GMAT® Official Guide 2019 Quantitative Review
Algebra Simultaneous equations
Solving the second equation for y gives
y = l -4x. Then, substituting 1 - 4x for y in
the first equation gives
2x+2(l-4x)=- 4
2x+ 2 -8x=- 4
The correct answer is D.
PS07080
Last week Jack worked 70 hours and earned $1,260.
If he earned his regular hourly wage for the first 40 hours
worked, 1 ½ times his regular hourly wage for the next
20 hours worked, and 2 times his regular hourly wage
for the remaining 10 hours worked, what was his
regular hourly wage?
(Al $7.00
(B) $14.00
(C) $18.00
(D) $22.00
(E) $31.50
Algebra , t r u
If w represents Jack's regular hourly wage, then
Jack's earnings for the week can be represented by
the sum of the following amounts, in dollars: 40w
(his earnings for the first 40 hours he worked),
(20)(1.Sw) (his earnings for the next 20 hours he
worked), and (10)(2w) (his earnings for the last
10 hours he worked). Therefore,
40w + (20)(1.Sw) + (10)(2w) = 1,260 given
90w = 1,260 add like
terms
w= 14
Jack's regular hourly wage was $14.00.
The correct answer is B.
divide both
sides by 90
PS02402
- If Mel saved more than $10 by purchasing a sweater at
a 15 percent discount, what is the smallest amount the
original price of the sweater could be, to the nearest dollar?
(A) 45
(B) 67
(C) 75
(D) 83
(E) 150
Arithmetiic; Algebra F~rcents; Inequalities;
r I i r 1£ r
Letting P be the original price of the sweater in
dollars, the given information can be expressed as
(0.15)P > 10. Solving for P gives
(0.l5)P > 10
p > _1Q_ = 1,000 = 200
0.15 15 3
P > 661.
3
Thus, to the nearest dollar, the smallest amount P
could have been is $67.
The corre,ct answer is B.
PSl3426
53. If a and bare positive integers and (2a)b = 23 , what is
the value o·f 2a 2b?
(A) 6
(B) 8
(C) 16
(D) 32
(E) 64
Algebra E p n n ,
It is given that (2a)b = 23, or 2ab = 23. Therefore,
ab= 3. Since a and bare positive integers, it
follows th:at either a = land b = 3, or a = 3
and b = l. In either case a + b = 4, and so
2a2b = 2a+b = 24 = 16.
The correct answer is C.
