divelab/Sys2Bench huggingface dataset:
Question: Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
Options:
A)18%
B)20%
C)21%
D)23%
E)Cannot be determined
Rationale: Mixture 1 and 2 having individual profit % of 10 and 20 respectively.
individual profits of vodka A for mixture 1 = 1/3 * 10 = 3.33
individual profits of vodka B for mixture 1 = 2/3 * 10 = 6.77
Individual profits for A and B are increased 4/3 and 5/3 times.
Means profits of mixtures 1 and 2 will increase too.
Increased profits of Vodka A for mixture 1 = 4/3 * 3.33 = 4.44
Increased profits of Vodka B for mixture 2 = 5/3 * 6.77 = 10.55
total increased profits for mixture 1 = 14.99
Similarly
total increased profits for mixture 2 = 24.42
using allegation formula
Va: Vb = 1:1 = [24.42 - (profit of mixture)] / [(profit of mixture)- 14.99]
hence profit of mixture = 19.705 approx = 20%
ANSWER:B
Answer: B
Question: A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
Options:
A)1/20
B)1/6
C)1/5
D)4/21
E)5/21
Rationale: Series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 4*x
Hence, a1+a2+..+a20+n = 24x
So, the fraction asked = 4x/24x = 1/6;
Answer: B.
Answer: B
Question: Calculate the time it will take for a train that is 220 meter long to pass a bridge of 120 meter length, if the speed of the train is Ckm/hour ?
Options:
A)16.32 seconds
B)12.32 seconds
C)13.32 seconds
D)15.32 seconds
E)17.32 seconds
Rationale: Speed = 65 Km/hr = 75*(5/18) m/sec = 20.8333 m/sec
Total distance = 220+120 = 340 meter
Time = Distance/speed
= 340 * (1/20.8333) =16.32 seconds
Answer: A
Answer: A
Question: A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 83. How many points altogether did the team score?
Options:
A)662
B)672
C)654
D)642
E)721
Rationale: 8 * 83 = 664 – 10 = 654
ANSWER:C
Answer: C
Question: An aeroplane covers a certain distance of 530 Kmph in 5 hours. to cover the same distance in 3 2/3 hours, it Must travel at a speed of
Options:
A)440
B)540
C)640
D)722
E)250
Rationale: Speed of aeroplane = 530 Kmph
Distance travelled in 5 hours
= 530 * 5 = 2650 Km
Speed of aeroplane to acver 2650 Km in 11/3
= 2650*3/11 = 722 Km
Answer D
Answer: D
Question: 10 play kabadi, 15 play kho kho only, 5 play both gmaes. Then how many in total?
Options:
A)25
B)35
C)38
D)40
E)45
Rationale: 10 play kabadi =>n(A)=10,
5 play both gmaes.=> n(AnB)=5
15 play kho kho only,=>n(B)=n(B only)+n(AnB)=15+5=20
Total => n(AUB)= n(A)+n(B)-n(AnB)
= 10+20-5
= 25
ANSWER:A
Answer: A
Question: A train 100 meters long completely crosses a 300 meters long bridge in 24 seconds. What is the speed of the train is?
Options:
A)60 kmph
B)76 kmph
C)34 kmph
D)43 kmph
E)40 kmph
Rationale: S = (100 + 300)/24
= 400/24 * 18/5
= 60
Answer:A
Answer: A
Question: The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
Options:
A)74
B)94
C)184
D)364
E)286
Rationale: L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be 90k + 4, which is multiple of 7.
Least value of k for which (90k + 4) is divisible by 7 is k = 4.
Required number = (90 x 4) + 4 = 364. Answer: Option D
Answer: D
Question: Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time R will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did?
Options:
A)2 minute and 12 seconds.
B)two minutes.
C)44 seconds.
D)20 seconds.
E)12 seconds.
Rationale: Tom is running alone for 20 seconds.
So he will cover a distance of 20*2.5 = 50 m in 20 seconds=R
Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side
D is the answer
Answer: D
Question: In a bag, there are four 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?
Options:
A)60
B)61
C)424
D)840
E)960
Rationale: As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited:
1) The minimum number on any given die is 1
2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each.
With 4 dice, we could end up with any SUM between:
4 (if we rolled 1s on all 4 dice)
to
64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice).
Thus, there are only 61 possible sums.
B
Answer: B
Question: If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 1 hours longer and at an average rate of 10 miles per hour faster on that day?
