Answers to the 25 tough GMAT Quants question.
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Answers:-
1. n = 79
2. E
3. 3
4. 35
5. D
6. A
7. B
8. E
9. D
10. A
11. B
12. B
13. C
14. B
15. 2/5
16. C
17. 33.5K
18. 40320, 5040, 6!*3!, 8!- 6!3!, 4X720
19. B
20. A
21. E
22. C
23. E
24. A
25. C
Following are some of the tough Quants and this set includes very good questions on probability, permutation and combination. Feel free to contact us if you find any doubt in this GMAT tough Quants question set
1. The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?
2. The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?(A) $4.50
(B) $5.10
(C) $5.30
(D) $5.50
(E) $5.60
3. How many randomly assembled people does u need to have a better than 50% prob. that at least 1 of them was born in a leap year?
4. In a basketball contest, players must make 10 free throws. Assuming a player has 90% chance of making each of his shots, how likely is it that he will make all of his first 10 shots?
5. AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?(A) 1(B) 3(C) 7(D) 9(E) Cannot be determined
6. A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
7. A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) ¾
8. A person buys a share for $ 50 and sells it for $ 52 after a year. What is the total profit made by him from the share?
(I) A company pays annual dividend
(II) The rate of dividend is 25%
(A) Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
(B) Statement (II) ALONE is sufficient, but statement (I) is not sufficient
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
(D) Each statement ALONE is sufficient
(E) Statements (I) and (II) TOGETHER are NOT sufficient
9. A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?
(A) 2/27
(B) 1/9
(C) 1/3
(D) 4/27
(E) 2/9
10. What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y = 3/4*x - 3?A) 1.4
B) sqrt (2)
C) 1.7
D) sqrt (3)
E) 2.0
11. In the square above, 12w = 3x = 4y. What fractional part of the square is shaded?
A) 2/3B) 14/25C) 5/9D) 11/25E) 3/7
12. The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the possible maximum range of the temperatures?
a) 20
b) 25
c) 40
d) 45
e) 75
13. If n is an integer from 1 to 96, what is the probability for n*(n+1)*(n+2) being divisible by 8?A) 25%
B) 50%
C) 62.5%
D) 72.5%
E) 75%
14. krut , a painter, has 9 jars of paint:
4 are yellow
2 are red
rest are brown
Kurt will combine 3 jars of paint into a new container to make a new color, which he will name accordingly to the following conditions:Brun Y if the paint contains 2 jars of brown paint and no yellow
Brun X if the paint contains 3 jars of brown paint
Jaune X if the paint contains at least 2 jars of yellow
Jaune Y if the paint contains exactly 1 jar of yellow
What is the probability that the new color will be Jaunea) 5/42
b) 37/42
c) 1/21
d) 4/9
e) 5/9
15. TWO couples and a single person are to be seated on 5 chairs such that no couple is seated next to each other. What is the probability of the above?16. An express train traveled at an average speed of 100 kilometers per hour, stopping for 3 minutes after every 75 kilometers. A local train traveled at an average speed of 50 kilometers, stopping for 1 minute after every 25 kilometers. If the trains began traveling at the same time, how many kilometers did the local train travel in the time it took the express train to travel 600 kilometers?a. 300
b. 305
c. 307.5
d. 1200
e. 1236
17. An express train traveled at an average speed of 100 kilometers per hour, stopping for 3 minutes after every 75 kilometers. A local train traveled at an average speed of 50 kilometers, stopping for 1 minute after every 25 kilometers. If the trains began traveling at the same time, how many kilometers did the local train travel in the time it took the express train to travel 600 kilometers?a. 300
b. 305
c. 307.5
d. 1200
e. 1236
18. On how many ways can the letters of the word "COMPUTER" be arranged?
a) Without any restrictions.
b) M must always occur at the third place.
c) All the vowels are together.
d) All the vowels are never together.
e) Vowels occupy the even positions.
