divelab/Sys2Bench huggingface dataset:
Question: A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?
Options:
A)14700
B)14500
C)14000
D)15000
E)15200
Rationale: Total amount invested = 50000
Assume that investment of C =x.
Then investment of B =5000+x,
Investment of A =4000+5000+x=9000+x
x+5000+x+9000+x=50000
⇒3x+14000=50000
⇒3x=50000–14000=36000
⇒x=36000/3=12000
Investment of C =x=12000
Investment of B =5000+x=17000
Investment of A =9000+x=21000
Ratio of the investment of A, B and C
=21000:17000:12000=21:17:12
Share of A = Total profit ×21/50
=35000×2150=700×21=14700
Answer is A.
Answer: A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Options:
A)2/26
B)2/20
C)2/21
D)2/22
E)6/21
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21.Answer:C
Answer: C
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
Options:
A)Rs.500
B)Rs.1000
C)Rs. 3630
D)Rs.2500
E)Rs.6000
Rationale: Explanation:
6300:4200:10500
3:2:5
3/10 * 12100 =Rs. 3630
ANSWER:C
Answer: C
Question: When 5 + 6 = 305, 6 + 7 = 425, 7 + 8 = 565, then 8 + 9 = ?
Options:
A)705
B)735
C)685
D)665
E)725
Rationale: 5 + 6 => 5 Ã— 6 = 30 => 30 Ã— 10 + 5 = 305
6 + 7 => 6 Ã— 7 = 42 => 42 Ã— 10 + 5 = 425
7 + 8 => 7 Ã— 8 = 56 => 56 Ã— 10 + 5 = 565
Then 8 + 9 => 8 Ã— 9 = 72 => 72 Ã— 10 + 5 = 725
Answer : E
Answer: E
Question: How long does a train 120 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
Options:
A)sec
B)sec
C)sec
D)sec
E)sec
Rationale: D = 120+ 170 = 290 m
S = 60 * 5/18 = 50/3
T = 290 * 3/50 = 17.4 sec
Answer: D
Answer: D
Question: |x+3| – |4-x| = |8+x| How many solutions Zwill this equation have?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Z=|x| = x when x >= 0 (x is either positive or 0)
|x| = -x when x < 0 (note here that you can put the equal to sign here as well x <= 0 because if x = 0,
|0| = 0 = -0 (all are the same)
So the '=' sign can be put with x > 0 or with x < 0. We usually put it with 'x > 0' for consistency.A
Answer: A
Question: A does a work in 30 days and B does the same work in 15 days. In how many days they together will do the same work ?
Options:
A)7 days
B)8 days
C)9 days
D)10 days
E)None of these
Rationale: Explanation:
Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,
So,
A's 1 day work = 1/30
B's 1 day work = 1/15
(A+B)'s 1 day work =
(1/30+1/15)=1/10
So together they can complete work in 10 days.
Answer: D
Answer: D
Question: A man cycling along the road noticed that every 6 minutes a bus overtakes him and every 2 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
Options:
A)3 minutes
B)6 minutes
C)8 minutes
D)9 minutes
E)10 minutes
Rationale: Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.
Let the speed of cyclist be c.
Every 6 minutes a bus overtakes cyclist: \frac{d}{b-c}=6, d=6b-6c;
Every 2 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=2, d=2b+2c;
d=6b-6c=2b+2c, --> b=2c, --> d=6b-3b=3b.
Interval=\frac{d}{b}=\frac{3b}{b}=3
Answer: A (3 minutes).
Answer: A
Question: A certain Maroon paint contains 50 percent blue pigment and 50 percent red pigment by weight. A certain green paint contains 30 percent blue pigment and 70 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?
Options:
A)3
B)3.5
C)2.5
D)4
E)4.5
Rationale: 10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5*.5 = 2.5 Grams of red pigment
Answer: C
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets $500 more than D, what is B's share?
Options:
A)$500
B)$1000
C)$1500
D)$2000
E)$2500
Rationale: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x respectively.
Then, 4x - 3x = 500
x = $500
B's share = 2x = 2*$500 = $1000
The answer is B.
Answer: B
Question: In what time a sum of money double itself at 4% per annum simple interest?
Options:
A)33 1/8%
B)33 1/3%
C)33 7/3%
D)32 1/3%
E)25 %
Rationale: P = (P*4*R)/100
R = 25%
Answer: E
Answer: E
Question: In a throw of a coin find the probability of getting a head?
