Answers and Explanations to Test 1

1. Translate piece by piece into numbers. R (Roy) = Erik (E) + 4. The second equation: R = I (Iris)+ 2. The third equation: R +7 = 2(E + 7). We have three equations with three variables. Roy is 6, Iris is 4 and Erik is 2. In four years Erik would be 6 and Iris 8, the answer is 48. The correct answer is C.

2. Principal × percent interest × time = interest earned Principle × (0.09)× 1/12 = $228. Solve to find the principal (228 × 12)/0.09= $30,400. The correct answer is B.

3. The first expression is even and the second is odd, the only difference between the expressions is that the first expression has X and the second has W. So, if X is even W must be odd and the correct answer is C.

4. The area of the triangle is XY/2. Statement (1) tells us that X is a prime number, that can be even (2) or odd (3, 5, 7, etc.). Statement (2) tells us that Y is an odd integer. The multiplication of X and Y can be an odd number or an even number, thus we cannot determine if the area of the triangle is an integer or not. The correct answer is E.

5. Statement (1) is insufficient since the size of the reservoir is irrelevant. Statement (2) is sufficient since it tells us that the second tanker has the same work rate as the first. So, it will take them both half the time it took the first tanker alone. The correct answer is B.

6. 3Q is a prime number so it can be divide equally by 3Q, by 1 and by the components 3 and Q. The smallest number therefore is 3. The correct answer is C.

7. The number of green and yellow balls in the box is A+2. The total number of balls is 4A +8. The probability of taking out a green or a yellow ball is: 41842=++AA. The correct answer is D.

8. The price of the ticket is unknown. It would be most convenient to plug in 100 as the price of the ticket. A 30% discount of 100 is $30, that amount remained the same after the price of a ticket increased by 50%. The new price of a ticket is $150, so 30/150 is 20%. The correct answer is B.

9. If you square each digit {0, 1, 2,..., 8, 9}, you will see that the possible last digits for a square are 0, 1, 4, 5, 6 and 9. Thus, if the last digit of A is 8, A cannot be a square and the square root of A is not an integer. Statement (1) by itself is sufficient. Statement (2) by itself is insufficient since there are numbers that are divisible by 6 and have an integer square root and numbers divisible by 6 that do not have an integer square root. The correct answer is A.

10. We want to find the number value of Q. In statement (1) we are given the ratio between Q and T, which is not sufficient. Statement (2) can be simplified: 277277214774)2(727QTQTQTQT=⇒+=+⇒+=+⇒+=+. We can see that the same ratio is given in statement (2) also and more data is required to answer the question. Both statements give the same information. The correct answer is E.

11. From the grade 40 at the end of the first year we learn that his age is 20. At the end of the second year, he will be 21 and his grade will be (21 x 2 + ½ x 40 = 62). At the end of the third year, he will be 22 and his grade will be (22 x 2 + ½ x 62 = 75). The correct answer is D.

12. Factorize C: C = A x A x A: C can be equally divided into 1, A, A2, and A3 =C 4 numbers total. The correct answer is B.

13. Find the factors of (405) 4 and see what the largest value of X can be. 405 = 81 x 5 = 9 x 9 x 5 = 3 x 3 x 3 x 3 x 5 (405) 4 = (3 x 3 x 3 x 3 x 5) 4 = 316 x 54. The largest possible value of 3X that is still a factor of (405) 4 is the largest possible value of X and that is 316. X = 16. The correct answer is C.

14. Statement (1) is sufficient. If X2 is a fraction, X must also be a fraction. Meaning that X3 and Y will also be fractions. Statement (2) is sufficient. If X3 is a fraction then X must be greater than X3, which is also equal to Y. We get that from X > Y, so X3 and Y are fractions.
The correct answer is D.

15. Statement (1) gives us the average speed of the turtle; this statement is insufficient since the time is not given.
Statement (2) is also insufficient by itself since we don’t know what the average speed is.
Both statements combined are sufficient since we can calculate the distance
2*T=D and 3(T-40)=D, solve to get D=240 meters. The correct answer is C.

16. We are told that the stock increases its value by a constant rate and therefore we need to find some kind of pattern in order to know the value every year.
Statements (1) and (2) taken together are sufficient since they give us the percent increase of the stock from 1991 to 1992, which is 15%. The value of the stock in 1998 can be easily calculated, add 15% every year until 1998. The correct answer is C.

17. Answer D is a multiplication of two consecutive numbers, therefore one of them must be even, and an even number multiplied by a different number is an even number. The correct answer is D.

18. 25,200 x 1.1 = 27,720. 27,720 x 0.9 = 24,948. The correct answer is C.

19. Dividing the requested amount of miles by the reference amount would give us the answer in inches. 383.6 / 28 = 13.7 inches. The correct answer is C.

