Data Sufficiency Test 1

1. If a, b and c are integers, is a - b + c  greater than a + b -c ?
   (1) b is negative
   (2) c is positive
2. What is the value of the sum of a list of n odd integers?
   (1) n = 8
   (2) The square of the number of the integers on the list is 64
3. If l and w represent the length and width of a rectangle, what is the perimeter?
   (1). 2l + w = 20
   (2) l + w = 25
4. How many of the men in a group of 100 people have brown hair?
   (1) Of the people in the group, 60 percent have brown hair
   (2) Of the people in the group, 40 are men.
5. What is the value of a² - b²?
   (1) a - b = a +2
   (2) a - b = 1/(a + b)
6. How many apples were sold at a certain market today?
   (1) A total of 100 apples were sold at the market yesterday, 10 fewer than twice the number sold today
   (2) The number of apples sold at the market yesterday was 45 more than the number sold today
7. If ab < 3, is a < 1?
   (1) b > 3
   (2) a < 3
8. A certain bottle can hold a maximum of how many liters of liquid?
   (1) The bottle currently contains 9 liters of liquid
   (2) If a liter of liquid are added to the bottle when it is half full of liquid, the amount of liquid in the bottle will increase by 1/3
9. What is the value of lxl (absolute value of x)?
   (1) x = l-xl
   (2) x² = 16
10. a, b and c are three angles of a certain triangle. What is the value of c?
    (1) a + b = 139
    (2) b + c = 108
     

Answers

1. The point is whether  a - b +c > a + b - c  OR whether  2c > 2b  OR whether  c > b.
   To answer this question (whether c > b), you have to know both c and b. Therefore both (1) and (2) are necessary. (C)
2. Sufficient data are (a) what is n (for example n = 5 or 6 or ....) and (b) what are all of the n numbers (for instance if n = 5, you still need to know a1, a2, a3, a4 and a5 so that you can find the sum of them.)
   (1) is obviously not enough.
   (2) , like (1), simply says that n = 8. (Don’t be confused with its wording!) (E)
3. The perimeter of the rectangular can be found by this simple formula: 2(l + w)
   (1) is not sufficiency.
   (2) implies that 2(l + w) = 2 x 25. Great! (B)
4. We know that we have a group of 100 people (men and women). Assuming we have m = the number of men and w = the number of women. The relationship is m + w = 100. The question wants to know B = am, when B = the number of men who have brown hair, and a = percent of such men in the group.
   (1) gives the total number of the people in the group who have brown hair. Not OK
   (2) gives m = 40. Not OK
   (1) and (2) still not enough since we need both m (from 2) and a from nowhere! (E)
5. a² - b² = (a - b)(a + b). If you face such an algebra problem, try to simplify. Also notice that either (1) or (2) is very likely to be enough.
   (1) should be left like this as you can do nothing much.
   (2) (a - b)(a + b) = 1 Great! (B)
6. You don’t have anything much from the info given. Just assuming that A = the number of apples sold today.
   (1) gives Y (the number of apples sold yesterday) = 100 and the relationship that Y = 2A - 10. That is enough to solve for A.
   (2), unlike (1), gives only the relationship that Y = 45 + A. What is Y? NOT OK. (A)
7. If you find such a problem in the problem solving section, you’re likely to substitute a few sets of numbers. But in this particular case, just try according to the conditions given.
   (1) if b > 3, try (in contrary to what the question is asking, that is, a > 1) a = 1.1, then ab = 3 x 1.1 = 3.3. This does not comply with the condition given. To be compatible with it, a > 1. OK
   (2) a < 3, then try b = 1/3 and a = 2. So ab = 2/3 < 3 but a > 1. And try b = -1/3, a = 10, ab = -10/3 < 3. See the point? We cannot conclude anything about a, that is a can be anything according to b. NOT OK (A)
8. (1) You can do absolutely nothing from this info. Skip to (2).
   (2) Seems to tell much more than expected. Relate such info as follows:
   Assuming X = the capacity of the bottle, then you see that 1 (liter) + X/2  = 1/3 of (X/2) + X/2. You can solve for X. OK (B)
9. (1) x can be anything greater than 0. So you will never know what lxl is
   (2) says that x = 2 or -2. Usually, you cannot simply tell ETS that you know that the answers are either 2 or -2. (See the instruction carefully: it says that if the question is asking for a solution, the solution must be only one, that is, it must be 2 alone or -2 alone.) However, it doesn’t ask what the solution is but what absolute of the solution is instead. You simply find that it is 2. (B)
10. Remember that a + b + c = 180
    (1) a + b = 139 then c = 180 - (a +b) = 180 - 139. Get it? OK
    (2) gives a instead of c. NOT OK (A)