Options:
A)1/2
B)1/3
C)1/4
D)2/3
E)2/5
Rationale: S = {H,T}
E = {H}
P(E) = 1/2
Answer is A
Answer: A
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
Options:
A)2 days
B)6 days
C)8 days
D)9 days
E)5 days
Rationale: Explanation:
3/12 + (3 + x)/16 = 1
x = 9 days
Answer:D
Answer: D
Question: 23, 18, 16, 11, 9, 4 ?
Options:
A)3
B)2
C)7
D)5
E)1
Rationale: This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....
Answer : B.
Answer: B
Question: What should come in place of the question mark (?) in the following number series?
5690 5121 4552 3983 3414 2845 ?
Options:
A)2276
B)2516
C)2746
D)2356
E)None of these
Rationale: Explanation:
By Subtracting 569,We Get the Next Term,
5690-569=5121
5121-569=4552
4552-569=3983
3983-569=3414
3414-569=2845
2845-569=2276
Answer: A
Answer: A
Question: is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, then how old is B?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 22
5x = 20 => x = 4
Hence, B's age = 2x = 8 years.
ANSWER:B
Answer: B
Question: 16 men can complete a piece of work in 25 days. In how many days can 15 men complete that piece of work?
Options:
A)26.7 days
B)77 days
C)20 days
D)88 days
E)44 days
Rationale: 16 * 25 = 15 * x => x
= 26.7 days
Answer: A
Answer: A
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Options:
A)25200
B)33232
C)23228
D)29982
E)20822
Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
=7C3X4C2
= 210.
Number of groups, each having 3 consonants and 2 vowels = 210.
Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves
= 5!
= 120
Required number of ways = (210 x 120) = 25200.
Answer: A
Answer: A
Question: If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 12 women together do the work?
Options:
A)22 days
B)88 days
C)40 days
D)55 days
E)44 days
Rationale: Given that 12m = 20w => 3m = 5w
9 men + 12 women = 15 women + 12 women = 27 women
20 women can do the work in 54 days. So, 27 women can do it in (20 * 54) /27
= 40 days.
Answer: C:
Answer: C
Question: On tuesday Morning, Chris receives tickets to a baseball game that will be played at 8pm on the next evening that it does not rain. However, Chris is only in town until Thursday morning, at which point he must fly to another city. If there is a 30% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
Options:
A) 36%
B) 91%
C) 66%
D) 80%
E) 84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.3*0.3 = 0.09. So, the probability that he will be able to attend is 1 - 0.09 = 0.91.
Answer: B.
Answer: B
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5412, 6336
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.
ANSWER:B
Answer: B
Question: Current age of Bruce and Tomy r in the ratio of 5:4 respectively. 3 years hence, the ratio of their ages will become 11:9 respectively. What is Tomy 's present age in years?
Options:
A)12 years
B)16 years
C)24 years
D)32 years
E)36 years
Rationale: Let the present ages of Bruce and Tomy be 5x years and 4x years respectively.
Then, 5x + 3 = 11
4x + 3 9
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x - 44x = 33 - 27
x = 6.
Anand's present age = 4x = 24 years.
C
Answer: C
Question: In traveling from a dormitory to a certain city, a student went 1/3 of the way by foot, 1/4 of the way by bus, and the remaining 5 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
Options:
A)13
B)17
C)42
D)15
E)12
Rationale: Whole trip = distance by foot + distance by bus + distance by car
x = 1/2x + 3/5x + 5
x - 1/2x - 3/5x = 5
x = 12km
Option: E
Answer: E
Question: How many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other?
Options:
A)120
B)148
C)360
D)540
E)720
Rationale: Let the 3 math books be M1,M2,M3 while the rest be A,B,C,D for a total of 7 different books.
Consider 3 math books to be 1 collective item (=M1M2M3 = M , as they need to be together). Thus, number of arrangements of 3 different books (M1M2M3)= 3P3 = 3!
Total number of arrangements of M,A,B,C,D = 5P5= 5!
Thus, The total possible arrangements will be : M1M2M3 ABCD = 5!*3! = 720, E is the correct answer
Answer: E
Question: John bought 9.25m of cloth for $444. Find the cost price per metre.
