# Data Sufficiency Questions and Answers

## Data Sufficiency Questions and Answers

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## Data Sufficiency Statements

• If data in statement I alone is sufficient to acquire the answer, but statement II alone is insufficient.
• If data in statement II alone is sufficient to acquire the answer, but the statement I alone is insufficient
• If data in both the statements together are sufficient to acquire the answer, but neither statement I and II alone is sufficient to answer the question;
• If the data in each statement individually is sufficient to acquire the answer;
• If data given in both the statement I and II are not sufficient to acquire, and more information is needed to answer the question.

### Rules

• Consider each statement as an individual statement and treat it as an independent statement.
• To solve every question, first, check the statement I and ensure that whether the answer can be acquired from the statement I alone. If a confirmed answer is developed from the first statement, then the answer will be (a) or (d).
• Now, consider the second statement. If statement II is autonomously adequate to provide the answer to the question and statement, I is not adequate to answer, then mark the option (b) or (d) as the answer.
• There is a possibility where both the statements are required to provide the answer to the question, and neither of both the statement alone has the essential information to acquire the answer. In that case, it is required to choose option (c) as the correct answer.
• After looking carefully at statement I, the options such as either A and D or B, C, and E can be eliminated immediately. This tool is very powerful and can be on every question of Data Sufficiency.

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### Practice Data Sufficiency Questions and Answers

1. What is Glory's age ?
I. Glory, Vijay and Katie are all of the similar age.
II. Total age of Vijay, Katie and Arica is 32 and Arica is as old as Vijay and Katie together.

If the data in statement I alone are sufficient to answer the question

If the data in statement I alone are sufficient to answer the question

16.16%

If the data in statement II alone are sufficient answer the question

If the data in statement II alone are sufficient answer the question

15.45%

If the data either in I or II alone are sufficient to answer the question

If the data either in I or II alone are sufficient to answer the question

11.2%

If the data in both the statements together are needed.

If the data in both the statements together are needed.

57.19%

As given in statements I and II, we have Glory = Vijay = Katie, Vijay + Katie + Arica = 32 and Arica = Vijay + Katie.

Putting Vijay + Katie = Arica in second. we get 2Arica = 32 or Arica = 16.

Thus, Vijay + Katie = 16 and Vijay = Katie. So, Vijay = Katie = 8. Thus, Glory = 8. Hence, both the statements are needed.

2. In a certain code language, ‘23’ means ‘No More and ‘79’ means ‘harmful thing’. What is the meaning of ‘9’ and ‘7’ respectively in that code?
I. ‘274’ means ‘no bad thing’
II. ‘839’ means ‘more is harmful’.

If the data in statement I alone are sufficient to answer the question

If the data in statement I alone are sufficient to answer the question

18.09%

If the data either in I or II alone are sufficient to answer the question

If the data either in I or II alone are sufficient to answer the question

35.36%

If the data in statement II alone are sufficient to answer the question

If the data in statement II alone are sufficient to answer the question

11.19%

If the data even in both the statements together are not sufficient to answer the question

If the data even in both the statements together are not sufficient to answer the question

35.36%

‘79’ means ‘harmful thing’ and ‘274’ means ‘no bad thing’. Hence common letter ‘7’ denotes ‘thing’. Hence ‘9’ is obviously ‘harmful’. So I alone can be sufficient. Also, ‘79’ is ‘harmful thing’ and ‘839’ is ‘more is harmful’ from which it can be implied that ‘9’ is ‘harmful’. Hence II alone can also be sufficient. Hence either I or II alone can be sufficient.

3. Five friends- Aka, Bka, Cka, Dka and Eka are sitting in a row. Among all who is sitting in the middle?
I. Bka is in between Eka and Cka.
II. Bka is to the right of Eka.
III. Dka is in between Aka and Eka.

I and II together

I and II together

8.58%

II and III together

II and III together

8.87%

I and III together

I and III together

15.55%

I, II and III together

I, II and III together

55.81%

Data insufficient.

Data insufficient.

11.19%

From I, the correct order is Eka, Bka, Cka or Cka, Bka, Eka.
From II, the order is Eka, Bka.
From III, the order is Aka, Dka, Eka.
Combining all the three, we get the order as: Aka, Dka, Eka, Bka, Cka.
Clearly, Eka is sitting in the middle. Thus all the three statements are required.

4. Four Subjects --- Psychology, Accounting, Arts and Zoology were taught in four successive periods of one hour each starting from 2.00 p.m. At what time was the Accounting period scheduled?
I. Arts period ended at 4.00 pm which was preceded by Zoology.
II. Psychology was scheduled in the last period.
III. Arts period was immediately followed by Accounting.

Only I

Only I

7.57%

Only I or II

Only I or II

14.46%

Only II

Only II

6.71%

II and III together.

II and III together.

15.32%

I and II together or I and III together

I and II together or I and III together

55.94%

From I and II we conclude that Arts period began at 3.00 p.m. Zoology period began at 2.00 p.m. and Psychology period began at 5.00 p.m. So, the Accounting period began at 4.00 p.m. From I and III, it is clearly seen that Arts period ended at 4.00 p.m. followed by Accounting to start at 4.00 p.m.

5. How many sons does Arjuna have?
I. Sapura and Adyta are brothers of Sassy.
II. Nubba is sister of Carmela and Adyta.
III. Nubba and Sassy are daughters of Arjuna.

