divelab/Sys2Bench huggingface dataset:
Question: (9568422 x 558) = ?
Options:
A)5846381256
B)5339179476
C)5346381356
D)5846381406
E)5346381456
Rationale: 9568422 x 558=5339179476Ans B
Answer: B
Question: A number is missing from the number series below.
Can you find it ?
84, ?, 258, 399 , 584, 819.
Options:
A)155
B)350
C)399
D)421
E)449
Rationale: A
The missing number is 155.
84 = 4^3 + 3^2 + 4
258 = 6^3 + 6^2 + 6
399 = 7^3 + 7^2 + 7
584 = 8^3 + 8^2 + 8
819 = 9^3 + 9^2 + 9
Thus,
155 = 5^3 + 5^2 + 5
Answer: A
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.75 only. Menâ€™s wages are?
Options:
A)6Rs
B)7Rs
C)8Rs
D)5Rs
E)1Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 75 Rs.
5M + 5M + 5M ----- 75 Rs.
15M ------ 75 Rs. => 1M = 5Rs.
Answer:D
Answer: D
Question: If in a certain sequence of consecutive multiples of 100, the median is 750, and the greatest term is 1200, how many terms that are smaller than 650 are there in the sequence?
Options:
A)6
B)7
C)8
D)12
E)13
Rationale: Since the median is 750 we know there must be a even number of integers
So the list around 750 must go. 700 (750) 800 900 1000 1100 ,1200
Since we know there are 5 numbers greater than 750 then there must be 5 numbers less then 750
C
Answer: C
Question: Pipe A fills a tank in 56 minutes. Pipe B can fill the same tank 7 times as fast as pipe A. If both the pipes are kept open when the tank is empty, how many minutes will it take to fill the tank?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: A's rate is 1/56 and B's rate is 1/8.
The combined rate is 1/56 + 1/8 = 1/7
The pipes will fill the tank in 7 minutes.
The answer is D.
Answer: D
Question: If x and y are distinct prime numbers less than ten, what must be true about the product of x and y?
Options:
A)xy is even
B)xy is odd
C)xy < 0
D)xy < 36
E)xy > 6
Rationale: Prime numbers less than 10 = 2, 3, 5, 7. x and y can take any oth the values
On checking the options
A. xy is even
xy can be even or odd both
B. xy is odd
xy can be even or odd both
C. xy < 0
Product of two prime numbers can never be < 0
Prime numbers are always positive
D. xy < 36
The maximum value of multiplication can be 5*7 = 35.
Hence this is true always
E. xy > 6
x = 2, y = 3
In this case, xy = 6. FALSE
Correct Option: D
Answer: D
Question: One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 24 cm2. Find the lengths of all sides.
Options:
A)10 and 3
B)7 and 10
C)10 and 7
D)3 and 10
E)13 and 10
Rationale: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 24 cm2 more than the first area. Therefore
A1+24=A2
x(x−3)+24=(x+1)(x−2)
x2−3x+24=x2+x−2x−2
2x=26
x=13. So, the sides of the rectangle are 13 cm and (13−3)=10 cm long.
So answer is E.
Answer: E
Question: The angles of a triangle are in the ratio 1:3:8. Find the measurement of the three angles of triangle.
Options:
A)90°
B)100°
C)120°
D)140°
E)160°
Rationale: If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 3x + 8x = 180
Solve for x
12x = 180
x = 15
The measures of the three angles are
x = 15°
3x = 3 × 15 = 45°
8x = 8 × 15 = 120°
C
Answer: C
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
Options:
A)228
B)105
C)288
D)267
E)168
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer:B
Answer: B
Question: Cost of 16 mirror and 8 comb is Rs.360 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?
Options:
A)10
B)12
C)20
D)21
E)22
Rationale: Let the cost of each pen and pencil be 'p' and 'q' respectively.
16m + 8c = 360 --- (1)
4m + 4c = 96
8m + 8c = 192 --- (2)
(1) - (2) => 8p = 168
=> m = 21
D
Answer: D
Question: A 90-liter solution of cool-drink is made from 5% jasmine water. If 6.5 liters of jasmine and 13.5 liters of water were added to the solution, what percent of the solution is jasmine?
Options:
A)8%
B)8.5%
C)9%
D)9.5%
E)10%
Rationale: The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume)
(0.05(90) + 6.5) / 110 = 11/110 = 10%
The answer is E.