Options:
A)48
B)47
C)58
D)56
E)54
Rationale: Cloth bought by John = 9.25 m
Cost of 9.25 m = $444
Cost per metre = 444 ÷ 9.25
The cost of the cloth per metre = $ 48
Answers: A
Answer: A
Question: A certain team has 15 members, including Joey. A three-member relay team will be selected as follows: one of the 15 members is to be chosen at random to run first, one of the remaining 14 members is to be chosen at random to run second, and one of the remaining 13 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
Options:
A)1/1320
B)1/132
C)1/110
D)1/12
E)2/15
Rationale: Total outcomes= 15*14*13
Favorable Outcomes= 14*1*13 and 14*13*1
P=2*14*13*1/15*14*13
P=2/15
Ans E
Answer: E
Question: Employee A work from 01:00 to 08:45 (24 hour clock) on each of the five days this week. Next week, he is scheduled to work the same total hours, but will work a compressed 4 day work schedule. If he starts work at 01:00 next week, what time will he finish each day?
Options:
A)09:04
B)10:41
C)10:45
D)11:56
E)16:19
Rationale: working hours between 01:00 - 08:45 for 5 days are 7:45*5 (5 days) = 38:45
same total hours are to be scheduled for 4 days,
so 38:45/4 = 10:41
ANSWER:B
Answer: B
Question: A certain restaurant offers 4 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
Options:
A)8
B)12
C)15
D)21
E)14
Rationale: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:
A. 2 kinds of cheese and 2 kinds of fruits --> 4C2*2C2=6*1=6
B. 1 kind of cheese and 1 kind of fruit --> 4C1*2C1=4*2=8
A+B=6+8=14
Answer: E.
Answer: E
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 10 machines to produce 100 units?
Options:
A)25
B)30
C)35
D)24
E)96
Rationale: 5 machines would produce 100 units in 50 hours. Increasing the amount of machines by 2 would mean dividing 50 hours by 2.
50/2 = 25
Answer : A
Answer: A
Question: A certain vehicle is undergoing performance adjustments during a set of three trials on an 8-mile track. The first time it travels around the track at a constant rate of p miles per minute, the second time at a constant rate of p^2 miles per minute, and the third time at a constant rate of p^3 miles per minute. If the vehicle takes the same time to travel the first 18 miles of these trials as it does to travel the last 8 miles, how many minutes does it take to complete all three trials (not counting any time between trials)?
Options:
A)18
B)36
C)60
D)96
E)112 minutes
Rationale: The first journey takes 18 miles whereas the last journey takes 8 miles.
r1= p
r2=p^2
and r3= p^3 so we set up a table like
r x t = d
p x t1 = 8
p^2 x t2= 8
p^3 x t3 = 2 (because 18-16)
so the time taken to complete each leg individually amounts to t1 + t2 + t3 = (8/p) + (8/p^2) + (2/p^3). ----> (equation 1)
On the other hand, the time taken to complete the last leg of miles is (8/p^3) ---> (equation 2) because p^3 is the speed on the last leg. Since both the times are equal, equate them to get:
(8/p) + (8/p^2) + (2/p^3) = (8/p^3)
Taking the LCM of the Left hand equation and solving both these equations gives us the value of p=1/2 and p= (-3/2) Since p can not be negative, we have p=1/2 as our value.
Now put this value in the time taken to finish each trial which is the sume of (8/p) + (8/p^2) + (8/p^3) and it will become 16+32+64 = 112 minutes.
Option E is the correct answer.
Answer: E
Question: Of the two square fields, the area of the one is 1 hectare, while anothe one is broader by 1%. There differences in area is:
Options:
A)201 m(power)2
B)220 m(power)2
C)211 m(power)2
D)219 m(power)2
E)205 m(power)2
Rationale: Area of one square field = 10000 m(power)2
10000 × 1 = 10000
Side of this field = √10000 m = 100 m
Side of another square = 101 m
Difference of areas = [ 101(power)2 - 100(power)2 ] m(power)2
[101+100][101-100] m(power)2
(201)(1) m2 = 201 m(power)2
Answer is A.
Answer: A
Question: Evaluate: 19 + sqrt(- 2 + 12Ã—6Ã·9) =?
Options:
A)51
B)53
C)55
D)57
E)59
Rationale: According to order of operations, inner brackets first where 12x6Ã·9 is first calculated since it has a multiplication and a division.
12x6Ã·9 = 72Ã·9 = 8
Hence
19 + sqrt(- 2 + 12Ã—6Ã·9) = 19+ sqrt(- 2 + 8)
= 19 + sqrt(6) = 19 + 36 = 55
correct answer C)55
Answer: C
Question: How many ways are there to arrange the letters in the word tenant ?