19. In the infinite sequence A, ,where x is a positive integer constant. For what value of n is the ratio of to equal to ?(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
20. In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present?
a. (13^4) x 48 x 47
b. (13^4) x 27 x 47
c. 48C6
d. 13^4
e. (13^4) x 48C6
21. Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
A) 3
B) 4
C) 5
D) 6
E) 7
22. Two missiles are launched simultaneously. Missile 1 launches at a speed of x miles per hour, increasing its speed by a factor of every 10 minutes (so that after 10 minutes its speed is , after 20 minutes its speed is , and so forth. Missile 2 launches at a speed of y miles per hour, doubling its speed every 10 minutes. After 1 hour, is the speed of Missile 1 greater than that of Missile 2?1) 2)(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.
23. . If ((13!)^16 - (13!)^8)/ ((13!)^8 + (13!)^4) = a, what is the unit’s digit of a/ ((13!)^4)?(A) 0
(B) 1
(C) 3
(D) 5
(E) 9
24. The dimensions of a rectangular floor are 16 feet by 20 feet. When a rectangular rug is placed on the floor, a strip of floor 3 feet wide is exposed on all sides. What are the dimensions of the rug, in feet?(A) 10 by 14 (B) 10 by 17 (C) 13 by 14 (D) 13 by 17 (E) 14 by 16
25. How many different subsets of the set {10,14,17,24} are there that contain an odd number of elements?(a) 3 (b) 6 (c) 8 (d) 10 (e) 12
DATA SUFFICIENCY (DS)
Data Sufficiency (DS) is a part of the quantitative section on the GMAT exam. As the name suggests you have to find out whether the given data is sufficient to answer the question or no. The data sufficiency question in GMAT exam is slightly different from the regular CAT data sufficiency question. It is comparatively more tricky and forms a major part of the quantitative section on GMAT.
The data sufficiency (DS) problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your
knowledge of mathematics and everyday facts, you must indicate whether
A. statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the
question asked;
B. statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the
question asked;
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but
NEITHER statement ALONE is sufficient;
D. EACH statement ALONE is sufficient to answer the question asked;
E. BOTH statements (1) and (2) TOGETHER are not sufficient to answer the question asked;
The easiest way to solve this question and to avoid any confusion is to take one statement at a time. There are two parts to this questions. One is the data that is already given and the other partial data given in statements (1) and (2).
Now you have to imagine that say statement (2) does not exist and only statement (1) does. Will you able to solve the given problem now? Let me give you an example here :
1. At a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?
(1) At the picnic, 60 percent of the guests were served a double scoop of ice scream.
(2) A total of 120 scoops of ice cream were served to all the guests at the picnic.
The question asks you how many guests got a double scoop. The information you already have is that there were only two type of scoops : double and single.
Now just cover up statement (2) and see if the information in (1) is enough to answer this question. You can see that it gives only a percentage and total number of people is unknown. Hence (1) is not sufficient to answer this question.
For the same example now cover up statement (1) and see if you can answer the question. Again you can easily see that (2) gives only the total number of ice creams served. Therefore (2) also is not sufficient to answer this question.
Now see if you can answer the question using both (1) and (2). Viola!!! you can.
(1) gives you the percentage being served one kind of ice cream and (2) gives you the total number of ice creams. Using these two you can find the number of ice creams of both kinds and answer the question.
Therefore, your answer would be C.
Remember you are not supposed to find the answer in DS questions. Hence don't go about solving the whole problem and waste your time. The key is to just plug in the data given and see if you can solve for a single variable. To achieve sufficiency, there must be as many equations as there are variables.
TIPS and TRICKS for DS :
(1) Person C got 49% of the vote.
(2) Person A got 25,000 of the 100,000 votes cast.
Most people would assume here that there are only 2 persons A and C and take (1) as sufficient. Be very careful with such type of questions and do not make this mistake of assuming the data not given.
On YES/NO DS questions, if a statement answers the
question conclusively in the affirmative or in the
negative, then IT IS SUFFICIENT.
Example :
Is it true that a>b?
(1) 2a > 2b
(2) a + c > b + c
You can see that both (1) and (2) can answer this question independently. Hence you should not care about any real values here. I am assuming you would be able to solve this on your own and hence not putting the explanation here.