Answer: E
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.24, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]
Options:
A) 0.20
B) 0.24
C) 20
D) 24
E) 55
Rationale: A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 24 cents;
A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*24 = 24 cents.
Answer: D.
Answer: D
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)22
B)88
C)36
D)88
E)27
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: C
Answer: C
Question: How many months are in 3 years?
Options:
A)48
B)12
C)30
D)36
E)30
Rationale: D. 36 months
Answer: D
Question: What will be the fraction of 10%
Options:
A)1/4
B)1/5
C)1/10
D)1/11
E)None of above
Rationale: Explanation:
It will 10*1/100 = 1/10
Option C
Answer: C
Question: The number of arrangements that can be made with the letters of the word COPY so that the vowels occupy the even places?
Options:
A)6
B)144
C)777
D)992
E)221
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways.
Hence the total ways are 1 * 6 = 6.
Answer:A
Answer: A
Question: A bowl has only 6 apples and 6 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?
Options:
A)1/10
B)1/5
C)2/9
D)30/131
E)1/2
Rationale: 6/12 * 5/11
=30/131
D. 30/131
Answer: D
Question: If n ≠ 0, which of the following must be greater than n?
I. 4n
II. n^2
III. 2 - n
Options:
A)II only
B)I only
C)I and II only
D)II and III only
E)None
Rationale: n ≠ 0 => n = negative or n = positive
if n = negative:
2n < n (n = -1 then 2n = -2 => -2 < -1)
n^2 > n (n =-1 then n^2 = 1 => n^2 > n)
2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n)
but if n = positive:
n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II
2 - n < n(n =2 then 2-2 = 0)
=> only II
=>answer is A
Answer: A
Question: A train 250 m long running at 72 kmph crosses a platform in 30 sec. What is the length of the platform?
Options:
A)350m
B)200m
C)250m
D)270m
E)300 m
Rationale: D = 72 * 5/18 = 30 = 600 â€“ 250 = 350m
ANSWER:A
Answer: A
Question: A train 300 m long passed a pole in 22 sec. How long will it take to pass a platform 725 m long?
Options:
A)12 sec
B)59 sec
C)73 sec
D)67 sec
E)76 sec
Rationale: Speed = 300/22
= 14 m/sec.
Required time = (300 + 725)/14
= 73 sec.
Answer: C
Answer: C
Question: From 5 positive numbers and 6 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?
Options:
A)170
B)625
C)30
D)960
E)255
Rationale: The number of ways to choose 4 positive numbers is 5C4 = 5.
The number of ways to choose 4 negative numbers is 6C4 = 15.
The number of ways to choose 2 positive and 2 negative numbers is 5C2*6C2 = 10*15 = 150.
The total number of groups is 5+15+150 = 170.
The answer is A.
Answer: A
Question: A man can row a boat at 14 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 80 km downstream?
Options:
A)85/19
B)90/18
C)80/19
D)70/19
E)60/19
Rationale: Speed downstream = 14 + 5 =19 kmph.
Time required to cover 80 km downstream = d/s = 80/19
= 80/19 hours.
Answer: C
Answer: C
Question: Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in q hours. In terms of x and q, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
Options:
A)x/(x+y)
B)y/(x+y)
C)xy/(x+y)
D)xy/(x-y)
E)xq/(q-x)
Rationale: Pick some smart numbers for x and q.
Say x=1 hour and q=2 hours (notice that q must be greater than x, since the time for machine A to do the job, which is q hours, must be more than the time for machines A and B working together to do the same job, which is x hours).
In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.
Now, plug x=1 and q=2 in the options to see which one yields 2. Only option E fits.
Answer: E.
Answer: E
Question: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days.In how many days can 2 men and 1 boy do the work?
Options:
A)29/2
B)21/2
C)27/2
D)23/2
E)25/2
Rationale: Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.
Then, 2x+3y = 1/10 and 3x+2y = 1/8
Solving,we get: x = 7/200 and y = 1/100
(2 men + 1 boy)’s 1 day’s work = (2 x 7/200 + 1 x 1/100 ) = 16/200 = 2/25
So, 2 men and 1 boy together can finish the work in 25/2 days
Answer is E.
Answer: E
Question: The ratio of the incomes of A and B is 5:4 and the ratio of their expenditure is 3:2. If at the end of the year, each saves $1600 then the income of A is?
