Test Prep Test Prep Certifications OAT Questions & Answers

• Question 191:

  Sin(30+50) = ?

  A. cos30sin50 - sin30cos50

  B. cos80

  C. sin30cos50 + cos30sin50

  D. tan80 - cos30

  E. 2sin30cos50

  Correct Answer: C

  Sin(x + y) = sinxcosy + cosxsiny

• Question 192:

  With a standard deck, what are the odds of drawing a 8 of hearts followed by a 2 of diamonds, without replacement?

  A. 1/2652

  B. 1/2704

  C. 1/50

  D. 1/3042

  E. 1/1064

  Correct Answer: A

  The chance of drawing a 8 of hearts in a standard deck (52 cards) is simply 1/52. There is only one 8 of hearts in a deck. Without replacement of the 8 of hearts, the chance of drawing a 2 of diamonds is 1/51 (again, 51 because we did not put the 8 of hearts back in the deck, and there is only one 2 of diamonds in a deck). These 2 events are then multiplied because the questions asks for the chance of BOTH happening, not EITHER happening.

  Thus: 1/52 × 1/51 = 1/2652

• Question 193:

  The difference between one half of a number and one eighth of a number is 15. What is this number?

  A. 32

  B. 40

  C. 48

  D. 56

  E. 64

  Correct Answer: B

  Start with 32. If you half it, that is 16. One eighth of 32 is 4. Thus the difference between these numbers is

  12.

  Proceed to 40. Half of 40 = 20. One eighth of 40 is 5. Thus, the difference is 20 - 5 = 15, which is the answer.

• Question 194:

  For the following equation: 2x2 - 10x + 12 = 0, find the roots.

  A. x = 1, x = 4

  B. x = 2, x = 6

  C. x = 0, x = 1

  D. x = 2, x = 3

  E. None of the above

  Correct Answer: D

• Question 195:

  Kevin throws 3 dice. What is his probability of rolling 3 fours?

  A. 1/6

  B. 1/36

  C. 1/216

  D. 1/12

  E. 1/3

  Correct Answer: C

  Rolling 3 fours is an independent event. Chance of rolling 1 four is 1/6. So chance of rolling 3 fours is: 1/6 × 1/6 × 1/6 = 1/216

• Question 196:

  A 1-gallon bottle containing 20% apple juice is mixed with a 2-gallon bottle containing 30% apple juice. What is the percentage of apple juice in the 3-gallon mixture?

  A. 23%

  B. 27%

  C. 30%

  D. 50%

  E. 59%

  Correct Answer: B

  This question can be solved in numerous ways. If 1 gallon has 20% apple juice, it means apple juice consists of 0.2 gallons. If the 2 gallon has 30% apple juice, it means apple juice consists of 0.6 gallons. Thus, there are a total of 0.8 gallons of apple juice in the mixture of the total 3 gallons.

  Find the percentage: (0.8 gallons of apple juice / 3 total gallons) × 100 = ~27%

• Question 197:

  This figure represents the score range for 520 students who took the OAT. How many students scored 360 or more points?

  

  A. 52

  B. 104

  C. 130

  D. 234

  E. 240

  Correct Answer: A

  If 10% of test takers got a 360+ score, then find 10% of 520.

  0.10 × 520 = 52

• Question 198:

  If (3a + a) - (2b - 3) = 7, find the values for 'a' and 'b'.

  A. a = 2, b = 3

  B. a = 2, b = 4

  C. a = 4, b = 6

  D. a = 2, b = 2

  E. More than 1 answer choice is correct.

  Correct Answer: E

  The easiest way to solve these is NOT to perform step by step algebra solutions that practice test makers put in their solutions manual, but to simply (and quickly) plugin the answer choices and see if it works! Especially for a short, simple algebra problem like this one. In this scenario, both answer choices C and D work.

• Question 199:

  Three consecutive prime numbers add up to 223. What is the smallest of these numbers?

  A. 61

  B. 67

  C. 68

  D. 71

  E. 79

  Correct Answer: D

  Begin tackling these problems by first looking at the answer choices. One can eliminate `68' immediately because it is not a prime number. From there, pick an answer choice and work from there. Because the question asks for the first number in the set of 3 prime numbers, it means you pick an answer choice, and then figure out the next two prime numbers that follow it. Add them up and see if they add up to 223. With 71, the next two prime numbers will be 73 and 79. 71 + 73 + 79 = 223.

• Question 200:

  At a central bus station, Bus A travels north at a rate of 20 mph and Bus B travels east at a rate of 30 mph. How far apart, approximately, are the buses after 3 hours?

  A. 50 miles

  B. 88 miles

  C. 108 miles

  D. 120 miles

  E. 145 miles

  Correct Answer: C

  Think of this problem as figuring out the hypotenuse of a triangle. After 3 hours, Bus A will have traveled 60 miles (leg A). Bus B will have traveled 90 miles (leg B). To figure out the hypotenuse, simply use a2 + b2 = c2.

  602 + 902 = c2 3600 + 8100 = c2 11700 = c2 c = ~108 miles