Options:
A) 100
B) 120
C) 130
D) 150
E) 160
Rationale: Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+70)=(R+5)(T+1)
Case 3:
(D+X)=(R+10)(T+1)
X=130
Ans C
Answer: C
Question: The average marks of a class of 20 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
Options:
A)44.28
B)54.28
C)34.28
D)64.28
E)74.28
Rationale: Sum of the marks for the class of 20 students = 20 * 40 = 800
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 70 students =
800 + 3000 = 3800
Average marks of all the students = 3800/70 = 54.28
ANSWER:B
Answer: B
Question: The value of x + x(xx) when x = 2 is
Options:
A)6
B)2
C)8
D)10
E)9
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10.
Answer is D.
Answer: D
Question: 897.7 – 573.07 – 95.007 = ?
Options:
A)229.623
B)224.777
C)233.523
D)414.637
E)None of these
Rationale: Solution
Given expression = 897.7 - (573.07 + 95.007) = 897.7 - 668.077 = 229.623. Answer A
Answer: A
Question: A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)2
B)1.4
C)1.2
D)1.5
E)1.1
Rationale: M = 6
S = x
DS = 6 + x
US = 6 + x
6 + x = (6 - x)2
6 + x = 12 -2x
3x = 6
x = 2
Answer: A
Answer: A
Question: The average of 9 results is 50. The average of first four results is 52 and average of last four results is 49 . what is the fifth result?
Options:
A)46
B)82
C)26
D)11
E)99
Rationale: Total of results = 50 x 9 = 450
Total of first four results = 52 x 4 = 208
Total of Last four results = 49 x 4 = 196
Hence the fifth result = 450 - (208 + 196) = 46
ANSWER=A
Answer: A
Question: Find the value of 5 + 2 â€¢ (8 â€“ 3)
Options:
A)25
B)13
C)17
D)24
E)15
Rationale: 5 + 2 â€¢ (8 â€“ 3)
= 5 + 2 (5)
= 5 + 2 *5
= 5 + 10
= 15
correct answer E
Answer: E
Question: .3+33+333+3.33=?
Options:
A)369.63
B)372.33
C)702.33
D)702
E)None of them
Rationale: .3
33
333
3.33
----------
369.63
----------
Answer is A
Answer: A
Question: An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth?
Options:
A)488
B)204
C)195
D)178
E)133
Rationale: Let the required time be x seconds.
More metres, More time (Direct Proportion)
0.128 : 25 :: 1 : x 0.128x = 25 x 1
x =25/0.128 =	(25 x 1000)/128
x = 195.31.
Required time = 195 sec (approximately).
Answer is C.
Answer: C
Question: Walking 5/4 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
Options:
A)22
B)99
C)27
D)28
E)20
Rationale: Speed Ratio = 1:5/4 = 4:5
Time Ratio = 5:4
1 -------- 5
4 --------- ?20 m.Answer:E
Answer: E
Question: Find the odd man out. 1050, 510, 242, 106, 46, 16, 3
Options:
A)46
B)106
C)510
D)1050
E)None of these
Rationale: Explanation :
1050
(1050 - 30)/2 = 510
(510 - 26)/2 = 242
(242 - 22)/2 = 110
(110 - 18)/2 = 46
(46- 14)/2 = 16
(16- 10)/2 = 3
Hence, 110 should have come in place of 106. Answer : Option B
Answer: B
Question: If (200)(900) = (180)(10^x), what is the value of x?
Options:
A)5
B)4
C)3
D)2
E)1
Rationale: (200)(900) = (180)(10^x)
=> (200)(900)/180 = 10^x
=> 1,000 = 10^x
=> 10^3 = 10^x
Since, base is same so powers will be same too.
So, x=3
Answer will be C
Answer: C
Question: A man can row upstream at 15 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)65
B)86
C)30
D)78
E)25
Rationale: US = 15
DS = 35
M = (35 + 15)/2
= 25
Answer: E
Answer: E
Question: Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and 1/3 of the remaining funds have 4-star ratings. If the remaining 300 funds on the list have 3-star ratings, how many funds are on the list?
Options:
A)500
B)750
C)1,000
D)1,200
E)900
Rationale: E
Fraction of 5- and 4-star funds: 1/3 + (1/3)*(2/3) = 1/3 + 1/3 = 2/3
Fraction of 3-star funds = 1 - 2/3 = 1/3
(1/3)*Total = 300
Total = 900
Answer: E
Question: What is the sum of all the multiples of 10 between 0 and 99?
