start solving, spend two minutes, and then pick the wrong option anyway because they mixed up the two statements.

The good news is that the topics inside these questions are the ones you already practise: ages, ranks, directions, relations, days and codes. If you can solve those, you only need a strict checking order.

The five options

The letters and wording in your paper may differ, so read the options in the first question you meet and keep their meaning in your head for the rest.

The checking order

1. Check statement I alone. Is it enough? Note yes or no.
2. Check statement II alone. Forget statement I completely while you do this.
3. If both are enough alone, the answer is (c). If only one is, it is (a) or (b).
4. Only if neither works alone, combine them. Enough together gives (d); still not enough gives (e).

Three rules that save time

Stop as soon as you know. You do not need the final number. For an age question, once you see that one unknown can be found, you are done.

A definite "No" is sufficient. If the question is "Is n divisible by 6?" and a statement lets you answer "definitely not", that statement is sufficient. Sufficient means the answer is fixed, whether it is yes or no. Candidates who miss this pick (e) too often.

Use only common facts. You may use facts everyone knows, such as a week having 7 days or a square having four equal sides. You may not invent extra facts, such as assuming a person's gender from a name or assuming numbers are whole unless told.

Worked examples

Example 1 (ages). What is P's age? I. P is twice as old as Q. II. Q is 15 years old.

• I alone: one equation, two unknowns. Not enough.
• II alone: says nothing about P. Not enough.
• Together: P = 2 × 15 = 30. Answer: (d).

Example 2 (numbers). Is the whole number x odd? I. x + 1 is even. II. 2x is even.

• I: if x + 1 is even, x must be odd. Enough.
• II: 2x is even for every whole number. Not enough.
• Answer: (a).

Example 3 (the "No" rule). Is the whole number n divisible by 6? I. n is odd. II. n is divisible by 3.

• I: no odd number is divisible by 6, so the answer is a definite No. Enough.
• II: 3 is not divisible by 6, but 6 is. The answer could go either way. Not enough.
• Answer: (a).

Example 4 (directions). In which direction is the school from the house? I. The school is 2 km north of the market. II. The market is 3 km east of the house.

• Neither alone links the school to the house.
• Together: from the house, go 3 km east, then 2 km north. The school is to the north-east of the house. Answer: (d).

Example 5 (averages). How many students are in the class? I. Their average age is 15 years. II. The total of all their ages is 600 years.

• Together: 600 ÷ 15 = 40 students. Neither alone is enough. Answer: (d).

Example 6 (ranking). How many children are in the row? I. K is 12th from the left. II. K is 8th from the right.

• Together: total = 12 + 8 − 1 = 19. Answer: (d).

Example 7 (days). On which day of the week is 10 March? I. 8 March is a Friday. II. 13 March is a Wednesday.

• I: 8 Friday, 9 Saturday, 10 Sunday. Enough.
• II: 13 Wednesday, 12 Tuesday, 11 Monday, 10 Sunday. Enough.
• Answer: (c).

Example 8 (comparison). Is P taller than R? I. P is taller than Q. II. Q is taller than R.

• I alone says nothing about R; II alone says nothing about P.
• Together: P > Q > R, so yes. Answer: (d).

Example 9 (coding). In a code language, what is the code for "rain"? I. "heavy rain today" is written "pa lo mi". II. "rain stopped today" is written "lo ta mi".

• Together, the common words are "rain" and "today", and the common codes are "lo" and "mi". But nothing tells you which code belongs to which word.
• Answer: (e).

How each topic usually behaves

Common mistakes

• Borrowing a fact from statement I while judging statement II.
• Choosing (d) when one statement alone was already enough.
• Treating "definitely No" as "not sufficient".
• Solving the whole question when you only needed to know that it can be solved.
• Assuming gender from a name, or assuming a number is a whole number when the question does not say so.

Practice set

1. What is the value of y? I. y + 5 = 12. II. y is positive.
2. What is the perimeter of a square? I. Its area is 49 cm². II. Its diagonal is 7√2 cm.
3. On which day was the meeting? I. It was the day after Tuesday. II. It was two days before Friday.
4. How is A related to B? I. A is B's only sibling. II. A is female.
5. Is x greater than 10? I. x is less than 15. II. x is greater than 12.
6. What is Q's age? I. Q is 5 years older than R. II. R is 3 years younger than S.
7. What is the speed of a train? I. It covers 180 km in 3 hours. II. It covers 60 km in one hour, at the same steady speed.
8. In a code language, what is the code for "go"? I. "go home now" is written "ki la mo". II. "come home now" is written "la mo ti".

Answers:

1. (a). I gives y = 7. II allows many values.
2. (c). Area 49 gives side 7 cm. A diagonal of 7√2 also gives side 7 cm. Either way the perimeter is 28 cm.
3. (c). Each statement alone gives Wednesday.
4. (d). I gives "sibling" but not the word; II adds the gender. Together, A is B's sister.
5. (b). II gives a definite yes. I allows 5 or 13.
6. (e). Even together, Q, R and S have no fixed value.
7. (c). Each gives 60 km/h.
8. (d). Neither alone works. Together, "home" and "now" share "la" and "mo", so "go" is "ki".

What to do next

• Learn the five options and the four-step checking order.
• Solve 15 questions over three days, saying "I alone, II alone, together" out loud for each.
• Revise the topics these questions borrow from: ranking and coding-decoding.
• Pair this topic with statements and conclusions, which trains the same "use only what is given" habit.