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# GMAT EXERCISES; data sufficiency, word problem. 20 items, Algebra, proportion, ratio, rate, range, data sufficiency, Word problem

Sábado 21 de julio de 2018,

Algebra, proportion, ratio, rate, range, data sufficiency, Word problem
1. In the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 86% of the students that play soccer are obviously boys. How many girl student are in Parkway that are not playing soccer?
69.
73.
81.
91.
108.

2. In the quiet town of “Nothintodo” there are 600 inhabitants, 400 are unemployed and 300 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
50.
100.
150.
200.
300.

3. In the youth summer village there are 150 people, 75 of them are not working, 50 of them have families and 100 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that doesn’t have families and that are singing in the shower?
25.
50.
75.
,100.
150.

4. In the junior basketball league there are 18 teams, 2/3 of them are bad and ½ are rich. What can’t be the number of teams that are rich and bad?
4.
6.
10.
7.
8.

5. In the third grade of Windblow School there are 108 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?
0.
6.
8.
10.
12.

6. If 1/X = 2.5, then what is the value of 1/(X – 2/3)?
2.25.
–3.5.
–3.75.
1.75.
3.75.

8. Travis is working as a programmer of IBW. Travis earns \$3,500 annually.
If Travis pays 2.5% of that amount quarterly to support groups and he paid \$525 so far, for how many years now has Travis been paying?
2.
2.5.
4.
5.5.
6.

9. Dana borrows 5500 pounds annually for her college education. If Dana gives her parents 3% of that amount back each month, how much will she still owe her parents after four years of college?
12,430.
13,640.
14,000.
14,080.
15,020.

10. Mr. Rusty owes the bank \$1,040,000, he returns \$40,000 quarterly to the bank. If the tax on the money Rusty owes is compounded quarterly by 0.25% starting before Rusty paid the first payment, how months would it take poor Rusty to reach a point where he owes the bank no more than 1 million dollars?
3.
6.
9.
12.
15.

11. Simba borrowed \$12,000 from his brothers so he can buy a new sports car. If Simba returns 4.5% of that amount every 2 weeks, after how many months Simba wouldn’t owe his brothers any more money?
8.
12.
15.
18.
20.

12. If A and B are two roots of the equation X2 –6.5X – 17, then what is the value of A x B?
15.
–18.
16.5.
–17.
22.

13. If A,B and C are roots of the equation X3 – 16X2 +48X, what is the sum of the roots?
16.
14.
17.
18.5.
22.5.

14. If R is a root of the equation X2 +3X – 54, than which of the following equations have also the root R ?
X2 – 12X +27.
X2 – 6X – 16.
X2 – 10X – 31.25.
X2 – 15X + 54.
X2 + 10X + 16.

15. If P is a root of the equation X3 +10X2 + 16X, than which of the following equations have also the root P ?
X2 – 10X +16.
X + 8.
X2 +3X – 54.
X2 – 6X – 187.
X2 + 8X - 20.

16. If X is a root of the equation a3 +8a2 – 20a, than which of the following equations Don’t have the root X as one of their roots?
X3 + 4X2 – 32X.
X2 + 18X + 80.
X2 – 12X + 20.
X2 + 5X – 14.
X2 + 10X + 16.

17. Gwen has to divide her money between her three sons. If the older brother received 65% of the total amount and the other two received the same amount of money, how much money did the median brother get?

(1) The combined amount of money of the older brother and the small one is \$45,000.

(2) The older brother received \$35,454.5.

(a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

(b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

(c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

(d)Either statement BY ITSELF is sufficient to answer the question.

(e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

18. Little Timmy spends half of his allowance on his favorite pet Din and the other half on candies. How much money did Timmy spend on Din?

(1) Din eats 1.5Kg of food every day.

(2) Timmy buys 110 gr. Of candies each day. One Kg of candies costs \$7.5.

(a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

(b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

(c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

(d)Either statement BY ITSELF is sufficient to answer the question.

(e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

19. A, B, C and D are four consecutive points on a straight line. What is the distance between A to D?

(1) AC = 6.

(2) BD = 8.

(a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

(b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

(c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

(d)Either statement BY ITSELF is sufficient to answer the question.

(e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

20. A, B, C, D and E are five consecutive points with equal spacing on a straight line. What is the distance between A to E?

(1) AB = 3.

(2) BE = 9.

(a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

(b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

(c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

(d)Either statement BY ITSELF is sufficient to answer the question.

(e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

21. A, B and C are 3 consecutive points on an arc with a constant radius. What is the distance between A and C?

(1) The radius of the arc is 25 Cm.

(2) The length of AB is 5 Cm.

(a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

(b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

(c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

(d)Either statement BY ITSELF is sufficient to answer the question.

(e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

clases personalizadas preparacion GMAT GRE SAT parte matematicas. contacto claudio hurtado, whatsapp +56999410328, correo electronico clasesgmatchile@gmail.com, sitio web www.gmatchile.cl

Resp: 1/b, 2/a, 3/c, 4/c, 5/a, 6/c, 8/b, 9/d, 10/b, 11/b, 12/d, 13/a, 14/d, 15/b, 16/e. 17/d, 18/b, 19/e, 20/d, 21/e

SOLVED

1.- The best answer is B.
There are (420 – 312 = 108) girls in Parkway.
86% of 250 are boys, therefore 14% of 250 are girls that play soccer, which is 35 girls.
The number of girls that do not play soccer is (108 – 35 = 73).