Options:
A)500
B)620
C)450
D)340
E)440
Rationale: The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70, 80, and 90. If these are all added together, the result is 450.
Final Answer:
C
Answer: C
Question: Mohan purchased 15 kgs of rice at the rate of Rs.26 per kg and 15 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?
Options:
A)A)Rs.780
B)B)Rs.760
C)C)Rs.700
D)D)Rs.595
E)None of these
Rationale: Explanation:
Price of 15 kgs of rice at Rs.26/kg = 15x26 = Rs.390
Price of 15 kgs of pulses at Rs.26/kg = 15x26 = Rs.390
Therefore, Total amount = Rs.390+Rs.390 = Rs.780
Answer: Option A
Answer: A
Question: Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability of a tie?
Options:
A)5/6
B)2/3
C)1/2
D)5/12
E)3/9
Rationale: There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability of a tie is (favorable outcomes) / (total # of outcomes) = 3/9
Answer: E
Answer: E
Question: If 5^21 x 8^7 = 10^n what is the value of n?
Options:
A)26
B)24
C)21
D)28
E)20
Rationale: 5^21* (2^3)^7 = 10^n
or 5^21* 2^21 = 10^n
or 10^21 =10^n
n=21
C
Answer: C
Question: The difference between two integers is 5. Their product is 500. Find the numbers.
Options:
A)15, 20
B)20, 25
C)30, 25
D)21, 26
E)none
Rationale: Let the integers be x and (x + 5). Then,
x(x + 5) = 500
x2 + 5x - 500 = 0
(x + 25)(x - 20) = 0
x = 20
So, the numbers are 20 and 25.
ANSWER:B
Answer: B
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 10 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)s.9060
B)s.4520
C)s.4527
D)s.4530
E)s.4521
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)
= 906 sq.ft.
Total cost = 906 * 10
= Rs.9060
Answer:A
Answer: A
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)65 sec
B)16 sec
C)87 sec
D)99 sec
E)96 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Answer: B
Answer: B
Question: What is the difference between the place value of 2 in the numeral 7229?
Options:
A)150
B)160
C)180
D)190
E)210
Rationale: 200 - 20 = 180
C
Answer: C
Question: The total of 324 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is :
Options:
A)50
B)100
C)150
D)200
E)250
Rationale: Explanation:
Let the number of 20 paise coins be x. Then the no of 25 paise coins = (324 - x).
0.20 × (x) + 0.25 (324 - x) = 71 => x = 200.
Answer: D
Answer: D
Question: Solve the equation for x : 21(x + y) + 5 = 21(-x + y) + 47
Options:
A)-2
B)-1
C)0
D)2
E)1
Rationale: E
1
21(x + y) + 5 = 21(-x + y) + 47
21x + 21y + 5 = -21x + 21y + 47
21x + 5 = -21x + 47
42x = 42
=> x = 1
Answer: E
Question: A sum of money becomes 7/6 of itself in 4 years at a certain rate of simple interest. The rate per annum is?
Options:
A)25/6
B)5 5/7
C)5 5/2
D)5 5/8
E)5 5/1
Rationale: Let sum = x. Then, amount = 7x/6
S.I. = 7x/6 - x = x/6; Time = 4 years.
Rate = (100 * x) / (x * 6 * 4) = 25/6 %.
Answer:A
Answer: A
Question: A technology company made a $5 million profit on its first $15 million in sales and a $12 million profit on its next $30 million in sales. By what percent did the ratio of profit to sales increase from the first $15 million in sales to the next $30 million in sales?
Options:
A)10%
B)20%
C)30%
D)40%
E)50%
Rationale: Solution:
This is a percent increase problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.
We first set up the ratios of profits to sales. The first ratio will be for the first 15 million in sales, and the second ratio will be for the next 30 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.
First 15 Million
profit/sales = 5/15 =1/3
Next 30 Million
profit/sales = 12/30 = 2/5
We can simplify each ratio by multiplying each by the LCM of the two denominators, which is 15. Keep in mind that we are able to do this only because our answer choices are expressed in percents.
First 15 Million
royalties/sales = (1/3) x 15 = 5
Next 30 Million
royalties/sales = (2/5) x 15 = 6
We can plug 5 and 6 into our percent change formula:
(new – old)/old x 100
[(6 – 5)/5] x 100
1/5 x 100, so a 20% increase.
