divelab/Sys2Bench huggingface dataset:
Question: Find the value of x. (47% of 1442 - 36% of 1412) + 65 = x?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: E) 5
Answer: E
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
Options:
A)Rs.488
B)Rs.480
C)Rs.482
D)Rs.487
E)Rs.481
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640
= Rs.160
SP = CP - Loss
= 640 - 160
= Rs.480
Answer: B
Answer: B
Question: The North-South Express is a pair of trains between Jammu and Chennai. A train leaves Jammu for Chennai exactly at 12 noon everyday of the week. Similarly, there's a train that leaves Chennai bound for Jammu on everyday of the week exactly at 12 noon. The time required by a train to cover the distance between Chennai and Jammu is exactly 7 days and 1 minute. Find the number of trains from Chennai to Jammu which a train from Jammu to Chennai would cross in completing its journey, assuming all the trains are on time.
Options:
A)7
B)8
C)15
D)16
E)17
Rationale: Explanation :
Let a train from Chennai to Jammu starts on Day 1 and it reaches jammu on day 8 at 12:01 Hrs
The train which starts from Jammu on Day 8 at 12:00 will cross this Day 1 train (from Chennai) at approx. 12:00:30 Hrs and this train will reach Chennai on day 15 at 12:01 Hrs so it will cross the train which started from Chennai at 12:00 Hrs on day 15 (in between 12:00 Hrs and 12:01 Hrs).
So it will cross a total of 15 trains.
Answer : C
Answer: C
Question: 0.99998+0.11112=?
Options:
A)1
B)1.0001
C)1.0021
D)1.1111
E)1.111
Rationale: 0.99998 + 0.11112
= 0.99998 + 0.1111 + 0.00002
= (0.99998 + 0.00002) + 0.1111
= 1 + 0.1111
= 1.1111
D
Answer: D
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
Options:
A)120 gallons
B)200 gallons
C)170 gallons
D)180 gallons
E)250 gallons
Rationale: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons\
Volume of whole = 3 * 40 = 120 gallons.
ANSWER A
Answer: A
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Options:
A)24
B)26
C)42
D)46
E)48
Rationale: Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) = 144
2x2 + 26x - 140 = 0
(x - 2)(11x + 35) = 0
x = 2
Hence, required number = 11x + 2 = 24.
ANSWER:A
Answer: A
Question: At present the ratio between the ages of Arun and Deepak is 2:5. After 10 years Arun's age will be 30 years. What is the age of the Deepak?
Options:
A)20
B)40
C)50
D)60
E)45
Rationale: Let the present age of Arun and Deepak be 4x and 3x
2x+10 = 30
2x = 20
x = 10
Deepak's age = 5x = 50 years
Answer is C
Answer: C
Question: Fifthty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 10 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
Options:
A) 60
B) 80
C) 100
D) 120
E) 140
Rationale: 50% of the members have passed the test, thus 50% have not passed the test.
We also know that 30+10=40 members have not passed the test, thus 0.5*Total=40 --> Total=80.
Answer: B.
Answer: B
Question: How many words of 3 letters can be formed from the letters "AABBCC"?
Options:
A)18
B)21
C)24
D)27
E)29
Rationale: There are 3 distinct letters: A, B, C
There are repetition: 2A, 2B, 2C
1. All 3 letters are different: 3!=6
2. Two letters are similar, third is different:
- choose 1 out of 3 letters: 3C1
- choose 1 out of remaining 2 letters: 2C1
- count in repetitions: 3!/2!
3C1x2C1x3!/2! = 18
Total: 18+6=24 ANSWER:C
Answer: C
Question: Which of the following numbers is not prime?
Options:
A)79+52
B)33+88
C)166-3
D)100+67
E)50-7
Rationale: The number 11 can be factored out of Choice B which shows that it can not be a prime number. --> 33+11= 11*(3+8). The correct answer is B.
Answer: B
Question: Which of the following triples of numbers have the same standard deviation as the numbers u, v and w?
I. u-2, v-2, w-2
II. 0, u-v, w-v
III. u-4, v+5, w-1
Options:
A)I only
B)II only
C)I and III only
D)II and I only
E)I, II, and III
Rationale: If we add or subtract a constant to each term in a set the standard deviation will not change.
Set {u-2, v-2, w-2} is obtained by subtracting 2 from each term of {u, v, w}.
Set {0, u-v, w-v} is obtained by subtracting s from each term of {u, v, w}.
Set {u-4, v+5, w-1} is totally different from {u, v, w}.
Thus the answer is I and II only.
Answer: D.
