divelab/Sys2Bench huggingface dataset:
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 4 kg more than Peter. Together the three of them picked 28 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?
Options:
A)6, 10 and 12
B)12, 10 and 6
C)10, 6 and 12
D)12, 6 and 10
E)6, 12 and 10
Rationale: M = 2P
L = P+4
M + P + L = 28
2P + P + (P+4) = 28
P = 6, M = 12, L = 10
Therefore, Mary, Peter, and Lucy picked 12, 6, and 10 kg, respectively.
The answer is D.
Answer: D
Question: Consider a right triangle WBC with length of sides being x,y and z where y represents the hypotenuse , Which of these represent the radius of the circle which is inscribed in triangle WBC
Options:
A)[A] x+y+z/3
B)[B] x-y+z/3
C)[C] x-y+z/2
D)[D] (x^2 + y^2 + z^2)/3
E)[E] cannot be determined
Rationale: Radius of a circle inscribed in the right triangle WBC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.
Answer: C
Answer: C
Question: A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
Options:
A)4 litres, 8 litres
B)6 litres, 6 litres
C)5 litres, 7 litres
D)7 litres, 5 litres
E)8 litres, 6 litres
Rationale: Explanation:
Let the cost of 1 litre milk be Re. 1
Milk in 1 litre mix. in 1st can =	3/4litre, C.P. of 1 litre mix. in 1st can Re.3/4
Milk in 1 litre mix. in 2nd can = 1/2litre, C.P. of 1 litre mix. in 2nd can Re.1/2
Milk in 1 litre of final mix. =	5/8litre, Mean price = Re.5/8
By the rule of alligation, we have:
C.P. of 1 litre mixture in 1st can C.P. of 1 litre mixture in 2nd can
Ratio of two mixtures =	1/8:1/8=1:1
So, quantity of mixture taken from each can =(1/2 x 12)=6 litres.
ANSWER IS B
Answer: B
Question: If 16% of 40% of a number is 4, then the number is
Options:
A)200
B)225
C)62.5
D)320
E)None of these
Rationale: Explanation:
Let 16/100×40/100×a=4
a = 4×100×100/16×40=62.5
Correct Option: C
Answer: C
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 4 employees to 2 different offices?
Options:
A)12
B)11
C)10
D)16
E)12
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2=2^4=16.
Answer: D.
Answer: D
Question: If a fair coin is tossed five times, what is the probability of getting exactly four heads in a row?
Options:
A)1/64
B)1/32
C)1/16
D)1/8
E)1/4
Rationale: P(HHHHT) = 1/32
P(THHHH) = 1/32
The sum of these probabilities is 2/32 = 1/16
The answer is C.
Answer: C
Question: A restaurant meal cost $30.00 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between
Options:
A) $40 and $42
B) $39 and $41
C) $38 and $40
D) $37 and $39
E) $33 and $35
Rationale: The total amount for the meal was between 30.0*1.1=33.00 and 30.0*1.15=34.5. Only option which covers all possible values of the meal is E.
Answer: E.
Answer: E
Question: A certain number X when divided by 243 leaves a remainder of 95. Which of the following can be subtracted from X to make X divisible by 79?
Options:
A)17
B)22
C)37
D)47
E)57
Rationale: Least possible value of the number is 243 + 95 = 338
Further it is given the number must be divisible by 79 .
338/79 = Gives remainder as 22
So, 22 must be subtracted from the number , answer is (B)
Answer: B
Question: Two heavily loaded sixteen-wheeler transport trucks are 690 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway?
Options:
A)120
B)130
C)150
D)320
E)450
Rationale: I've been reading the website for a while and I'm always keen to see different approaches so I would like to share one that works for me:
Short version:
Truck A travels for an hour.
Distance remaining = 690-90 = 600k
Ratio of speeds 9:8 -> 510/17 = 30
Truck A = 90 + 30*9 = 360
Truck B = 30*8 = 240
Delta = 120km
Answer A
Answer: A
Question: one person Tharak speed with the current is 10 km/hr and the speed of the current is 5 km/hr. Tharak's speed against the current is:
Options:
A)0 km/hr
B)1 km/hr
C)2 km/hr
D)3 km/hr
E)4 km/hr
Rationale: Man's speed with the current = 10 km/hr
=> speed of the man + speed of the current = 10 km/hr
speed of the current is 5 km/hr
Hence, speed of the man = 10-5 = 5 km/hr
man's speed against the current = speed of the man - speed of the current
= 5-5 = 0 km/hr
ANSWER:A
Answer: A
Question: The length and breadth of a rectangle is increased by 11% and 22% respectively. What is the increase in the area?