Options:
A)$1500
B)$4000
C)$2000
D)$2500
E)$3200
Rationale: Let the income of A and B be $5x and $4x
Let their expenditures be $3y and $2y
5x-3y = 1600-------1)
4x-2y = 1600-------2)
From 1) and 2)
x = 800
A's income = 5x = 5*800 = $4000
Answer is B
Answer: B
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
Options:
A)18997
B)12000
C)28992
D)13009
E)28811
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100)
= 600
X = 12000
Answer: B
Answer: B
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
Options:
A)18
B)27
C)20
D)80
E)81
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer: D
Answer: D
Question: Mr Shivkumar started a business, investing 25000 in 1996. In 1997 he invested an additional amount of 10000 and Mr Rakesh joined him with an amount of 35000. In 1998, Mr Shivkumar invested another additional amount of 10000 and Mr Suresh joined them with an amount of 35000. What will be Rakesh’s share in the profit of 150000 earned at the end of three years from the start of the business in 1996?
Options:
A)70000
B)50000
C)45000
D)75000
E)None of these
Rationale: Ratio of their investments = 25,000 × 1 + 35000 × 1 + 45000 × 1 : 35000 × 2 : 35000 × 1 = 3 : 2 : 1.
∴ Rakesh’s share = 2⁄6 × 150000 = 50000
Answer B
Answer: B
Question: There are 250 scraps. For each 11 cutting one extra can be obtained. How much maximum is possible, if one cut by one unit?
Options:
A)271
B)272
C)273
D)274
E)275
Rationale: 242 is divisible by 11.s0,22 extra will come.and another 8 remained.so,242+8+22=272
ANSWER:B
Answer: B
Question: a man have 800kg mango.he found 8% of its mango are rotten.then how much mango is rotten?
Options:
A)64
B)72
C)68
D)65
E)82
Rationale: 8% of 800kg =(800*8)/100.
=64 mangoes
answer A
Answer: A
Question: In a graduating class, 40 percent of the students are male. In this class, 50 percent of the male students and 40 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
Options:
A)0.44
B)0.5
C)0.56
D)0.62
E)0.68
Rationale: Let x be the total number of students.
The number students who are younger than 25 is 0.5*0.4x+0.6*0.6x = 0.56x
The answer is C.
Answer: C
Question: If 2x=y=6z, what is x-z, in terms of y?
Options:
A)y
B)2y
C)y/2
D)y/3
E)y/4
Rationale: 2x=y=6z
x = y/2
and z = y/6
x-z = y/2 - y/6 = y/3
Answer is D
Answer: D
Question: which of the following could be the greatest common factor of positive integers 4 and 6 ? I) 8 II) 4 III) 2
Options:
A)I only
B)II only
C)II,III only
D)I, II only
E)III only
Rationale: 4=2*2
6=2*3
GCF =2
Answer : E
Answer: E
Question: Ajay pays Rs 8.0 per litre of spirit. He adds water and sells the mixture at Rs 9 per litre, thereby making 40 % profit. The proportion of water to spirit received by the customers is
Options:
A)45:11
B)11:45
C)2:45
D)45:2
E)None of these
Rationale: Suppose the quantity of spirit purchased = X lites
Suppose quantity of water mixed = Y litres
Required ratio of the water and the spirit in the mixture = Y:X
C.P. of x litres of spirit = Rs 8.0X
S.P of x litres of spirit = 9(X + Y)
Thus,C.P = S.P x 100/(100 + gain% )
=> 64 = (9X+9Y) x 100/100 + 40
=> 1120X =900X +900Y
=> 220X= 900Y
=> Y/X = 220/900 = 11/45
ANSWER:B
Answer: B
Question: Cole drove from home to work at an average speed of 80 kmh. He then returned home at an average speed of 120 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
Options:
A)66
B)70
C)72
D)75
E)78
Rationale: First round distance travelled (say) = d
Speed = 80 k/h
Time taken, T2 = d/80 hr
Second round distance traveled = d (same distance)
Speed = 120 k/h
Time taken, T2 = d/120 hr
Total time taken = 2 hrs
Therefore , 2 = d/80 + d/120
LCM of 80 and 120 = 240
2= d/80 + d/120
=> 2 = 3d/240 + 2d/240
=> d = 240 * 2/ 5 Km
Therefore, T1= d/80
=> T1 = (240 *2) / (5 x 80)
=> T1 = (6 x 60) / 5 -- in minutes
=> T1 = 72 minutes.