Answer: D
Question: AAA manufacturing owns 2 plants. Tikon plant and Mikon plant. The policy is that 50% of all workers get bonuses every year. If the ratio of employees at the plants is 3:2, respectively, and the percentage of employees getting bonuses at Tikon is 55%, what percentage of employees at Mikon get bonuses?
Options:
A)42.5%
B)56%
C)25.5%
D)55%
E)22.5%
Rationale: Let T and M be number employees at Tikon and Mikon, respectively, and b represent bonus.
T + M = total employees.
T:M = 3:2
Tb/T = 55%
Mb/M = ?
[(3)(Tb/T) + (2)(Mb/M)]/(3 + 2) = 50%
[(3)(55%) + (2)(Mb/M)]/5 = 50%
Mb/M = 42.5%
Answer: A
Answer: A
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is?
Options:
A)6! * 7P7
B)6! * 7P6
C)6! * 7P1
D)6! * 7P5
E)6! * 7P2
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in 7P6 ways.
Hence required number of ways = 6! * 7P6
Answer: B
Answer: B
Question: A ferry can transport 50 tons of vehicles. Automobiles range in weight from 1,800 to 3,200 pounds. What is the greatest number of automobiles that can be loaded onto the ferry?
Options:
A)23
B)55
C)48
D)62
E)70
Rationale: to get maximum vehicles we must take into consideration the minimum weight i.e 1800 pounds here
since , 1 ton = 2000 pounds
50 tons will be 100,000 pounds
from the answer choices:
let max number of vehicles be
total weight will be = 55*1800 = 99000 pounds , which is lesser than the maximum weight allowed .
Ans: B
Answer: B
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 99 km/hr. What is the length of the platform?
Options:
A)440
B)488
C)477
D)426
E)422
Rationale: Speed = 99 * 5/18 = 27.5 m/sec.
Length of the train = 27.5 * 20 = 550 m.
Let the length of the platform be x m . Then,
(x + 550)/36 = 27.5 => x = 440 m.
Answer: A
Answer: A
Question: A certain rectangular crate measures 6 feet by 8 feet by 10 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?
Options:
A)4
B)4
C)6
D)8
E)10
Rationale: Ans is "B".
For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. . Therefore for max vol base should be 8x10 i.e. of radius 8/2 = 4
B
Answer: B
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)70,10 kmph
B)78,10 kmph
C)70,70 kmph
D)78,10 kmph
E)70,12 kmph
Rationale: Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer:A
Answer: A
Question: In filling a lot with sand, that is 40 m * 20 m * 2m the volumes of the sand filled will be?
Options:
A)1200 cu.m
B)2200 cu.m
C)4800 cu.m
D)1600 cu.m
E)4000 cu.m
Rationale: 40 * 20 * 2 = 1600
ANSWER:D
Answer: D
Question: what is the smallest integer that is multiple of 5,7,20
Options:
A)70
B)35
C)200
D)280
E)140
Rationale: It is the lcm of 5, 7 and 20 which is 140.
The answer is E.
Answer: E
Question: One student's mark was wrongly entered as 73 instead of 63. Due to that the average marks for the class got increased by 1/3. What is the number of students in the class?
Options:
A)30
B)32
C)35
D)40
E)45
Rationale: Let the total number of students = a
The average marks increased by 1/3 due to an increase of 73 - 63 = 10 marks.
But total increase in the marks = 1/3 *x =x/3
Hence we can write as
=>x/3=10
=>x=30
ANSWER:A
Answer: A
Question: A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 12 km, if the person completes half of the distance by walking and the other half by running?
Options:
A)1.25
B)1.75
C)2.25
D)2.75
E)3.25
Rationale: time = 6/4 + 6/8 = 18/8 = 2.25 hours
The answer is C.
Answer: C
Question: The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years while that of girls is 15.4 years. What is the ratio of boys to girls in the class?
Options:
A)1:2
B)3:4
C)3:5
D)2:3
E)None of these
Rationale: let x = number of girls
y = number of boys
sum of girls ages / x = 15.4
sum of boys ages / y = 16.4
The sum of the girls' ages is 15.4x, and boys' sum is 16.4y
(sum of girls ages + sum of boys ages) / (x+y)= 15.8
(15.4x + 16.4y) / (x+y) = 15.8
15.4x + 16.4y = 15.8(x+y)
15.4x + 16.4y = 15.8x + 15.8y
0.6y = 0.4x
0.6y/x = 0.4
y/x = 0.4/0.6
y/x = 2/3 which is the ratio of boys to girls
ANSWER:D
Answer: D
Question: When positive integer n is divided by 3, the remainder is 1. When n is divided by 5, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 15?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: n = 3p + 1 = 5q + 3
n+2 = 3p + 3 = 5q + 5
n+2 is a multiple of 3 and 5, so it is a multiple of 15.