Options:
A)35.22
B)33.52
C)35.42
D)36.22
E)38.42
Rationale: 100*100=10000
111*122=13542
------------
3542
10000-------3542
100----------35.42
Answer C
Answer: C
Question: How many positive integer solutions does the equation 2x+5y = 100 have?
Options:
A)50
B)33
C)16
D)35
E)10
Rationale: formula: (constant)/(lcm of two nos)
=100/(2*5)=10
ANSWER:E
Answer: E
Question: The compound ratio of 5:6, 3:2 and 6:5?
Options:
A)1:1
B)1:87
C)1:6
D)3:2
E)1:2
Rationale: 5/6 * 3/2 * 6/5 = 3/2
3:2
Answer: D
Answer: D
Question: Real-estate salesman Z is selling a house at a 20 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 10 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 25 percent discount. Salesman Y's final price is what fraction of salesman X's final price?
Options:
A)72/80
B)72/100
C)57/80
D)19/24
E)76/100
Rationale: Let retail price = $100.
Z sells with 20% discount. So z sells at $80.
X matches the price and gives additional 10%. So, X sells at 80-(10% of 80) = 80-8= $72
Y avgs X and Z [(72+80)/2 = 76]. Y gives additional 25% discount. So, Y sells at 76-(25% of 76) = 76-19= $57
Now, ratio of Y to X = 57/72 = 19/24
Answer will be D.
Answer: D
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARI', if repetition of letters is not allowed?
Options:
A)690
B)120
C)740
D)760
E)780
Rationale: The word 'LOGARI' has 6 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 6P3
=
6
×
5
×
4
=
120
Option B
Answer: B
Question: A part of certain sum of money is invested at 16% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
Options:
A)5:4
B)1:4
C)3:1
D)3:5
E)3:4
Rationale: 12:16
= 3:4
ANSWER:E
Answer: E
Question: How many four-digit numbers that do not contain the digits 2, 3, 4, 5, or 6 are there?
Options:
A)200
B)400
C)500
D)600
E)800
Rationale: The 1st digit can be filled up by the numbers: {1,7,8,9} = 4 ways
The 2nd digit can be filled up by the numbers: {0,1,7,8,9} = 5 ways
The 3rd digit can be filled up by the numbers: {0,1,7,8,9} = 5 ways
The 4th digit can be filled up by the numbers: {0,1,7,8,9} = 5 ways
The total number of such four-digit numbers is 4*5*5*5 = 500
The answer is C.
Answer: C
Question: In how many ways can a team of 5 persons be formed out of a total of 10 persons such that two particular persons should not be included in any team?
Options:
A)56
B)63
C)69
D)67
E)23
Rationale: Two particular persons should not be included in each team.
i.e., we have to select 5 persons from 10-2 = 8 persons.
Hence, required number of ways
= 8C5
= 8*7
=56
Ans - A
Answer: A
Question: An employer pays Rs. 30 for each day a worker works, and forfeits Rs. 5 for each day he is idle. At the end of 60 days, a worker gets Rs. 500. For how many days did the worker remain idle?
Options:
A)52
B)27
C)99
D)61
E)11
Rationale: Explanation:
Suppose the worker remained idle for m days. Then, he worked for (60 - m) days.
30 (60 - m) – 5m = 500
1800 – 25m = 500
25m = 1300
m = 52
So, the worker remained idle for 52 days.
ANSWER: A
Answer: A
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5sec
B)4.25sec
C)5sec
D)12.5sec
E)6sec
Rationale: Answer: Option A
Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: A
Question: Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water?
Options:
A)3:2
B)1:4
C)3:1
D)5:2
E)4:3
Rationale: G = 10W
C = 5W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
10W+5Wx = x+1 * 6W
10+5x = 6(x+1)
x = 4
Ratio of gold with copper = 1:4 = 1:4
Answer is B
Answer: B
Question: If x is a positive integer, which of the following could NOT be the square of x?
Options:
A)9526
B)4532
C)4066
D)6515
E)3255
Rationale: A number ending in 2 cannot be a perfect square.
4532 ends in a number 2, making that the correct answer
(B) 4532
Answer: B
Question: A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 10 people to travel x miles if he decides to give them a 50% discount?