Answer B.
Answer: B
Question: J is 25% less than P and 20% less than T. T is e% less than P. What is the value of e?
Options:
A)93.5
B)90
C)6.75
D)6.25
E)2
Rationale: Usually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables.
Let, P = 400
then J = (75/100)*400 = 300
also J = (80/100)*T
i.e. T = 300*100/80 = 375
and T = [1-(e/100)]*P
i.e. 100-e = 100*T/P = 100*375/400 = 93.75
i.e. e = 6.25
Answer: Option D
Answer: D
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)21
B)12
C)9
D)108
E)101
Rationale: Explanation:
The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer is D
Answer: D
Question: The smallest number when increased by " 1 " is exactly divisible by 12, 18, 24, 32 and 40 is:
Options:
A)1439
B)1500
C)1440
D)1450
E)1448
Rationale: LCM = 1440
1440 - 1 = 1439
ANSWER A
Answer: A
Question: A clock is started at noon. By 10 minutes past 3, the hour hand has turned through how many degrees?
Options:
A)95Â°
B)100Â°
C)105Â°
D)110Â°
E)115Â°
Rationale: The angle traced by the hour hand in 12 hrs is 360Â°
The angle traced by the hour hand in 1 hour is 30Â°
The angle traced by the hour hand in 10 minutes is 5Â°
The angle traced by the hour hand in 3 hours and 10 minutes is 3*30Â° + 5Â° = 95Â°
The answer is A.
Answer: A
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
Options:
A)22772
B)24000
C)23877
D)23789
E)28222
Rationale: Explanation:
Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs. 24000
Answer: B
Answer: B
Question: The average Weight of 15 students in a class is increased by 3 Kg. when a student who weights 48 Kg. is replaced by a new student. Find the weight of new student?
Options:
A)39
B)83
C)88
D)93
E)97
Rationale: Explanation:
New weight = Old weight +- no . of item * decrease (or) increase in average
= 48 + 15 *3= 93
Answer: Option D
Answer: D
Question: A dog takes 5 leaps for every 7 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
Options:
A)16 : 7
B)15 : 7
C)20 : 7
D)7 :15
E)14 : 7
Rationale: Explanation:
Dog : Hare = (5*3) leaps of hare : 7 leaps of hare = 15 : 7
Answer: B
Answer: B
Question: In an examination, 35% candidates failed in one subject and 40% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both?
Options:
A)975
B)1020
C)1175
D)1243
E)1125
Rationale: Failed in 1st subject = 35*2500/100 = 875
Failed in 2nd subject = 40*2500/100 = 1000
Failed in both = 15*2500/100 = 375
Failed in 1st subject only = 875-375 = 500
Failed in 2nd subject only = 1000-375 = 625
Passed in either subject but not in both = 625+500 = 1125
Answer is E
Answer: E
Question: If a positive integer n has 211 factors,then how many prime factors does n have?
Options:
A)3
B)2
C)cannot be determined
D)4
E)1
Rationale: Let the factor be a^x*b^y.....
So (x+1)(y+1).....=211..
Now 211 is a prime number...
So only one variable x or y is 210 and the others are 0..
(210+1)(0+1)...
So the number becomes a^210..
Thus only ONE prime factor is there.
Answer: E
Question: How many cubes of 10 cm edge can be put in a cubical box of 1 m edge.
Options:
A)10000 cubes
B)1000 cubes
C)100 cubes
D)50 cubes
E)70 cubes
Rationale: Explanation:
Number of cubes =(100∗100∗100)/(10∗10∗10)=1000
Note: 1 m = 100 cm
ANSWER IS B
Answer: B
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Options:
A)2.85
B)2.88
C)2.89
D)2.83
E)2.81
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: B
Question: Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?
Options:
A)$13.90
B)$18.67
C)$19.00
D)$12.76
E)$15.75
Rationale: The price with 30% off
30 - 30% of 30 = 30 - (30 / 100) × 30 = 30 - 9 = 21
The price with another 25% off
21 - 25% of 21 = 21 - (25/100) × 21
= 21 - (525 / 100) = 21 - 5.25 = $15.75
correct answer E
Answer: E
Question: workers in a notebook factory stores the notebooks in two different sized boxes. the bigger box contains 18 notebooks while the smaller box contains 10 notebooks. If the workers were to store 89 notebooks in total, what is the least number of notebook that will remain unboxed?