The answer is A.
Answer: A
Question: How many three-digit integers exist such that all their digits are
odd?
Options:
A)80
B)100
C)120
D)125
E)135
Rationale: so last digit can be filled in 5 ways- 1,3,5,7,9
there are 5 possibilities. The answer is 5∗5∗5=125
The correct answer is D
Answer: D
Question: A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weights 8g/cm cube, then find the weight of the pipe.
Options:
A)3.696 kg
B)3.686 kg
C)2.696 kg
D)2.686 kg
E)None of these
Rationale: Explanation:
In this type of question, we need to subtract external radius and internal radius to get the answer using the volume formula as the pipe is hollow. Oh! line become a bit complicated, sorry for that, lets solve it.
External radius = 4 cm
Internal radius = 3 cm [because thickness of pipe is 1 cm]
Volume of iron =πr2h=22/7∗[42−32]∗21cm3
=22/7∗1∗21cm3=462cm3
Weight of iron = 462*8 = 3696 gm
= 3.696 kg
Option A
Answer: A
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
Options:
A)Rs. 6825
B)Rs. 6721
C)Rs. 6725.
D)Rs. 4298
E)Rs. 6729
Rationale: CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725.
Answer:C
Answer: C
Question: Two cards are selected at random from 10 cards numbered 1 to 10. Find the probability that the sum is odd if two cards are drawn together.
Options:
A)11
B)88
C)77
D)19
E)17
Rationale: Answer:C
Answer: C
Question: A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
Options:
A)50 kmph
B)58 kmph
C)62 kmph
D)65 kmph
E)75 kmph
Rationale: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 50) kmph = 62 kmph.
Answer : C.
Answer: C
Question: The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-half of the males and one-fourth of the females in the class?
Options:
A)120
B)126
C)132
D)138
E)144
Rationale: 1/2*2/5 + 1/4*3/5 = 4/20 + 3/20 = 7/20
The number of degrees is 7/20 * 360 = 126 degrees
The answer is B.
Answer: B
Question: On a sum of money, the S.I. for 2 years is Rs. 660, while the C.I. is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is?
Options:
A)10%
B)10.5%
C)12%
D)13%
E)None of these
Rationale: Difference in C.I. and S.I for 2 years = (696.30 - 660) = Rs. 36.30.
S.I for one year = Rs. 330.
S.I. on Rs. 330 for 1 year = Rs. 36.30
Rate = (100 * 36.30)/(330 * 1) = 11%
ANSWER:D
Answer: D
Question: Jonathan can type a 50 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?
Options:
A)5 minutes
B)10 minutes
C)15 minutes
D)18 minutes
E)20 minutes
Rationale: You may set up common equation like this:
job/A+job/B+job/C=job/x
Memorize this universal formula, you will need it definitely for GMAT.
and find x from this equation
In this specific case, the equation will look like this:
50/40+50/30+50/24=50/x
If you solve this equation, you get the same answer B (10)
Answer: B
Question: A wheel that has 6 cogs is meshed with a larger wheel of 21 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:
Options:
A)9
B)10
C)6
D)8
E)7
Rationale: Explanation :
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
21:6::21:x => 21 * x = 21 * 6
=> x = (21 * 6)/21
=> x = 6
Answer : C
Answer: C
Question: What is the sum of all the multiples of 9 between 0 and 99?
Options:
A)500
B)594
C)450
D)340
E)440
Rationale: The multiples of 9 between 0 and 99 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99. If these are all added together, the result is 594.
Final Answer:
B
Answer: B
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
Options:
A)33
B)27
C)20
D)98
E)21
Rationale: Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.
Rate of interest = (100 * 240) / (100 * 1) = 20% p.a
Answer:C
Answer: C
Question: A can do a piece of work in 3 hours; B and C together can do it in 6 hours, while A and C together can do it in 9 hours. How long will B alone take to do it?
Options:
A)4 9/7 hours
B)3 5/7 hours
C)2 4/7 hours
D)3 8/7 hours
E)none of the above
Rationale: A's 1 hour's work = 1/3 ;
(B + C)'s 1 hour's work = 1/6 ;
(B + C)'s 1 hour's work = 1/9
(A + B + C)'s 1 hour's work = (1/3 + 1/6) = 1/2
B's 1 hour's work = (1/2 - 1/9) = 7/18
B alone will take 18/7 hours to do the work.
=2 4/7
Answer = C
Answer: C
Question: If N is a positive integer and 14N/60 is an integer, then N has how many different positive prime factors?