These tricks really helped me in scoring well on DS and I hope they would be useful for you too.
To download problems for DS you can go to the download section of the blog. It contains more than enough for you to get good practice on this section! All problems come with detailed solutions and in case you find any difficulty understanding any problem you can always ping me!
Currently the download section is not ready but if you need the material immediately you can ping me again!
GMAT is an aptitude test conducted worldwide as a selection criteria for entrance into many B schools. It is a computer adaptive multiple choice test. By adaptive i mean that based on your answer to a previous question, right or wrong, your next question will be tougher or easier. The GMAT consists of 3 sections :
1. Verbal
2. Quantitative
3. Analytical Writing
The GMAT is a three-and-one-half hour computer adaptive test (CAT). The exam time is divided as follows:
| Section | Time | |
| Writing | Analysis of Issue Essay | 30 minutes |
| Writing | Analysis of Argument Essay | 30 minutes |
| Math | 37 Questions | 75 minutes |
| Verbal | 41 Questions | 75 minutes |
-Which of the following, if true, would most weaken the author’s assertion?
B. as if to indicate
C. indicative of
D. to indicate that
E. like an indication of
The correct answer here is D according to standard English rules that I will talk about in my later posts. Remember that in SC questions the first option will always be the repetition of the exact phrase in the given sentence. It may or may not be correct. There would be questions where the given phrase is the correct phrase.
Critical Reasoning
This question on the verbal section of the GMAT tests your logic and reasoning skills. It tests whether you can understand a given set of logically connected sentences and can draw inferences based on them.
You could be asked to draw conclusions, evaluate underlying assumptions, point out any erroneous argument, correct an argument, analyze the given options and see if any of them strengthen/weaken the argument.
Let me give you a simple example here to help you understand this section better.
Monthly employee evaluations are an excellent tool for managers. With them, employees that are not productive can be removed from the company, and efficient workers rewarded, and all within the space of a month.
B Unproductive employees often refuse to co-operate with the managers doing the evaluations, because they see these evaluations as a violation of their privacy.
C Most studies indicate that employee evaluations have no bearing whatsoever on worker satisfaction.
D Evaluations can identify with some accuracy whether an employee is productive or not.
E Employee evaluations are a better source of information about employee grievances than are monthly staff meetings.
The correct answer for the above question is D. Now lets understand how.
6. If ∠XYZ in the figure above is a right angle, what is the value of x? (A) 155
(B) 145
(C) 135
(D) 125
(E) 110
The answer is B - 145. This was a very basic question but you might get some tricky questions on your actual GMAT paper. More on that in the detailed section later.
Let me now give you an example of a DS type of question. You will be provided with some data in the main question and some partial data in two separate options. Now you have to check whether you can answer the main question with the help of these two sub options. The question can be answered with both options exclusively, with any one of them, both of them put together or by none of them. Thats exactly what you need to find out in this question.
Here is the example :
A. statement (1) ALONE is sufficient, but statement (2) alone
is not sufficient to answer the question asked;
B. statement (2) ALONE is sufficient, but statement (1) alone
is not sufficient to answer the question asked;
C. BOTH statements (1) and (2) TOGETHER are sufficient
to answer the question asked, but NEITHER statement
ALONE is sufficient;
D. EACH statement ALONE is sufficient to answer the
question asked;
E. statements (1) and (2) TOGETHER are NOT sufficient
to answer the question asked, and additional data specific to
the problem are needed.
1. If today the price of an item is $3,600, what was the price of the item exactly 2 years ago?
(1) The price of the item increased by 10 per-cent per year during this 2-year period.
(2) Today the price of the item is 1.21 times its price exactly 2 years ago.
Here you can see that both options 1 and 2 can be used to answer this question exclusively. Hence you choose answer option which says that both statements can answer the question exclusively that is D.
Thats all on the format and the type of questions on all sections in GMAT. I would get back with more details and question banks on each section in my later posts.
I guess this is enough to get you accustomed to the format and sections of GMAT as of now!!