C
Answer: C
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 5% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Options:
A)2:5
B)3:5
C)4:7
D)2:6
E)1:4
Rationale: 2% is 3%-points below 5% and 10% is 5%-points above 5%.
The ratio of A:B should be 3:5.
The answer is B.
Answer: B
Question: What will be the cost of building a fence around a square plot with area equal to 36 sq ft, if the price per foot of building the fence is Rs. 58?
Options:
A)3944
B)2287
C)2977
D)2668
E)1392
Rationale: Let the side of the square plot be a ft.
a2 = 36=> a = 6
Length of the fence = Perimeter of the plot = 4a = 24 ft.
Cost of building the fence = 24 * 58 = Rs. 1392.
Answer:E
Answer: E
Question: 2 dice are tossed. What is the probability that the total score is a prime no. is?
Options:
A)3/13
B)5/12
C)6/13
D)7/15
E)8/21
Rationale: 5/12
B
Answer: B
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Options:
A)Rs.18000
B)Rs.15000
C)s.17000
D)Rs.14000
E)Rs.19000
Rationale: Explanation:
25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: Option D
Answer: D
Question: 9 men are equal to as many women as are equal to 7 boys. All of them earn Rs.216 only. Men’s wages are?
Options:
A)6
B)5
C)2
D)8
E)2
Rationale: 9M = xW = 7B
9M + xW + 7B ----- 216 Rs.
9M + 9M + 9M ----- 216 Rs.
27M ------ 216 Rs. => 1M = 8Rs. Answer: D
Answer: D
Question: The average age of 3 girls is 24 years and their ages are in the proportion 1:2:3. The age of the youngest girl is?
Options:
A)10 years
B)11 years
C)12 years
D)13 years
E)14 years
Rationale: Total age of 3 boys = 24*3 =72
ratio of their ages = 1:2:3
Age of the youngest = 72*1/6 = 12 years
Answer is C
Answer: C
Question: In flip of coin seven times in a row, what is the probability that the result will not be tails at any ?
Options:
A)1/128
B)29/128
C)35/128
D)1/16
E)1/4
Rationale: In a flip of a coin seven times in a row, tails at no time means heads all the time
Heads = at least 7 heads
Atleast 7 heads in 7 flip.
The total outcome of flip is = 2^7 = 128
For any Coins problem write the ask in the shown format.
HHHHHHH
Once you have written in the above mentioned format the answer is pretty straight.
HHHHHHH = [7!]/[7!] = 1
Sum = 1 =
Answer = 1/128
Answer - A
Answer: A
Question: 12 buckets of water fill a tank when the capacity of each bucket is 49 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 7 litres?
Options:
A)39
B)84
C)80
D)82
E)86
Rationale: Capacity of the tank = (12 Ã— 49) litre
Number of buckets required of capacity of each bucket is 17 litre = 12Ã—49/7=12Ã—7=84
Answer is B
Answer: B
Question: As they say, beggars can't be choosers, in fact begger take what they can get. A begger on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the begger finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?
Options:
A)14
B)18
C)15
D)10
E)13
Rationale: A
14
If the beggar can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14.
Answer: A
Question: Given that x and y are nonnegative integers, compute the number of pairs (x, y) such that
5x + y = 20.
Options:
A)2
B)3
C)5
D)9
E)8
Rationale: For x = 0,1,2,3,4, there is a valid y, giving the answer 5 .
correct answer C
Answer: C
Question: A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
Options:
A)87 days
B)48 days
C)17 days
D)87 days
E)12 days
Rationale: B = 1/16 – 1/24
= 1/48
=> 48 days
Answer: B
Answer: B
Question: Of 64 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Options:
A)54
B)55
C)59
D)71
E)92
Rationale: Total = 64
Thrower = 37
Rest = 64 - 37 = 27
Left Handed = 27/3 = 9
Right handed = 18
If all Thrower are right handed then total right handed is 37 + 18 = 55
so B. 55 is the right answer
Answer: B
Question: Roger can read a book in k minutes. What part of the book can he read in 9 minutes? (k>8)
Options:
A)8+k
B)8/k
C)k/8
D)(k+ 8)/k
E)(k-8) / k
Rationale: Let's sayk = 24
That is, it takes 24 minutes to read the entire book.