Options:
A)2
B)3
C)5
D)6
E)cannot be determined
Rationale: 14N/60 = (2)(7)(N)/(2)(2)(3)(5)
= (7)(N)/(2)(3)(5)
For (7)(N)/(2)(3)(5) to be an integer, N must have a 2, 3 and 5 in its prime factorization (so the 2, 3 and 5 can cancel out in the denominator).
So, for example, if N = (2)(3)(5), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)/(2)(3)(5) = 7, which is an integer.
Likewise, if N = (2)(3)(5)(7), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)(7)/(2)(3)(5) = (7)(7) = 49, which is an integer.
Also, if N = (2)(3)(5)(7)(11), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)(7)(11)/(2)(3)(5) = (7)(7)(11), which will evaluate to be an integer.
If N = (2)(3)(5)(7)(11)(13), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)(7)(11)(13)/(2)(3)(5) = (7)(7)(11)(13), which will evaluate to be an integer.
And so on....
As we can see, we can continue this line of reasoning so that N has EVERY PRIME number in its prime factorization.
cannot be determined
ANSWER:E
Answer: E
Question: Calculate the value of 2.71 x 10^9 ?
Options:
A)2710000000
B)271000
C)2710000
D)27100000
E)271000000
Rationale: 2.71 x 10^9 = 2.71 x 1000000000 = 2710000000.
Answer = A
Answer: A
Question: A is thrice good a workman as B and therefore is able to finish a job in 60 days less than B. Working together they can do it in?
Options:
A)20
B)22 ½
C)25
D)30
E)40
Rationale: Explanation:
Ratio of times by A and B= 1:3
difference of time is 2 days B takes 3 days if diff of time is 60 days B takes 3/2 *60 =90 days
A’s 1day work is=1/30
B’s 1 day work =1/90
(A+B )’s one day work is=1/90 +1/30 =2/45
together can do work in 45/2 = 22 ½ days
Answer: Option B
Answer: B
Question: If s=(10^10)-47, what is the sum of all the digit of s?
Options:
A)40
B)45
C)50
D)55
E)80
Rationale: Start small and check for any pattern:
10^2 - 47 = 53 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits
10^3 - 47 = 953 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits
...extrapolate
10^10 - 47 -> number of digits = 10; number of 9s = 8; 53 will be the last 2 digits
s = 9*8 + 5 + 3 = 80.
Answer (E).
Answer: E
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
Options:
A)23 m
B)23 (2/9)m
C)27 (7/9)m
D)29 m
E)28 m
Rationale: Relative speed = (40 - 20) km/hr =	(20 x(5/18))m/sec =	(50/9)m/sec.
Therefore Length of faster train =	((50/9)	x 5) m =	(250/9)m = 27	(7/9)	m.
C
Answer: C
Question: If the product of all the factors of a positive integer, N, is 2 ^ 18 * 3 ^ 12, how many values can N take?
Options:
A)None
B)1
C)2
D)3
E)4
Rationale: Lets say
2^0 *3^0 * 2^0 * 3^1....2^0 * 3^n ...A0 >> 2^{0*(N+1)} * 3^{N(N+1)/2}
2^1 *3^0 * 2^1 * 3^1....2^1 * 3^n ...A2 >> 2^{1*(N+1)} * 3^{N(N+1)/2}
.
.
.
2^m *3^0 * 2^m * 3^1....2^m * 3^n ...AM >> 2^{M*(N+1)} * 3^[N(N+1)/2}
So product of all the factors are: A0 * A1 *...*AM = 2^{M(M+1)*(N+1)/2} * 3^{N(N+1)*(M+1)/2}
From the equation:
M(M+1)*(N+1)/2 = 18 --- X
N(N+1)*(M+1)/2 = 12 --- Y
dividing X, Y, we get M/N = 3/2
Lets say M = 3X, N = 2X
substituting the value in X OR Y we got X = 1 is the only integer satisfying
Hence the number is 2 ^ 3 * 3 ^ 2
Answer is B
Answer: B
Question: Ramya took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If she paid Rs.686 as interest at the end of the loan period, Find the rate of the interest?
Options:
A)5%
B)6%
C)4%
D)3%
E)7%
Rationale: SI = 686
P = 1400
==>1400*R*R/100
686=14R^2
R^2 = 49
R = 7
ANSWER E
Answer: E
Question: MAN1 is 30% more efficient than MAN2. How much time will they, working together, take to complete a job which MAN1 alone could have done in 23 days?
