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Using all 12 kg, let x = amount of sea water (in kg), giving salt content as 1.2 + .4x. The
amount of solution is 12 + x, so 20% salt occurs when 1.2 + .4x = .2(12 +x). Solve for x; x =
6. So we have 12 kg of 10% solution and 6 kg of 40% solution, a total of 18 kg of solution. B
x2 - 4 > 0. From graph of x2 – 4 we see that this condition is met for x values in (,2) U
(2,  ). D
Let x be the employee’s age. Their years of service are given by x – 24. x + (x – 24) = 90.
2x = 114. x = 57. 5 +7 = 12. B
15<x<24. Subtract 19.5 from all sides. -4.5<x-19.5<4.5 a.k.a. x-19.5 < 4.5. D
Since f(x) and its inverse are both functions f(a) = f(b) if and only if a = b. Therefore y =
f(y). y = -5y + 7. 6y = 7. y = 7/6. 7 + 6 = 13. A
9x – 27 = 9x – 28 cannot be true. Empty set. D
Let k = distance between Washington and New York along track, x = distance from
Washington along track, t = time in hours after 4p.m. Position x of Regional: kt/4 Position
x of Express: k – (k/3)(t – 2). Trains meet when kt/4 = k – (k/3)(t – 2). For any nonzero
value of k (which is the case here) dividing by k gives t/4 = 1 – (1/3)(t – 2). Solve for t; t =
20/7. Trains meet 20/7 hours after 4 p.m. or 6/7 hours after 6 p.m. Thus 360/7 minutes after
6p.m. which is 51 and 3/7 minutes after 6p.m. To nearest minute, 6:51 p.m. B
3 + 2 = 5. B
Average speed given by harmonic mean. 2/((1/6)+(1/12)) = 2/(3/12) = 8. A
1 dime is worth 1/10 of a dollar, so d dimes are worth d/10 dollars. B
1 foot = 12 inches. Set up a proportion where the numerators are the actual distances in feet
and the denominators are the drawing distances in inches. 1/(3/8) = x/12. Solve for x; x =
32. C
Sum of squares cannot be factored. Hence, NOTA. E
Slope of first line is (6 – 0)/(3 – 5) = -3. Slope of perpendicular is opposite reciprocal, thus
1/3. Perpendicular passes through origin so its equation is y = (1/3)x. By point-slope
method y = -3(x – 5) for first line. Solving system (preferably by substitution, but any
method works with enough manipulation) we get (4.5,1.5). C
Let x = your earnings. You keep .75x, so $12000 = .75x, therefore x =$16000. B
The set of natural numbers is a subset (all of them but 0) of the set of whole numbers, so
the union gives the larger set, the set of whole numbers. C
5 3+3 3 =8 3.D
Abscissa is x, ordinate is y. x = 2y and x + y = 3. Solve system through any method.
Solution is (2,1). D
Multiply both sides by 12 (lowest common multiple of denominators).
10(3x – 2) = 3(7x – 5). 30x – 20 = 21x – 15. 9x = 5. x = 5/9. NOTA. E
Transitive (a property of addition and multiplication). D
Must be an even number whose digits add up to a multiple of 3. 7+5+8+6+4=30, so out of
the choices it’s 75864. B
Let d be the number of dollars, e the number of euros, and k the original value of a dollar in
euros. Therefore, originally e = kd, but when the dollar drops e = .8kd. Solving the first
equation for d we have d = e/k, solving the second equation for d we have d = 1.25e/k,
which is 25% more than the original, regardless of the original exchange rate k. C
3.125 = 3125/1000 = 25/8 1/(25/8) = 8/25 8 + 25 = 33. A
Solve system of equations through any desired method. Solution is (4,7). 4(7) = 28. A
23(4) – 17(3) = 92 – 51 = 41. E
B and D are both equations of the line, but only D is in standard form. D
*5 = 5 + 5/5 = 6 = x *x = *6 = 6 + 5/6 = 41/6. B
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Dividing any real number by zero does not yield a real number. Since 0 is a real number,
real numbers are not closed under division. D
1 mile = 5280 ft, so traveling at v miles per hour means traveling at 5280v ft/hr. 1 hr =
3600 seconds, so traveling at 5280v ft/hr means traveling at (5280/3600)v ft/sec.
Simplifying 5280/3600 might be tricky, but here’s one way to do it. Divide both sides by
10 to get 528/360. Divide both sides by 6 (see question 20) to get 88/60. Divide both sides
by 4 to get 22/15. So speed, in ft/sec, is (22/15)v or 22v/15. B
Realizing that 4 = 22 and that 8 = 23 and using the rules for exponents we get
2(x – 3) = 3(2x + 7). Thus 2x – 6 = 6x + 21. -4x = 27. x = -27/4 = -6.75, NOTA. E
(3x)3 = (33)x = 27x. D