Options:
A)3xr/2
B)3x/200r
C)3r/200x
D)3xr/200
E)xr/20
Rationale: 10xr/2 is in cents - 10xr/200 dollars = xr/20
Answer : E
Answer: E
Question: 6 persons standing in queue with different age group, after two years their average age will be 43 and seventh person joined with them. Hence the current average age has become 45. Find the age of seventh person?
Options:
A)65
B)67
C)68
D)69
E)50
Rationale: Explanation :
Let the sum of current ages of 6 persons = x
Given Average age of 6 person after 2 years = 43
=> x+6(2)/6=43
=> x+12=258
= x=246
Let the seventh's person age will be y
Given Current average age of 7 persons = 45
[Sum of current 6 person's age (x) + Seventh person's age (y)] /7= 45
=> 246+y=45(7)
=> y= 315 -246
=> y = 69
Hence Seventh person's age = 69
Hence (D) is the correct answer.
Answer : D
Answer: D
Question: In a class of 60 students, 20 did not opt for math. 15 did not opt for science and 5 did not opt for either. How many students of the class opted for both math and science?
Options:
A)23
B)25
C)27
D)30
E)48
Rationale: 60 students total
20 did not opt for math
15 did not opt for science
5 did not opt for either
Total of 40 students in math and 10 did not opt for sci but did for math
40-10=30
30 students of the class opted for both math and science
Answer:
D. 30
Answer: D
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
Options:
A)1
B)7
C)8
D)9
E)6
Rationale: C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days'
Answer: D
Answer: D
Question: A rectangular floor that measures 8 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters. If the carpet squares cost $10 apiece, what is the total cost for the number of carpet squares needed to cover the floor?
Options:
A) $200
B) $240
C) $480
D) $960
E) $1,920
Rationale: The width of the rectangular floor(8 m) is a multiple of one side of the square(2 m), and the length of the floor(10 m) is also a multiple of the side of the square. So the number of carpets to cover the floor is (8/2)*(10/2)=20.
The total cost is 20*10=$200.
The answer is, therefore, A.
Answer: A
Question: If 6 women can color 360 m long cloth in 3 days, then 5 women can color 100 m long cloth in?
Options:
A)2 days
B)3 days
C)2.5 days
D)4 days
E)1 day
Rationale: The length of cloth painted by one woman in one day = 360/ 6× 3 = 20 m
No. of days required to paint 100 m cloth by 5 women = 100/ 5 × 20 = 1 day
Answer : E
Answer: E
Question: If 25% of(x-y) = 15% of(x+y), then what percent of x is y?
Options:
A)20%
B)15%
C)30%
D)25%
E)None of these
Rationale: Explanation :
Solution: 25% of(x-y) = 15% of(x+y)
25(x-y)/100 = 15(x+y)/100
5(x-y) = 3 (x+y)
x = 4y.
.'. Required percentage = (y*100/x)% = y*100/4y = 25%
Answer : D
Answer: D
Question: When a certain number X is divided by 54, the remainder is 22. What is the remainder when X is divided by 18?
Options:
A)3
B)1
C)2
D)4
E)5
Rationale: Let possible value of x is 76
least possible value of x/18 is 76/18 =>4 quotient with remainder 4
Thus answer is (D) 4
Answer: D
Question: If y is 60% greater than x, than x is what % less than y?
Options:
A)29.3%
B)33.4%
C)37.5%
D)41.6%
E)45.7%
Rationale: y = 1.6x
x = y/1.6 = 10y/16 = 5y/8
x is 3/8 less which is 37.5% less than y.
The answer is C.
Answer: C
Question: Ayesha’s father was 38 years of age when she was born while her mother was 31 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)2 years
B)4 years
C)11 years
D)8 years
E)None
Rationale: EXPLANATION
Mother’s age when Ayesha’s brother was born = 31 years.
Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years.
Required difference = (42 – 31) years = 11 years.
Answer C
Answer: C
Question: There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 15% of all the students at Morse have cars, how many students are in the three lower grades?
Options:
A)600
B)900
C)1200
D)1600
E)2100
Rationale: Let x be the number of students in the lower three grades.
0.1x + 150 = 0.15(x+300)
0.05x = 105
x = 2100
The answer is E.
Answer: E
Question: The difference between the ages of two persons is 11 years. Ten years ago, the elder one was twice as old as the younger one. The present age of the elder person is
Options:
A)18
B)19
C)20
D)17
E)16
Rationale: Let their ages of x years and (x + 11) years respectively.
