Logical Reasoning · Judgment & Verbal Logic
Data Sufficiency — Questions & Answers
Data sufficiency questions ask whether the given statements are enough to answer a question — not for the answer itself. Test each statement alone, then both together.
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How to approach
Don't solve the question fully. Just ask: does this statement pin down one answer? Test I alone, then II alone, and only then both together.
Draw the row or order for each statement separately. The data is sufficient only if every possible arrangement gives the same answer.
For codes, a word is fixed only when it's the single word shared by two sentences, or all the others are known. For directions and days, work out every possibility the statement allows.
A relation needs both the family link and, for words like uncle/aunt or brother/sister, the person's gender.
5 solved Data Sufficiency questions
Question: What is Kala's age?
Statements:
I. Kala is 24 years younger than her mother.
II. Kala's mother is 50 years old.
Decide whether the statements give enough information to answer the question.Solution — answer E
Together: I gives the age gap and II the mother's age, so Kala is 50 − 24 = 26. Neither alone gives a number.
4 steps · reveal one at a timeStep 1: Evaluate Statement I
Statement I tells us that Kala is 24 years younger than her mother. This establishes a relationship between their ages, but it does not give us a specific age for either of them. We don't know the mother's age, so we cannot find Kala's age.
Step 2: Evaluate Statement II
Statement II tells us that Kala's mother is 50 years old. This gives us a specific age for the mother. However, it doesn't tell us how Kala's age relates to her mother's age, so we cannot determine Kala's age from this statement alone.
Step 3: Combine Statements I and II
When we use both statements together, we have the mother's age from Statement II (50 years) and the age difference from Statement I (Kala is 24 years younger). We can calculate Kala's age as her mother's age minus 24: 50−24=26 years.
Step 4: The answer
So the answer is (E) I and II together are needed; neither alone is sufficient. Both statements are required to find Kala's age; neither one provides enough information on its own.
Question: What is Tara's rank from the top in a class of 40?
Statements:
I. Uma is 15th from the top.
II. There are 6 students between Tara and Uma.
Which option describes the statements correctly?Solution — answer D
Not sufficient: together Tara could be 8th (above Uma) or 22nd (below Uma), because the order isn't stated.
5 steps · reveal one at a timeStep 1: Understand Statement I
Statement I tells us Uma's rank is 15th from the top. This gives us a fixed reference point for Uma within the class of 40 students.
Step 2: Understand Statement II
Statement II tells us there are 6 students between Tara and Uma. This means Tara's rank is either 7 places above Uma or 7 places below Uma in the sequence.
Step 3: Combine the statements
If Uma is 15th and there are 6 students between them, Tara could be 15−6−1=8th (above Uma) or 15+6+1=22nd (below Uma).
Step 4: Check sufficiency
Since the statements don't specify whether Tara is above or below Uma, we get two possible ranks for Tara (8th or 22nd). We cannot determine a single unique rank.
Step 5: The answer
So the answer is (D) Even I and II together are not sufficient because even with both statements, Tara's exact rank cannot be uniquely determined.
Question: In a code language, what is the code for 'rain'?
Statements:
I. 'rain falls today' is written as 'ka lo mi'.
II. 'heavy rain now' is written as 'su ka po'.
Which option describes the statements correctly?Solution — answer E
Together: 'rain' is the only word in both sentences and 'ka' the only code in both, so 'rain' = 'ka'. Each sentence alone leaves three possible codes.
4 steps · reveal one at a timeStep 1: Check Statement I
Statement I tells us 'rain falls today' is coded as 'ka lo mi'. With only this statement, the word 'rain' could correspond to 'ka', 'lo', or 'mi'. We cannot pinpoint the exact code.
Step 2: Check Statement II
Statement II tells us 'heavy rain now' is coded as 'su ka po'. Similar to Statement I, 'rain' could be 'su', 'ka', or 'po'. Neither statement alone is enough to find the code for 'rain'.
Step 3: Combine Statements
Now, let's look at both statements together. The word 'rain' is common to both sentences. The only code common to both 'ka lo mi' and 'su ka po' is 'ka'. Therefore, 'rain' must be 'ka'.
Step 4: The answer
So the answer is (E) I and II together are needed; neither alone is sufficient, because only by comparing both statements can we uniquely identify the code for 'rain'.
Question: How is Pavi related to Qadir?
Statements:
I. Pavi and Qadir are children of the same parents.
II. Pavi is a girl.
Which option describes the statements correctly?Solution — answer E
Together: they are siblings and Pavi is a girl, so she is his sister. I lacks her gender; II lacks the relationship.
4 steps · reveal one at a timeStep 1: Analyze Statement I
Statement I tells us that Pavi and Qadir share the same parents, meaning they are siblings. However, it does not reveal Pavi's gender. Pavi could be Qadir's brother or sister. So, I alone is not sufficient.
Step 2: Analyze Statement II
Statement II informs us that Pavi is a girl. This gives us Pavi's gender. But it doesn't tell us how Pavi is related to Qadir at all. Pavi could be a sister, a friend, or unrelated. So, II alone is not sufficient.
Step 3: Combine Statements
Let's consider both statements together. From Statement I, we know Pavi and Qadir are siblings. From Statement II, we know Pavi is a girl. Combining these, we can conclude that Pavi is Qadir's sister.
Step 4: The answer
So the answer is (E) I and II together are needed; neither alone is sufficient. Both pieces of information are required to determine the relationship fully.
Question: What is the value of x + y + z?
Statements:
I. x + y = 10
II. y + z = 12
III. x + z = 14
Which statements are sufficient to answer the question?Solution — answer E
All three are needed: adding them gives 2(x + y + z) = 36, so the sum is 18. Any two leave one number free.
5 steps · reveal one at a timeStep 1: Understand the Goal
The question asks for the value of the sum x+y+z. We are given three separate statements involving pairs of these variables. We need to determine which statements are sufficient to find the sum.
Step 2: Consider Two Statements
Let's try using any two statements, for example, (I) x+y=10 and (II) y+z=12. We can express x=10−y and z=12−y. Substituting these into x+y+z gives (10−y)+y+(12−y)=22−y. Since y is unknown, the sum is not uniquely determined.
Step 3: Try Another Pair
Similarly, if we use (I) x+y=10 and (III) x+z=14, we can find y=10−x and z=14−x. The sum becomes x+(10−x)+(14−x)=24−x. Again, the sum depends on an unknown variable, x. The same logic applies to statements (II) and (III).
Step 4: Use All Three Statements
Let's add all three equations together: (x+y)+(y+z)+(x+z)=10+12+14. This simplifies to 2x+2y+2z=36. We can factor out 2 to get 2(x+y+z)=36. Dividing by 2 gives x+y+z=18.
Step 5: The Answer
So the answer is (E) All three are needed. Using all three statements allows us to form a single equation that directly leads to the value of x+y+z, whereas any two statements leave one variable undetermined.
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