Options:
A)1
B)360
C)3780
D)7560
E)11340
Rationale: 6 total words, 2N
= 6! / 2! = 360. Answer B
Answer: B
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.300 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Options:
A)3377
B)2899
C)3750
D)2778
E)1991
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 300
B capital = 22500*1/6 = 3750
Answer: C
Answer: C
Question: How many integers are between 2 and 57/7, inclusive?
Options:
A)5
B)7
C)9
D)10
E)12
Rationale: 57/7 = 8.xx
We are not concerned about the exact value of 57/7 as we just need the integers.
The different integers between 2 and 57/7 would be 2,3, 4, 5, 6, 7, 8.
Total number of integers = 7
Option B
Answer: B
Question: In how many ways 4 Indians and 3 Englishmen can be seated in a row so that they are alternate?
Options:
A)120
B)96
C)144
D)202
E)256
Rationale: number of ways = 4!*3! = 144
Answer is C
Answer: C
Question: On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 45 centimeters assuming that 1-inch is 2.54 centimeters?
Options:
A)174.2
B)212
C)283
D)296
E)282.4
Rationale: 1.5 inch = 2.54*1.5 cm.
So, 2.54*1.5 represents 24 miles.
So for 45 cm.:
45/(2.54*1.5) = x / 24 ---> x = 24*45/(3.81) = 283
Answer will be C.
Answer: C
Question: The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
Options:
A)1:3
B)2:5
C)3:2
D)9:4
E)4:2
Rationale: Explanation:
Let C.P. = Rs. 5x and S.P. = Rs. 7x.
Then, Gain = Rs. 2x
Required ratio = 2x : 5x = 2:5
Answer: Option B
Answer: B
Question: The sum of the ages of 4 children born at the intervals of 5 years each is 58 years. what is the age of the youngest child ?
Options:
A)7
B)8
C)10
D)None of these
E)Cannot be determined
Rationale: Explanation:
Let x = the youngest child. Each of the other four children will then be x+5, x+10, x+15
We know that the sum of their ages is 58 .
so, x+(x+5)+(x+10)+(x+15) = 58
x= 7
The youngest child is 4 years old.
Answer: A
Answer: A
Question: The average of nine numbers is 17. The average of first four numbers is 20 and the average of last four numbers is 16. What is the middle number?
Options:
A)A)7
B)B)8
C)C)9
D)D)10
E)E)11
Rationale: The total of nine numbers = 9X17 = 153
The total of first 4 and last 4 numbers is = 4 X 20+4 X 16 = 144
So, the middle number is (153 - 144 ) = 9
C
Answer: C
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)10 sec
B)30 sec
C)40 sec
D)20 s
E)50 sec
Rationale: D
Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 s
Answer: D
Question: A certain company charges $6 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. If the company charged $28 to ship a certain package, which of the following was the weight of the package, in pounds?
Options:
A)7
B)9
C)11
D)13
E)15
Rationale: Let the weight of the package be X.
2X + 6= 28
X = 11
The answer is C.
Answer: C
Question: A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
Options:
A)31 8/7 years
B)31 5/7 years
C)31 5/8 years
D)35 5/7 years
E)31 3/7 years
Rationale: Required Average = [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)
= (134 + 70 + 18)/7 = 31 5/7 years.
Answer: B
Answer: B
Question: 34.96 + 240.016 + 23.98 = ?
Options:
A)298.956
B)298.694
C)289.496
D)289.469
E)298.964
Rationale: 34.96
240.016
+ 23.98
--------
298.956
Answer is A.
Answer: A
Question: M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 2. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
Options:
A){1, 4, 5, 10, 14}
B){1, 6, 7, 10, 12}
C){1, 5, 5, 10, 16}
D){1, 5, 7, 10, 18}
E){6, 6, 7, 10, 12}
Rationale: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 6 to 10 + 2*{SD} = 14.
A. {1, 4,5, 10, 14} --> only 2 numbers are in this range. Discard.
B. {1,6, 7, 10, 12} --> 4 numbers are in this range. OK.
C. {1,5, 5, 10, 16} --> only 1 number is in this range. Discard.
D. {1,5, 7, 10, 18} --> only 2 numbers are in this range. Discard.
E. {6, 6, 7, 10, 12} --> all 5 numbers are in this range. Discard.
Answer: B.
Answer: B
Question: Mudit's age 48 years hence will be thrice his age four years ago. Find Mudit's present age?
