Three consecutive prime numbers add up to 223. What is the smallest of these numbers?
Answer(s): 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.
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?
Answer(s): 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
Juliet is on the physics portion of her OAT. It has 40 questions to be done in 50 minutes. She has completed 20 questions in 30 minutes. How much time does she have for each remaining question?
Juliet has 20 questions remaining (40 total questions − 20 questions answered) with 20 minutes remaining (50 total minutes − 30 minutes used). Thus, she has 1 minute per question remaining.
In a classroom of 189 students, the ratio of boys to girls is 5 : 4. How many boys are there in the classroom?
The simplest way to approach these problems is to divide the total number of students (189) by the combined ‘parts’ (5 + 4 = 9). Thus 189 ÷ 9 = 21.Multiply 21 by the gender of interest ratio (5): 21 × 5 = 105 male students.For females you would multiply 21 by 4 = 84 female students.Add 105 + 84 to verify = 189.
A circle is stretched out and its circumference is increased by 10%. What is the percent increase of the area of that circle?
The circumference of a circle can be expressed with the following formula: C = 2πrNotice how this means the radius is proportional to the circumference. This means that a percentage increase in the circumference will have the same percentage increase in the radius. Thus, if the circumference increases by 10%, so does the radius. Insert a random value for the radius. For this example, 10 will be used. If we were to increase the circumference by 10%, the radius (10) must also be increased by 10%. 10% of 10 is 1, thus an additional 10% of 10 will be 11.The area of a circle can be expressed with the following formula: A = π(r2). If we insert our original radius value of 10, our area will be: π(102)= 100 π.The area of our modified and expanded circle will be: π(112)= 121 π.To find the percentage increase: [(121 π – 100 π) / (100 π)] × 100 = 21%
5 friends just got hired for a job. 4 of them will earn $12 an hour, and the fifth person will earn $3 more than the average of all five salaries. How much does the fifth person make?
Answer(s): E
Solve this algebraically. Solve for x (amount fifth person gets paid). x = [((4 × 12) + x) / 5] + 3 5x = 48 + x + 15 5x = 63 + x 4x = 63 x = 15.75The 5th friend makes $15.75. This can be confirmed by adding up all 5 people’s pay and finding the average: (12 + 12 + 12 + 12 + 15.75) / 5 = 12.75.$15.75 is $3 higher than the average of $12.75
What is the average of: 15, 25%, 1/2 and sin0?
Answer(s): B
The important part is to do these as quick as possible to leave room for the lengthier QR problems. Simply convert the numbers to 15, 0.25, 0.5 and 0. Add them up and divide by 4 to find the average.
Kevin throws 3 dice. What is his probability of rolling 3 fours?
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
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