Then, (x + 11) - 10 = 2(x - 10)
⇔ x +1 = 2x - 20
⇔ 3x = 21.
∴ Present age of the elder person = (7 + 11)
= 18years.
Answer :18 years
Answer: A
Question: There is 66x33m rectangular area. Ram is 11/8 times faster than Krishna. Both of them started walking at opposite ends and they met at some point then, Ram said "See you in the other end" Then they continued walking. After some time Ram thought he will have tea so he turned back walked back 15 meters then he changed his mind again and continued walking .How much Krishna has traveled by the time they meet?
Options:
A)93
B)34
C)95
D)96
E)85
Rationale: let x be the distance between the point they first met
total time taken by the two willbe equal
so (x+30)*8/11 = (198-x)
x= 102m
distance travelled by krishna= 198-102 = 96m
ANSWER:D
Answer: D
Question: A boy runs 200 metres in 30 seconds. What is his speed ?
Options:
A)20 km/hr
B)24 km/hr
C)30 km/hr
D)32 km/hr
E)34 km/hr
Rationale: 200/30 * 18/5 = 24 km/hr
ANSWER:B
Answer: B
Question: If y = 2 + 2K and y≠0y≠0, then 1/y + 1/y + 1/y + 1/y = ?
Options:
A)1/(8+8k)
B)2/(1+k)
C)1/(8+k)
D)4/(8+k)
E)4/(1+k)
Rationale: 1/Y + 1/Y + 1/Y + 1/Y
= 4/Y
= 4/(2 + 2K)
= 2/(1 + K)
ANSWER:B
Answer: B
Question: An automobile manufacturer offers a station wagon with either a 8-cylinder engine or a 6-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 8-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?
Options:
A) 4
B) 6
C) 8
D) 10
E) 12
Rationale: 8-cylinder engine wagons = 2*2*2 = 8 (manual or automatic, with or without trailer);
6-cylinder engine wagons = 2*2=4 (manual or automatic).
Total = 8 + 4 = 12.
Answer: E.
Answer: E
Question: In a simultaneous throw of 2 dice, what is the probability of not getting a doublet?
Options:
A)2/3
B)1/6
C)4/7
D)5/6
E)4/9
Rationale: n(S) = 6*6 = 36
E = event of not getting a doublet = 36- event of getting a doublet= 36-6 =30
{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}
Probability = 30/36 = 5/6
Answer is D
Answer: D
Question: 11, 13, 17, 19, 23, 29, 31, 37, 41, ?
Options:
A)47
B)43
C)51
D)53
E)50
Rationale: B
43
The series consists of prime numbers.
Answer: B
Question: One fourth of one third of two fifth of a number is 16. What will be40% of that number
Options:
A)140
B)150
C)180
D)192
E)250
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 16 then x = 16 * 30 = 480
40% of 480 = 192
Answer: Option D
Answer: D
Question: A man deposited 20% of 25% of 30% of an amount in a bank. If he deposited 750 then what was amount he had initially
Options:
A)55000
B)50000
C)40000
D)30000
E)20000
Rationale: if(20/100)*
(25/100)*(30/100)*x=750
then x=50000.
ANSWER:B
Answer: B
Question: There are 11engineers and 7 civil engineers in a company. Theyare selecting member for row. In how many ways can they be seated in a row so that no two of the civil engineers will sit together?
Options:
A)9!×11!/5!
B)11!×12!
C)11!×12!/5!
D)12!/5!
E)10!×12!/5!
Rationale: 11 software engineers can be arranged in 11! ways. ...(A)
Now we need to arrange civil engineers such that no two civil engineers can be seated together. i.e., we can arrange 7 civil engineers in any of the 12 (=11+1) positions marked as * below.
* 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 *
(where 1, 2… 11 represent software engineers)
This can be done in 12P7 ways. ...(B)
From (A) and (B),
required number of ways
= 11! × 12P7
=11!×12!/5!