Options:
A)12
B)19
C)27
D)18
E)30
Rationale: Explanation:
Let Mudit's present age be 'm' years.
m + 48 = 3(m - 4)
=> 2m = 60 => m = 30 years.
Answer:E
Answer: E
Question: The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
Options:
A)40
B)28
C)29
D)26
E)20
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 60 and C - P = 20 M + C / 2
= [(M + P) + (C - P)] / 2
= (60 + 20) / 2 = 40.
Answer:A
Answer: A
Question: In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what X percent of all the people in Smithtown are left-handed women?
Options:
A) 50%
B) 40%
C) 25%
D) 20%
E) 10%
Rationale: looking at the ratio we can take total number of people=20..
ans 5/20 or 25% C
Answer: C
Question: A sink has 12 liters of water some quantity of water is taken out. If the remaining water is 6 liters less then the water taken out then quantity of water taken out is.
Options:
A)5 liters
B)6 liters
C)7 liters
D)8 liters
E)9 liters
Rationale: Let x liter water taken out
Total=Water taken out + remaining water
12=x+(x-6)
18=2*x
x=9 liters
ANSWER:E
Answer: E
Question: 10 men can cut 10 trees in 2 hours. If 2men leave the job, how many trees will be cut in 3 hours?
Options:
A)12
B)15
C)16
D)18
E)20
Rationale: 10 men - working 2 hrs - cut 10 trees
1men - working 1hr - cuts = 10/10*2
Thus 8 men - working 3hrs - cut = 10*8*3 / 10*2 = 12 trees
Answer is A
Answer: A
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)3456
B)4567
C)4789
D)5678
E)y=5184
Rationale: Given Exp. = (12)3 x 64 = (12) 3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |Y|<3?
Options:
A)1/7
B)3/7
C)2/5
D)3/11
E)4/7
Rationale: |X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
B
Answer: B
Question: Two spinning machines A and B can together produce 3,00,000 m of cloth in 10 hour, if machine B alone can produce the same amount of cloth in 15 hour, then how much cloth can machine A produce alone in 10 hour?
Options:
A)2,00,000 m
B)1,00,000 m
C)1,50,000 m
D)50,000 m
E)None of these
Rationale: Explanation :
According to the question, machines A and B together produces 30,000 m of cloth in 1 hour.
And,machine B alone can produce 20,000 m cloth in 1 hour.
So, Machine A can produce (30,000 - 20,000) = 10,000 m cloth in 1 hour.
Hence, in 10 hour Machine A can produce 10 x 10,000 = 1,00,000 m of cloth.
Answer : B
Answer: B
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
Options:
A)Saturday
B)Monday
C)Tuesday
D)Friday
E)Sunday
Rationale: The year 2007 is an ordinary year. So, it has 1 odd day.
day of the year 2007 was Monday
day of the year 2008 will be 1 day beyond Monday
Hence, It will be Tuesday.
Answer is C.
Answer: C
Question: Amy has two decks of 54 cards each: Deck 1 and Deck 2. She takes 8 black cards from Deck 2 and adds them to Deck 1 and shuffles it thoroughly. She now picks a card from the newly formed pack of cards. If the probability of either picking a red ace or a king from the newly formed pack is greater than 1/8, what is the probability that Amy picks a black king or a red Jack from the new pack?
Options:
A)1/6
B)1/8
C)1/9
D)1/10
E)1/12
Rationale: Your solution is correct answer should be 1/12.
E
Answer: E
Question: What is the value of the following expression?
(1/ (2^2 – 1)) + (1/ (4^2 – 1)) + (1/ (6^2 – 1)) + .... + (1/ (14^2 – 1))
Options:
A)a. 9/19
B)b. 10/19
C)c. 7/30
D)d. 11/21
E)e. 11/19
Rationale: it can be written into
1/3+1/15+ 1/35.....1/196
i.e
1/3+1/2*(1/3-1/5)+1/2*(1/5-1/7).... til last term - 1/2*(1/15)
all terms from 1/5 .. to second last term get cancelled
left with
1/3+1/6-1/30=1/2-1/30=7/30 C
Answer: C
Question: 225 mtrs long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: 26 trees have 25 gaps between them,
Required distance (225/25) = 10
A
Answer: A
Question: Select the non termination decimal among the following.
Options:
A)2/5
B)3/4
C)4/5
D)19/3
E)9/10
Rationale: D. Non terminating decimal means that 19/3 = 6.3333333 and so on.
Answer: D