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PRACTICE TEST 3
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PRACTICE TEST 4
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3 Is 3x greater than 100 (1) 9x = 36 1 (2) x > 001 3
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ANSWER: D To be able to answer this question, we need to know a numerical value for x, because any numerical value will give a value for 3x that is either greater or less than 100 (1) gives the value of 4 for x, so it is sufficient (3x = 81; it is not greater) (2) can be restated as 100 > 3x, so 3x cannot be greater than 100, and (2) is sufficient to answer the question
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1 In the figure above, is AB > BC (Note: Figure not necessarily drawn to scale) (1) AB > CD (2) (AD AB) > (AD BC)
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ANSWER: B Statement (1) tells us nothing about the relationship of AB to BC, so the answer cannot be A or D Statement (2), however, tells us that AB must be a smaller number than BC This gives us sufficient information to answer the question in the negative, so the answer is B Note that it does not matter whether the answer to a Data Sufficiency question is yes or no; it only matters that you have sufficient data to answer the question
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4 How many more dogs than cats are in the veterinarian s office (1) There is a total of 30 dogs and cats in the office (2) The number of cats is the square root of the number of dogs
ANSWER: C Statement (1) alone is insufficient because it does not give the breakdown between dogs and cats of the 30 animals Statement (2) alone is insufficient because the pair of numbers described could be 2 and 4, 3 and 9, 4 and 16, and so on When the two statements are combined, however, there is only one pair of numbers that can match both statements: 5 and 25 That is sufficient information to answer the question
2 A box contains 90 jelly beans, of which some are orange, some are purple, and some are black How many black jelly beans are in the box (1) There are 27 orange jelly beans (2) There are twice as many purple jelly beans as orange jelly beans
ANSWER: C (1) alone is not sufficient, because there could be 6 or 60 black jelly beans in the jar (2) alone is not sufficient, because there could be 1 orange and 2 purples, or 20 oranges and 40 purples But (1) and (2) together tell us there are 27 orange jelly beans, 54 purple jelly beans, and therefore 9 black jelly beans
PRACTICE TEST 4
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5 If p is a positive integer, and p an integer
2 0, is p + p 2p
8 If the average (arithmetic mean) of a and b is 110, and the average of b and c is 160, what is the value of a c A B C D E 220 100 100 135 It cannot be determined from the information given
(1) p is an even number
(2) p is a multiple of 3
ANSWER: A One way to verify this is to plug in even numbers; the results soon show that the result is always half of p plus 1/2, which is never an integer You could also simplify the p +1 equation to , and since an even number 2 plus 1 is always an odd number, dividing the sum by 2 will never produce an integer So statement (1) alone is sufficient Statement (2) results in integers if p is an odd multiple of 3, but in nonintegers if p is an even multiple of 3, so this statement alone is not sufficient
ANSWER: B Restate both statements as equations: a + b = 220 and b + c = 320 Subtract the second equation from the first and you get a + b - b - c = 220-320 = a - c = -100
6 A certain prosthodontist specializes in implanting gold and silver teeth in his patients mouths He charges $650 for a gold tooth and $325 for a silver tooth If his total fees for implanting gold and silver teeth last week were $15,925 in total, and he implanted five more gold teeth than silver teeth, how many teeth in total did he implant over the week A B C D E 31 32 33 34 35
9 A travel company wants to charter a plane to the Bahamas Chartering the plane costs $8,000 So far, 18 people have signed up for the trip If the company charges $300 per ticket, how many more passengers must sign up for the trip before the company can make any profit on the charter A B C D E 7 9 13 27 45
ANSWER: A It is probably easiest to approach this question by plugging in the available answers and seeing which one works If it was 31 teeth (answer A), for example, then we know that the doctor implanted 18 gold and 13 silver 18 $650 + 13 $325 = $15,925, so A is the answer
ANSWER: B $8,000 divided by $300 per person means that the company must book 2667 passengers to make a profit, so in practice this means 27 passengers 27 required minus 18 already booked means that the company must find 9 more passengers
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