So, in 8 minutes, Roger can read1/3of the book
So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24
A) 8+24=32ELIMINATE
B) 8/24=1/3KEEP
C)24/8 =3ELIMINATE
D) (24+ 8)/24=32/24 = 4/3ELIMINATE
E) (24-8) /24=16/24 = 2/3ELIMINATE
Answer: C
Answer: C
Question: What is the dividend. divisor 14, the quotient is 9 and the remainder is 5?
Options:
A)A)130
B)B)131
C)C)148
D)D)158
E)E)160
Rationale: D = d * Q + R
D = 14 * 9 + 5
D = 126 + 5
D = 131
Answer B
Answer: B
Question: 4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 2 professor, how many ways can this committee be formed?
Options:
A)36
B)64
C)72
D)80
E)100
Rationale: you count up combinations twice.
4*9*8... and let me name 6 with students A,B,C,..,F
after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same.
I don't think that's the only mistake.
64 is a factor of = 2^2*4^2
144 is a factor of = 2^4*3^2.
These are very different numbers and you cannot divide 144 with something to get to 64.
Answer: B
Question: How many three letter words are formed using the letters of the word LUNCH?
Options:
A)A)15
B)B)150
C)C)12
D)D)120
E)E)18
Rationale: The number of letters in the given word is fIVE.
The number of three letter words that can be formed using these five letters is 5P4
= 5 * 4 * 3*2 = 120.
Answer:D
Answer: D
Question: A person covered one-fourth of the total distance at 15 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Options:
A)20 (1/8)kmph
B)20 (20/23)kmph
C)20 (17/23)kmph
D)27 (1/23)kmph
E)21 (1/8)kmph
Rationale: Let the total distance be x km
total time taken = (x/4)/15 + (3x/4)/24 = x/60 + x/32 = 23x/480
Average speed = x/(23x/480) = 480/23kmph
= 20 (20/23)kmph.
Answer:B
Answer: B
Question: Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
Options:
A)11 : 6
B)12 : 7
C)13 : 7
D)15 : 6
E)13 : 6
Rationale: Sol. Distance travelled by Car A = 65 × 8 = 520 km
Distance travelled by Car B = 70 × 4 = 280 km
Ratio = 520/280 = 13 : 7
C
Answer: C
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
Options:
A)4/5
B)4/6
C)4/0
D)4/2
E)4/1
Rationale: x/3 – x/4 = 4/60
x = 4/5 km
Answer: A
Answer: A
Question: On the number line, the number p is twice as many units from -2 as -2 is from 4. If p is less than –2, what is the value of p ?
Options:
A)–14
B)–10
C)–6
D)10
E)14
Rationale: Distance between -2 and 4 = 6
Since number p is twice as many units from -2 as -2 is from 4
, therefore p can be -14 Since , p is less than -2 ,
the value of p = -14
Answer A
Answer: A
Question: In a bag containing only blue, red and green marbles, all but 15 are blue, all but
13 are red and all but 12 are green. How many are red?
Options:
A)13
B)7
C)25
D)20
E)10
Rationale: All but blue means number of marbles except blue..hence, let x be the red marble,y
be the green marble,z be the blue marble...
x+y=15
y+z=13
x+z=12
solving this eqns, we get x=7 y=8 z=5 hence number of red marbles are 7
ANSWER:B
Answer: B
Question: A first grade teacher uses ten playing cards, each numbered from 1 to 10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?
Options:
A)70
B)60
C)50
D)40
E)30
Rationale: proble of combination 8C4 = 8!/4!*(8-4)! = 8*7*6*5*4!/4!*4! =70
A
Answer: A
Question: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 19th terms in the sequence?
Options:
A)2^18
B)3(2^17)
C)7(2^16)
D)3(2^16)
E)11(2^15)
Rationale: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
so 16th term will be 2^15
17th term 2^16
19th term 2^18
adding all three
we get
2^15+(2^15)*2+(2^15)*8
so answer is 2^15(1+2+8)=>11(2^15)
answer E
Answer: E
Question: In an xy-coordinate plane, a line is defined by y = kx + 1. If (1, b), (a, 4), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
Options:
A) 1/2
B) 1
C) 3/2
D) 2
E) 5/2
Rationale: b=k+1...(1)
b+1=ak+1...(2)
4=ak+1...(3)
Taking (2) and (3)
4=b+1
b=3
Taking (1)
3=k+1
k=2
Answer : D
Answer: D
Question: If the height of a cone is increased by 190% then its volume is increased by?
Options:
A)100
B)777
C)998
D)190
E)2879
Rationale: 100%
Answer:D
Answer: D