2.- The best answer is A.
There are 300 people that are not somnambulists. There are (600 – 400 = 200) people that are employed in the town, half of the somnambulists are employed (150), therefore (200 – 150 = 50) is the number of people that are employed which are also not somnambulists.

3.- The best answer is C.
The number of people that work is 75.
The number of people that doesn’t have families is (150 – 50 =100).
100 of the people like to sing in the shower.
The largest possible number of people that belong to all three groups is the smallest among them, Meaning 75.

4.- The best answer is C.
(2/3 x 18 = 12) teams are bad and 9 are rich.
The number of teams which are rich and that are bad must be between 9 and
(9+12-18 = 3).
The only answer, which is not in that range, is C.

5.- The best answer is A.
(1/3 x 108 = 36) failed the math test.
(1/6 x 108 = 18) failed that literature test.
The least amount of people that failed both tests is (18 + 36 –108 = -54), there cant be an negative Overlapping between the groups so the least amount of people who failed both tests is zero.

6.- The best answer is C.
If 1/X is 2.5 or 5/2 then X = 2/5.
1/(2/5 – 2/3) is 1/(6/15 – 10/15) = -15/4 = -3.75.

8.- The best answer is B.
Travis pays 2.5% of 3500, which is \$87.5 every 3 months (quarterly).
(525/87.5 = 6), therefore Travis has been paying for (6 x 3 = 18) months now, that is 2.5 years

9.- The best answer is D.
Dana takes 5500 each year and returns (0.03 x 5500 = 165) each month, which is (165 x 12 = 1980) each passing year. That means that each year Dana owes her parents (5500 – 1980 = 3520) pounds.
After 4 years in college she will owe them (4 x 3520 = 14,080) pounds.

10.- The best answer is B.
Every three months Rusty gives the bank \$40,000.
After the first quarter the bank took (0.0025 x 1040000 = 2600) and Rusty paid \$40,000 so the new
Debt is now (1,040,000 - 40,000 + 2,600 = 1,002,600).
After the second quarter the bank took (0.0025 x 1002600 = 2506.5) and Rusty paid again \$40,000 so the new Debt is now (1,002,600 – 40,000 + 2506.5 < 1 million dollars).

11.- The best answer is B.
Simba gives (0.045 x 12,000 = 540) to his brothers every 2 weeks, in a month he gives (540 x 2 = 1080). (12,000/1,080 is a little over 11), therefore after 12 months he won’t owe any more money.

12.- The best answer is D.
The roots of the equation are 8.5 and (-2).
The multiplication of the roots is equal to (-17).

13.- The best answer is A.
The equation can be written as: X(X2 – 16X +48) = X(X – 12)(X – 4).
The roots of the equation are: 0,4 and 12. The sum of the roots is 16.

14.- The best answer is D.
The original equation is X2 + 3X – 54, it can be written as (X – 6)(X + 9). The roots are 6 and (-9).
We are looking for an equation that has one of the same roots.
Answer D: X2 – 15X +54 = (X – 6)(X – 9)  This equation has the root 6.
All the other answers have different roots than the original equation.

15.- The best answer is B.
The original equation is X3 +10X2 + 16X, it can be written as X(X + 8)(X + 2). The roots are
(-8),0 and (-2).
We are looking for an equation that has one of the same roots.
Answer B: X + 8  This equation has the root (-8).
All the other answers have different roots than the original equation.

16.- The best answer is E.
The original equation is a3 +8a2 – 20a, it can be written as a(a – 2)(X + 10). The roots are 2,0 and (-10).
We are looking for an equation that has none of the same roots.
Answer E: X2 – 10X +16 = (X + 2)(X + 8)  This equation has none of the original roots. All the other answers have one or more of the same original roots.

17.- The best answer is D.
The data gave us the ratio of the amounts each one got (65 : 17.5 : 17.5), therefore all we need is one number to know how much each of the brothers received. Each of the statements above gives us enough information to solve the problem.

18.- The best answer is B.
From the question we know the ratio of the money that Timmy is spending on Din and on candies.
In order to know how much Timmy spends on each, we need to know one of the expanses in real
Amount of money and not in percent terms. The first statement doesn’t provide us any sufficient information but the second one gives us the exact amount of money that Timmy spends on Candies, which is equal to the amount that he spends on Din.

19.- The best answer is E.
First, draw the line with the points marked.
We know AC and BD but it’s not sufficient to know the length of AD.
If the question said the points are evenly spaced than the answer would be solvable.

20.- The best answer is D.
First, draw the line with the points marked.
Because the points are evenly spaced on the straight line, only one measurement is needed to answer the question. Both statements give us a measurement of some kind therefore each of them, by itself is sufficient.

21.- The best answer is E.
In order to know the distance between two points on an arc you need to know the angle that the points make and the radius of the arc.
Statement (1) gives us the radius.
Statement (2) gives us the length of AB, but the question didn’t mention that there is equal spacing and therefore the length of BC can’t be found with b

clases personalizadas preparacion GMAT GRE SAT parte matematicas. contacto claudio hurtado, whatsapp +56999410328, correo electronico clasesgmatchile@gmail.com, sitio web www.gmatchile.cl

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