400-820-0859GMAT数学真题精选（二）
11. In a weight-lifting competition, the total weight of Joe’s two lifts was 750 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?
(A) 225
(B) 275
(C) 325
(D) 350
(E) 400
Explanation:
Let F and S be the weights, in pounds, of Joe’s first and second lifts, respectively. Then F + S = 750 and 2F = S + 300. The second equation may be written as S = 2F – 300, and 2F = 300 may be substituted for S in the first equation to get F + (2F = 300) = 750. Thus, 3F = 1,050, or F = 350 pounds. D is the correct answer.
12. One hour after Yolanda started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolanda’s walking rate was 3 miles per hour and Bob’s was 4 miles per hour, how many miles had Bob walked when they met?
(A) 24
(B) 23
(C) 22
(D) 21
(E) 19.5
Explanation:
Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 3(t + 1) miles. These distances must sum to 45 miles, so 4t + 3(t + 1) = 45, which may be solved for t as follows. 4t + 3(t + 1) = 45, 4t + 3t + 3 =45, 7t = 42, so t = 6 (hours). Therefore, Bob had walked 4t = 4(6) = 24 miles when they met. A is the correct answer.
13. The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?
(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0
Explanation:
The sum of the 6 numbers is 6(8.5) = 51.0; the sum of the 5 remaining numbers is 5(7.2)
= 36.0. Thus, the discarded number must be 51.0 – 36.0 = 15.0. E is the correct nswer.
14. In the rectangular coordinate system above, the area of ΔRST is
(A)
(B)
(C)
(D)
(E)
Explanation:
If segment RT is chosen as the base of △ RST, then the height is b, the y-coordinate of point S. Since RT = c – 1 (the difference between the x-coordinate of R and T), the area of △RST is 0.5(RT)b = 0.5(c - 1)b.
So, B is the correct answer.
15. Which of the following equations has a root in common with x
2
– 6x + 5 =
0?
(A) x
2 + 1 = 0
(B) x
2
– x – 2 =0
(C) x
2
– 10x – 5 =0
(D) 2x
2
– 2 =0
(E) x
2
– 2x – 3 =0
Explanation:
Since x2
– 6x + 5 = (x - 5)(x - 1), the roots
of x2
– 6x + 5 = 0 are 1 and 5. when these two values are substituted in each of the five choices to determine whether or not they satisfy the equation, only in D does a value satisfy the equation, namely, 2(1)2 – 2 = 0. So, D
is the correct answer.
16. One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill 3 2 of the tank?
(A)
(B)
(C)
(D)
(E)
Explanation:
Since the first pipe fills 5
1
of the tank in
one hour and the second pipe fills 3
1
of
the tank in one hour, together they fill
15
8
3
1
5
1
+ = of the tank in one hour. At
this rate, if t is the number of hours
needed to fill
3
2 of the tank, then
,
3
2
15
8
t = or
4
5 ) 8
15 (
3
2
t = = hours.
So, C is the correct answer.