20. The total working days for finishing a web page are (15 x 3) 45. If after one day 9 programmers quit, only 15 working days are done and the rest of the programmers (6) Need to finish (45 – 15) 30 days of work. It will take them 5 more days. The correct answer is C.

21. Tim is traveling at twice the speed of Élan, and so will be after they double their speeds. The ratio between their velocities will always be 2:1 and the ratio between the distances they will pass will also be 2:1 or 60 miles to 30 miles. Tim will go through 60 miles. The correct answer is D.

22. In order to calculate the time it would take to complete one rotation, you need the radius and the velocity. Statement (1) provides the radius of rotation and (2) provides the velocity.
The distance the spaceship has to travel in order to complete one rotation is )000,21(22⋅⋅=⋅⋅ππR and the speed is 35 miles per second. Divide the first by the second and you’ll get the time it would take the spaceship to complete one rotation.
The correct answer is C.

23. Since we need to compare between X and Y, look at both statements together.
(1) and (2) state that: 12X = 4C = 12Y4 X = Y4.

Take Y=-1, X=1: X is bigger than Y.
Take X=1 and Y=1: X is not bigger than Y.
The answer is not distinct and therefore more data is required in order to solve the question. The correct answer E.

24. If a circle inscribers a square then the diagonal of the square is the diameter of the circle, which is sufficient to find the perimeter.
Statement (1) tells us about the square that is inscribed with out any further data.
Statement (2) gives us the perimeter, which is equal to 4 times the side of the square.
If we know the side of the square, we know its diagonal.
Both statements, taken together, are sufficient. The correct answer is C.

25. Draw the x and y-axes, then plot the points and connect them. The length of the base is 6 units [from (6, 3) to (6, -3)] and the height is 2 units [from (6, 0) to (4, 0)].
Area of a triangle = (base × height) / 2, so (6 × 2)/2 is 6. The correct answer is D.

26. [6.5] x [2/3] + [2] x 7.2 + [8.4] – 6.6 = 6 x 0 + 2 x 7.2 + 8 - 6.6 = 15.8. The correct answer is C.

27. ()()0.001610161021025144444=×===−. The correct answer is E.

28. The first digit has 7 possibilities (10 – 0,3 and 6). The other three digits have 8 possibilities each. 7*8*8*8= 3584. The correct answer is B.

29. From (1) by itself we can only learn that 90 kids have good grades. This statement is insufficient.
From (2) we can learn that there are 100 girls in the group.
Combining the statements doesn’t help much since we know nothing about the overlapping of (1) and (2) and more data is required. The correct answer is E.

30. Statement (1) tells us that 10 cans cost 4.2 dollars instead of 5 dollars and therefore the last two cans were sold for 20 cents. This statement is sufficient.
Statement (2) also tells us that the entire amount of cans cost 4.2 and therefore this statement is also sufficient. The correct answer is D.

31. From (1) we know the value of Y only, which is 1.
From (2) and (1) we know the value of all the other parameters, X = 4 and ZW = 4.
Therefore, (1) and (2) together are sufficient. The correct answer is C.

32. The phone company already created 122*122 area codes, now it can create 124*124. 1242-1222=(124+122)(124-122) = 246*2 = 492 additional codes. The correct answer is C.

33. If the average of 7 numbers is 12.2, we can solve for their sum: 7 × 12.2 = 85.4. If four of these numbers total 42.8, then by subtracting 42.8 from 85.4, we get the sum of the other three numbers, 42.6. To find the average of these three numbers, we divide their sum by their number: 42.6/3 = 14.2. The correct answer is B.

34. Statement (1) is insufficient. Take A=0 and B=0, (1) is correct yet A4 is not bigger than B4.
Take different numbers, A=6 and B=12 A4 is larger than B4.
Statement (2) is sufficient. The only possible way that A will not be larger than B is if they are both zero. (2) Claims that A <>

35. Lets look at two cases, where each one will give out different results. One of the numbers is 15 and three more are 15, 15 and 15 (with an average of 15). The sum of all the numbers should be (20 x 5 = 100). The sum of the numbers we picked up is (15 x 4 = 60) and therefore the last number should be 40 which is greater than 15. The answer in this case is 1. Take another case: One of the numbers is 15 and three more are 14, 15 and 16 (with an average of 15). In this case there will be 2 numbers over 15. More data is required. The correct answer is E.

36. Getting three red out of 4 that are taken out has 4 options (4!/(3!*1!)) each option has a probability of (1/2)4 since drawing a red or blue has a 50% chance. 4*1/16= ¼ to get three red hats. The same goes for three blue hats so ¼+¼ =1/2. The correct answer is C.

37. (2X + Y)(2Z + W) = 4XZ + 2XW + 2ZY + WY. Now, plug in this data to get: 3 + 2 x 6 = 15. The correct answer is C.