C
Answer: C
Question: A letter lock consists of three rings each marked with EIGHT different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Options:
A)4002
B)4090
C)4095
D)177
E)123
Rationale: Since each ring consists of eight different letters, the total number of attempts possible with the three rings is
= 8 * 8 * 8 = 4096. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 4096 - 1
= 4095
Answer:C
Answer: C
Question: A, B, C started a business with their investments in the ratio 1:3 :5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is :
Options:
A)5 : 6 : 18
B)5 : 6 : 12
C)5 : 6 : 11
D)5 : 6 : 10
E)5 : 6 : 128
Rationale: Let their initial investments be x, 3x and 5x respectively. Then,
20x : 24x : 40x = 5 : 6 : 10
Answer: D) 5 : 6 : 10
Answer: D
Question: The temperature of a certain cup of coffee 30 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*2^(-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
Options:
A)65
B)120
C)80
D)85
E)90
Rationale: First, we have to find a.
We know that after t=30 minutes the temperature F=120 degrees.
Hence:
120 = 120*(2^-30a)+60
60 = 120*(2^-30a)
60/120 = 2^-30a
1/2 = 2^-30a
2^-1 = 2^-30a
-1 = -30a
1/30 = a
Now we need to find F after t=30 minutes:
F = 120*(2^-1/30*30)+60
F = 120* (2^-1) +60
F = 120* (1/2^1) +60
F = 120*1/2 +60
F = 60+60 = 120
Answer B!
Answer: B
Question: A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
Options:
A)Rs.45
B)Rs.78
C)Rs.44
D)Rs.40
E)Rs.46
Rationale: π (152 - 132) = 176
176 * 1/4 = Rs.44
ANSWER:C
Answer: C
Question: The no. of girls in a class are seven times the no. of boys, which value can neverbe the of total students?
Options:
A)4
B)5
C)8
D)10
E)12
Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Answer: C
Question: The ratio of investments of A, B and C is 5:7:7. If they share the profit in the ratio of 5:9:14, then find the ratio of their periods of investments.
Options:
A)1:1:2
B)3:5:6
C)3:2:4
D)2:4:3
E)2:5:3
Rationale: The ratio of investments of A, B and C is 5:9:7.
The ratio of shares of A, B and C is 5:9:14.
Therefore, Ratio of their periods of investments is
(5/5) : (9/9) : (14/7) = 1:1:2
ANSWER:A
Answer: A
Question: Replace the ? by the correct Mathematics symbol to make the expression true
10 ? 10 ? 4 ? 7 = 12
Options:
A)10 ÷ 10 x 4 - 7 = 12
B)10 + 10 ÷ 4 + 7 = 12
C)10 x 10 + 4 - 7 = 12
D)10 x 10 ÷ 4 + 7 = 12
E)10 x 10 ÷ 4 - 7 = 12
Rationale: Answer : B
Answer: B
Question: If 144/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer.
Options:
A)I only
B)III only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: The largest possible value of x is 36 (the greatest common factor of 144 and 108), and if x=36 then ONLY III is true.
Answer: B.
Answer: B
Question: The average score of a cricketer in 6 matches is 27 and in other 4 matches is 32. Then find the average score in all the 10 matches?
Options:
A)25
B)27
C)30
D)29
E)42
Rationale: Average in 10 matches = (6*27 + 4*32)/6+4 = 162+128/ 10 = 290/10 = 29
Answer is D
Answer: D
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 171 games will be played during the tournament. Find the number of participants.
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: Let P be the number of participants.
PC2 = 171
(P)(P-1) = 342 = 19*18
P = 19
The answer is E.
Answer: E
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 15% while buying and by 20% while selling. What is his percentage profit?
Options:
A)10.22%
B)20.22%
C)21.22%
D)43.75%
E)Can't be calculated
Rationale: The owner buys 100 kg but actually gets 115kg;
The owner sells 100 kg but actually gives 80kg;
Profit: (115-80)/80*100=~43.75%
Answer: D.
Answer: D
Question: Two trains of equal lengths take 10 sec and 18 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)11
B)9
C)13
D)14
E)12.8
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/18 = 6.7 m/sec.
Relative speed = 12 + 6.7 = 18.7 m/sec.
Required time = (120 + 120)/18.7 = 12.8 sec.
Answer: Option E
Answer: E
Question: Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 36 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
Options:
A)2:5
B)5:14
C)3:5
D)4:15
E)14:5
Rationale: Answer = D) 4:15
........................ Rum ..................... Coke ................. Total
First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)
Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)
Total .................. 10 ............................. 28 .................... 38
Ratio = 8:30 = 4:15
D
Answer: D
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine W is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine W can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
Options:
A)14
B)13
C)11
D)9
E)7
Rationale: 'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days.
To finish a work Machine W say you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D
Answer: D