Options:
A)10 days
B)12 days
C)13 days
D)14 days
E)15 days
Rationale: Man1 and Man2 = 100:130 = 10:13
==> Man2 ==> x days
then 10:13:23 :x ==> x=(23*13/10)
x=299/10
Man 1 day work = 1/23
Man2 work = 10/299
(A+B) = 1/23+10/299 = 1/13
==>13 days
ANSWER C
Answer: C
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
Options:
A)400
B)500
C)600
D)530
E)630
Rationale: Explanation:
We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e., = 500 ways.
Answer: Option B
Answer: B
Question: The cross-section of a water channel is a trapezium in shape. If the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 990 square meters, what is the depth of the channel (in meters)?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: 1/2 * d * (14 + 8) = 990
d = 90
The answer is E.
Answer: E
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
Options:
A)10years
B)12 years
C)5 years
D)3 years
E)24 years
Rationale: Explanation:
9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3 years
Answer:D
Answer: D
Question: There are 6 gentlemen and 3 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are seated together.
Options:
A)8540
B)3640
C)2880
D)3880
E)88600
Rationale: First arrange the Gents. This is a circular arrangment. 6 Gents can be arranged in 5! ways.
Now there are 4 spaces (space in between two gents) and we have to seat 3 ladies there.
First select 3 places out of 4 available places. can be done in 4C3ways. Then arrange 3 ladies there in 3! ways.
Total: 5!*4C3*3! = 2880
C is the answer.
Answer: C
Question: A regular octagon is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ?
Options:
A)48 degrees
B)54 degrees
C)67.5 degrees
D)84 degrees
E)108 degrees
Rationale: its a regular pentagon so divide the globe by 8.
= 360/8
= 45
45 would be the angle at O.
Angles at A and B are equivalent, so
45 + 2x = 180
2x = 135
x = 67.5
Angles OAB and OBA will be 67.5 degrees each.
C
Answer: C
Question: Given distinct positive integers 1, 10, 3, x, 2, and 9, which of the following could be the median?
Options:
A)3
B)4
C)7
D)8
E)9
Rationale: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.
Arrange numbers in ascending order: 1, 2, 3, 9, 10, and x.
Now, x can not possibly be less than 3 as given that all integers are positive and distinct (and we already have 1, 2, and 3).
Next, if x is 3<x<9 then the median will be the average of 3 and x. As all answers for the median are integers, then try odd values for x:
If x=5, then median=(3+5)/2=4 --> OK;
Answer: B.
P.S. If x is more than 9 so 10 or more then the median will be the average of 3 and 9 so (3+9)/2=6 (the maximum median possible).
Answer: B
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 36 kmph. In how much time will the trains cross each other?
Options:
A)12 sec
B)13 sec
C)15 sec
D)16 sec
E)17 sec
Rationale: D
Relative speed = (54 + 36)* 5/18 = 5 * 5 = 25 mps.
The time required = d/s = (100 + 100 + 200)/25
= 400/25 = 16 sec.
Answer: D
Question: The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior points respectively on them. How many triangles can be formed using these points as vertices.
Options:
A)200
B)205
C)400
D)410
E)420
Rationale: Total points: 3+4+5=12;
Any 3 points out of 12 but those which are collinear will form a triangle, so C312−(C33+C34+C35)=220−(1+4+10)=205C123−(C33+C43+C53)=220−(1+4+10)=205.
Answer: B.
Answer: B
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
Options:
A)9000
B)9400
C)9600
D)9800
E)9700
Rationale: Explanation:
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
ANSWER IS C
Answer: C
Question: find two integers, neither of which ends in a zero, and whose product is exactly 1,000
Options:
A)64 and 15,625
B)60 and 15,625
C)8 and 125
D)64 and 15,635
E)64 and 16,625
Rationale: 1,000=10^3
=10x10x10
=(2x5)x(2x5)x(2x5)
=(2^3)x(5^3)
= 8x125
so the numbers are 8 and 125
ANSWER:C
Answer: C
Question: When x is multiplied by 3, the result is 16 more than the result of subtracting x from 36. What is the value of x?
Options:
A)-4
B)-2
C)11
D)13
E)22
Rationale: The equation that can be formed is:
3x-16=36-x
or, 4x=52
or, x=13.
Answer : D
Answer: D
Question: Three vehecle speed ratio 1:2:3 & time ratio 3:2:1...Distance ratio ??
Options:
A)3:4:2
B)3:4:3
C)3:4:6
D)3:4:9
E)3:2:3
Rationale: speed let ratio be x................x : 2x : 3x
time let ratio be y..................3y : 2y : y
since distance = speed * time ,,,,, 3xy : 4xy :3xy => 3:4:3
ANSWER:B
Answer: B