I and II only.

I and II only.

9.94%

II and III together.

II and III together.

6.12%

I, II and III together

I, II and III together

44.17%

I, II, III together are not sufficient

I, II, III together are not sufficient

22.75%

I and III together

I and III together

17.02%

From I, Sapura, Adyta and Sassy are siblings.
From II, Nubba, Carmela and Adyta are siblings. It infers that Sapura, Adyta, Nubba, Carmela and Sassy are siblings. Hence option C is correct.

6. Zuber, Krishna and Amrish will distribute their profit in what proportion?
I. Zuber gets 2/5th of the profit.
II. 75% of the total investment is made by Krishna and Amrish.

If the data in statement I alone are sufficient to answer the question

If the data in statement I alone are sufficient to answer the question

13.18%

If the data in statement II alone are sufficient answer the question

If the data in statement II alone are sufficient answer the question

15.48%

If the data either in I or II alone are sufficient to answer the question

If the data either in I or II alone are sufficient to answer the question

28.03%

If the data even in both the statements together are not sufficient to answer the question

If the data even in both the statements together are not sufficient to answer the question

43.31%

Even both the statements together are not sufficient to answer the question because we don’t have total profit or amount invested information.

7. A domesticated shop sells only parrots and rabbit. If the ratio of parrots to rabbits is 3:2, how many parrots are in the domesticated shop?
I. If the number of rabbits were to double, the ratio would be 3:4.
II. If 3 rabbits were added, there would be more rabbits than parrots.

If the data in statement I alone are sufficient to answer the question

If the data in statement I alone are sufficient to answer the question

19.44%

If the data in statement II alone are sufficient answer the question

If the data in statement II alone are sufficient answer the question

15.46%

If the data either in I or II alone are sufficient to answer the question

If the data either in I or II alone are sufficient to answer the question

20.84%

If the data even in both the statements together are not sufficient to answer the question

If the data even in both the statements together are not sufficient to answer the question

44.26%

Clearly information is not sufficient. As if 3x parrots and 2x rabbits, so doubling the number of rabbits would make it 2(2x) = 4x rabbits. By statement I we have ratio as 3:4. So option (B) is not sufficient. With a ratio of 3:2, the options are 3 parrots and 2 rabbits; 6 parrots and 4 rabbits; 9 parrots and 6 rabbits; etc.
Further as per statement ii three more rabbits would tip the ratio so that there were more rabbits: 3 parrots and 2+3 rabbits. And 6 parrots and 4 + 3 rabbits = more rabbits. Clearly there are 3-4 possible solutions not a concrete one hence option D is correct.

8. If x = 5, what is value of y + z?
(A) x is the average of the set {x,y,z}
(B) xy + xz = 10

If the data in statement I alone are sufficient to answer the question

If the data in statement I alone are sufficient to answer the question

15.93%

If the data in statement II alone are sufficient answer the question

If the data in statement II alone are sufficient answer the question

28.81%

If the data either in I or II alone are sufficient to answer the question

If the data either in I or II alone are sufficient to answer the question

21.08%

If the data either in I or II together are sufficient to answer the question

If the data either in I or II together are sufficient to answer the question

13.82%

If the data even in both the statements together are not sufficient to answer the question

If the data even in both the statements together are not sufficient to answer the question

20.37%

statement I= x+y+z; 3 = 5, which means that x+y+z = 15.
We know that x = 5, so y+z must equal 10. Thus it is sufficient.
By statement II. Knowing that x = 5, this statement tells us that 5y + 5z = 10. Divide both sides by 5 to find that y + z = 2.

9. In two sides of equal length triangle XYZ, what is the measure of angle X?
I. Angle Y = 30 degrees
II. Angle Z = 120 degrees

If the data in statement I alone are sufficient to answer the question

If the data in statement I alone are sufficient to answer the question

12.53%

If the data in statement II alone are sufficient answer the question

If the data in statement II alone are sufficient answer the question

14%

If the data either in I or II together are sufficient to answer the question

If the data either in I or II together are sufficient to answer the question

53.32%

If the data even in both the statements together are not sufficient to answer the question

If the data even in both the statements together are not sufficient to answer the question

20.15%

Clearly we know that in any triangle X+Y+Z=180 degrees, and we can also say that x=y, y=z, or x=z. now if we look towards statement I, we cannot say that X = Y = 30 and Z = 120, or X = 120 and Y = Z = 30. Hence I is not sufficient.
As per statement II: we have angle z=120. So if Z is 120, then X and Y will be summation of remaining 60, and as we know that two sides must be equal, thus this will be 30 at each side.

10. What day is the 14th of a specified month?
I. Wednesday is the last day
II. 17th is the 3rd Saturday

If the data in statement I alone are sufficient to answer the question

If the data in statement I alone are sufficient to answer the question

9.51%

If the data in statement II alone are sufficient answer the question

If the data in statement II alone are sufficient answer the question

49.76%

If the data either in I or II alone are sufficient to answer the question

If the data either in I or II alone are sufficient to answer the question

21.95%

If the data even in both the statements together are not sufficient to answer the question

If the data even in both the statements together are not sufficient to answer the question

18.78%

Clearly from the statement II 17th is the 3rd Saturday and so, 14th is Wednesday.

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