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# 10 exercises GMAT word problem: proportion, ratio, rate, range

Viernes 20 de julio de 2018,

proportion, ratio, rate, range
1. 15 Java programmers, working in a constant pace, finish a web page in 3 days. If after one day, 9 programmers quit, how many more days are needed to finish the remainder of the job?
(a) 5.
(b) 2.
(c) 8.
(d) 4.
(e) 6.
2. Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 4 hours?
(a) 2.4.
(b) 3.6.
(c) 4.2.
(d) 5.5.
(e) 6.4
3.- . There are 40 students in a classroom, 9/20 of them are boys and 4/5 of them are right-handed. How many right-handed boys are there in the classroom?
(a) Between 10 and 32.
(b) Between 14 and 32.
(c) Between 10 and 18.
(d) Between 14 and 18.
(e) Between 18 and 36.
4.- In Jonathan’s pen there are 300 sheep’s. 5/6 of the sheep’s are white, 2/3 of the sheep’s have soft wool. What can’t be the number of white sheep’s that also have soft wool in the pen?
(a) 100.
(b) 200.
(c) 190.
(d) 180.
(e) 160.

5.- Ross has 40 shirts, ¾ of the shirts are green and 1/10 is without buttons.
Therefore Ross has between ___ and ___ shirts with buttons that are not green.

(a) 6 ; 10.
(b) 4 ; 25.
(c) 4 ; 10.
(d) 5 ; 25.
(e) 3 ; 10.

6.- In the Kan film festival, 50 movies were presented. 3/5 of the movies are action movies and 4/5 is science fiction movies. How many of the movies were science fiction action movies?

(a) 10.
(b) 15.
(c) 20.
(d) 30.
(e) 35.

7.- In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey’s grade at the end of the first year is 40, what will be his grade at the end of the third year?

(a) 75.
(b) 62.
(c) 80.
(d) 44.
(e) 56.

8.- The value of an “Aerosoul” stock changes according to the following method:
At the end of each month her value is doubled but due to commission the stock’s value is decreases by \$10. If the value at the beginning of January is \$A, what would be her value at the end of February?

(a) 4A – 10.
(b) 4A – 20.
(c) 4A – 30.
(d) 4A – 40.
(e) 4A – 50 .

9.- A, B, C, D and E are 5 consecutive points on a straight line. If BC = 2CD, DE = 4, AB = 5 and AC = 11, what is the length of AE?
(a) 21.
(b) 26.
(c) 30.
(d) 18.
(e) 16.

10.- If (1 < A < 3 < B), then which of the following expressions is the largest?

(a) (B+2)/(A-1).
(b) (B-2)/(A+1).
(c) A/B.
(d) (B-2)/(A-1).
(e) B/A.

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Resp: 1/a, 2/e, 3/c, 4/a, 5/a, 6/c, 7/a, 8/c, 9/d, 10/a

SOLVED

1.- The best answer is A.
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.

2.- The best answer is E.
2 carpenters build 2 desks in 2.5 hours ---> 4 carpenters build 4 desks in 2.5 hours ----> In 4 hours there are (4/2.5 = 1.6) time units. And (4 x 1.6) is 6.4 desks.
3.- The best answer is C.
There are (9/20 x 40 = 18) boys in the class. 80% of them are right-handed, meaning that (4/5 x 18 = 14.4). Answer C is the best answer.
4.- The best answer is A.
There are (5/6 x 300 = 250) white sheep’s.
There are (2/3 x 300 = 200) soft woolen sheep’s.
The maximum overlap is the size of the smallest among the groups, thus 200. The minimum overlap is (250 + 200 – 300 = 150).
Therefore the number of sheep’s can be somewhere between 150 and 200.
5.- The best answer is A.
Notice that the groups that we are looking for a overlapping are the not-green shirts and the buttoned ones. The not-green shirts are a quarter of 40, 10 shirts.
The shirts with buttons are (9/10 x 40 = 36).
The maximum overlapping is the size of the smallest group: 10.
The minimum overlapping is: 36 + 10 – 40 = 6.
So now let’s go to the option choices:
a) Sheet measuring 7*10 : Lets half the larger side"10", we get 7:5, now is 5/7 equal to 7/10. I would say pretty close- lets keep.
b) A sheet measuring 8 inches by 14 inches: Half the larger side we get, 7/8 vs 8/14: No chance of being close- eliminate
c) A sheet measuring 10 inches by 13 inches: Half the larger side we get, 6.5/10 vs 10/13: Not close- eliminate
d) A sheet measuring 3 feet by 5 feet: 2.5/3 vs 3/5 : No chance
e) A sheet measuring 5 feet by 8 feet: 4/5 vs 5/8: Not close

6.- The best answer is C.
There were (3/5 x 50 = 30) action movies.
There were (4/5 x 50 = 40) science fiction movies.
Exact overlapping is calculated by minimum overlapping method.
Therefore there are (40 + 30 – 50 = 20) movies that belong to both categories.

7.- The best answer is A.
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).

8.- The best answer is C.
At the end of January her value is 2A – 10.
At the end of February her value is (2 x (2A – 10) – 10 = 4A – 30).

9.- The best answer is D.
First, draw the line and the points.
In order to find the length of AE, find the length of CD and BC first.
BC = AC – AB = 11 – 5 = 6.
BC = 2CD  CD = 3.
AE = 5 + 6 + 3 + 4 = 18.

10.- The best answer is A.
Try some numbers and check the answers. A=2, B=4.
(a) 6/1 = 6.
(b) 2/3.
(c) 1/2.
(d) 2.
(e) 2.

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