Data Sufficiency

Question 1

What are the answer options in any DS question? And how do you interpret it?

Answer 1

Five answer choices in any DS question:
(A) Statement (1) ALONE is sufficient, but statement (2) is NOT sufficient
(B) Statement (2) ALONE is sufficient, but statement (1) is NOT sufficient
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient
(E) Statements (1) and (2) TOGETHER are NOT sufficient

It means -
(A) = 1 alone
(B) = 2 alone
(C) = both together, but not separately
(D) = each separately
(E) = nothing works

Question 2

What is the DS strategy?

Answer 2

Step 1: Separate additional info from the actual question.

Step 2: Determine whether the question is Value or Yes/No.

• Value Question:

i) asks for the value of an unknown
ii) a statement is “Sufficient” when it provides “1 possible value”
iii) a statement is “Not Sufficient” when it provides “more than 1 possible values”.

• Yes/No Question:

i) has two possible answers: Yes or No
ii) a statement is “Sufficient” when it provides a “definite Yes” or a “definite No”
iii) a statement is “Not Sufficient” when the answer is “may be / could be Yes or No”

Step 3: Decide exactly what the question is asking. Answer 2 questions -

1. What, precisely, would be sufficient?
2. What, precisely, would not be sufficient?

Step 4: Look at each statement separately & analyze whether it is sufficient alone & by itself.
• If (1) works & (2) doesn’t - Option (A)
• If (2) works & (1) doesn’t - Option (B)
• If each works on its own - Option (D)
• If neither works, go to Step 5

Step 5: Look at evreything together
• Everything together works - Option (C)
• Everything together doesn’t work - Option (E)

Question 3

If “d=0.43t7”, what digit is t?

(1) If d were rounded to the nearest hundredth, the result would be 0.44.
(2) If d were rounded to the nearest thousandth, the result would be 0.436.

Answer 3

The correct answer is B; statement 2 alone is sufficient.

Determine t, the thousandths digit of d = 0.43t7.

(1) Since d rounded to the nearest hundredth is 0.44, t can be 5, 6, 7, 8, or 9 because each of 0.4357, 0.4367, 0.4377, 0.4387, and 0.4397 rounded to the nearest hundredth is 0.44; NOT sufficient.
(2) Since d rounded to the nearest thousandth is 0.436 and the digit in ten thousandths place of d is 7, the digit in thousandths place gets increased by 1 in the rounding process. Thus, t+1=6 and t=5; SUFFICIENT.

Question 4

If i and j are integers, is “i+j” an even integer?

(1) i < 10
(2) i = j

Answer 4

The correct answer is B; statement 2 alone is sufficient.

(1) Although i<10, i could be an even integer or an odd integer less than 10. There is no information about j, so j could be an even integer or an odd integer. If i and j are both even integers, then “i+j” is an even integer, and if i and j are both odd integers, then “i+j” is an even integer. If, however, either i or j is an even integer and the other is an odd integer, then “i+j” is an odd integer; NOT sufficient.
(2) If i=j, then “i+j” can also be represented as “i+i” when i is substituted for j in the expression. This can be simplified as 2i, and since 2 times any integer produces an even integer, then “i+j” must be an even integer; SUFFICIENT