Options:
A)10
B)14
C)12
D)17
E)11
Rationale: Total notebook to be stored 89
The big box can store 18
small box can store 10
storing 18 notebook in big box 84/18 =4 r 12
least number of notebook that will be left unboxed=17
Answer: D
Answer: D
Question: In what time will a train 320 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)8.0 sec
C)3.5 sec
D)2.9 sec
E)9.5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 320/40
= 8.0 sec.
Answer: B
Answer: B
Question: Three small cruise ships, each carrying 5 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
Options:
A)1100
B)1200
C)1300
D)1400
E)1500
Rationale: The number of ways for the ships to go to the ports is 3! = 6.
At Port A, the number of ways to choose two winners is 5C2 = 10.
At Port B, the number of ways to choose one winner is 5.
At Port C, the number of ways to choose one winner is 5.
The total number of ways to give out gift certificates is 6*10*5*5 = 1500
The answer is E.
Answer: E
Question: A grandpa called all his grandsons and decided to give them a total of $100 to spend in their vacations. He decided that the elder ones must receive more. So he planned to give a sum to the youngest one and then increase $2 with every elder one.
Can you calculate how much he gave to the youngest one if he gave all and only $100 to them in total?
Options:
A)$17
B)$15
C)$21
D)$16
E)$22
Rationale: D
$16
Answer: D
Question: 7, 10, 8, 11, 9, 12, ?
Options:
A)9
B)8
C)11
D)10
E)15
Rationale: D
10
This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
Answer: D
Question: Two cyclists start from the same place to ride in the same direction. A starts at noon at 8 kmph and B at 1.30 pm at 10 kmph. How far will A have ridden before he is over taken by B ?Find also at what times A and B will be 5 km apart.
Options:
A)5pm and 10pm
B)6pm and 10pm
C)4pm and 8 pm
D)5pm and 8 pm
E)None of these
Rationale: Sol. If A rides for X hours before he is overtaken, then B rides for(X – 15) hrs.
=> 8X = 10 (X – 1.5) => X = 7.5
=> A will have ridden 8 × 7.5 km ro 60 km.
For the second part, if Y = the required number of hours after noon, then
8X = 10 (X – 1.5) ± 5
=> X = 10 or 5 according as B is ahead or behind A.
=> The required times are 5 p.m. and 10 p.m. Answer A
Answer: A
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)277m
B)180m
C)272m
D)278m
E)267m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Answer: B
Question: If w/x = 1/6 and w/y = 1/5, then (x + y)/y =
Options:
A)4/5
B)6/5
C)7/5
D)11/5
E)9/5
Rationale: W/X = 1/6=>x=6w and W/Y = 1/5=>y=5w
(X+Y)/Y = (6w+5w)/5w = 11w/5w = 11/5
Correct Option: D
Answer: D
Question: If the number 517*324 is completely divisible by 5, then the smallest whole number in the place of * will be:
Options:
A)3
B)1
C)2
D)4
E)5
Rationale: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 5.
x = 3.
A
Answer: A
Question: A boat having a length 4 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
Options:
A)12 kg
B)60 kg
C)72 kg
D)80 kg
E)None of these
Rationale: Explanation:
Volume of water displaced = (4 x 2 x 0.01) m3
= 0.08 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.08 x 1000)kg
= 80 kg.
Answer: D
Answer: D
Question: Sonika deposited Rs.9000 which amounted to Rs.10200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
Options:
A)9680
B)2277
C)2999
D)10700
E)10740
Rationale: (9000*3*2)/100 = 540
10200
--------
10740
Answer:E
Answer: E
Question: If the height of a cone is increased by 130% then its volume is increased by?
Options:
A)100
B)777
C)998
D)729
E)130
Rationale: 100%
Answer:E
Answer: E
Question: If 5* nP3 = 4* (n+1)P3, find n?
Options:
A)10
B)11
C)12
D)14
E)None
Rationale: Solution:
nP3 = n*(n–1)*(n–2).
(n+1)P3 =(n+1)*n*(n–1).
Now,
5*n*(n–1)*(n–2) = 4* (n+1)*n*(n–1).
Or, 5(n−2) = 4(n+1).
Or, 5n−10 = 4n+4.
Or, 5n−4n = 4+10.
Hence, n = 14.
Note: nPr = [n! /(n -r)!].
Answer: Option D
Answer: D