divelab/Sys2Bench huggingface dataset:
Question: A rectangular cube has sides measuring 3 inches long by 2 inches wide by 0.5 inches high. If the surface area of the rectangle is the same as a cube, what do the sides/walls of the cube measure? Round to the nearest whole number.
Options:
A)4
B)5
C)6
D)7
E)2
Rationale: First calculate the surface area of the rectangle by multiplying the length and width of the rectangle together, then multiply by 2 to get both sides of the rectangle. This calculates to 12 inches. Find the surface area of the sides of the rectangular cube. Multiply the height by the length of the rectangle. Multiply the answer by 2 (for the 2 sides on the rectangular cube). This calculates to 3 inches. Then multiply the width of the rectangle by the height. Multiply the answer by 2 (for the 2 sides on the rectangular cube). This calculates to 2 inches. Add the totals together to get the rectangular cube surface area of 17 inches. Since a square cube has 6 sides, divide the surface area by 6. This calculates to 2.833 inches as the surface area of each side of the cube. The square root of 2.833 is 1.683. Rounding to the nearest whole number that makes each side of the cube measuring 2 inches. The correct answer is (E).
Answer: E
Question: If the sum of the interior angles of a regular polygon measures up to 1260 degrees, how many sides does the polygon have?
Options:
A)6
B)3
C)9
D)4
E)None of these
Rationale: 9 sides...answer is C
Answer: C
Question: 4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Options:
A)4 days
B)6 days
C)7 days
D)9 days
E)1 days
Rationale: 1 women's 1 day work = 1/28
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/28 + 10/140) = 1/4
5 women and 10 children will complete the work in 4 days.
Answer: A
Answer: A
Question: Raja and Abdul can finish the work 18 days if they work together. They worked together for 12 days and then Abdul left. Rja finished the remaining work in another 12 days. In how many days Raja alone can finish the work?
Options:
A)30 days
B)60 days
C)70 days
D)36 days
E)90 days
Rationale: Amount of work done by Raja and Abdul in 1 day = 1/18
Amount of work done by Raja and Abdul in 12 days = 12 Ã— (1/18) = 2/3
Remaining work â€“ 1 â€“ 2/3 = 1/3
Raja completes 1/3 work in 12 days
Amount of work JOHN can do in 1 day = (1/3)/12 = 1/36
=>Raja can complete the work in 36 days
Answer : D
Answer: D
Question: A cube painted red on two adjecent faces and black on the faces opposite to the red faces and green on the remaining faces is cut into sixty-four smaller cubes of equal size.How many cubes are there which have no face painted?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: If a painted cube is cut into 64 (4^3) smaller cubes then there will be
i. smaller cubes with three face painted (cubes at the corner)= 8
ii.smaller cubes with two face painted (cubes at the edges)= (4-2)*12= 24
iii.smaller cubes with one face painted (cubes at the faces)= ((4-2)^2)*6=24
iv.smaller cubes not painted = 64-(8+24+24)= 8
ANSWER:A
Answer: A
Question: There are 4 numbers A, B, C, and D. If A:B = 1/2, B:C = 2/7, C:D = 7/3, then A:D will be?
Options:
A)1 : 2
B)2 :1
C)2 : 7
D)1 : 7
E)1 : 3
Rationale: Solution
A : B = 1 : 2, B : C = 2 : 7, C : D = 7 : 3
âˆ´Aâˆ¶Bâˆ¶Câˆ¶D= 1 : 2 : 7 : 3.
Thus, A : D = 1 : 3
Correct Option E
Answer: E
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
Options:
A)587 × 10<10>(exponent) miles
B)587 × 10<-12> (exponent) miles
C)587 × 10<-10>(exponent) miles
D)587 × 10<12>(exponent) miles
E)587 × 10<8>(exponent) miles
Rationale: The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 ×10<12>(exponent) miles
Answer: D
Question: An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 40 miles per hour, then 50 miles per hour, then 60 miles per hour. If the test took 74 hours to complete, how many miles was the car driven during the entire test?
Options:
A)3600
B)3400
C)3300
D)3500
E)3200
Rationale: x is the segment to be traveled
x/40+x/50+x/60 =74
or 74x/1200 =74
x = 1200miles . total distance =3*1200 = 3600 miles
A
Answer: A
Question: Two pipes A and B can separately fill a tank in 12 minutes and 16 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)5min
B)7min
C)8min
D)9min
E)10min
Rationale: 4/12 + x/16 = 1
x = 10
ANSWER:E
Answer: E
Question: Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 60 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
Options:
A)20
B)34
C)38
D)40
E)48
Rationale: Nice question +1
We have that X/24 - (60-X)/2R = 40
Also X/R - (60-X)/2R = 120
So we get that 2x - 60 = 80R
3x - 60 = 240R
Get rid of R
120 = 3x
x = 48
Hence answer is E
Answer: E
Question: There are, in a certain league, 50 teams, and each team face another team for a total of 4 times. How many games are played in the season?
Options:
A)6660
B)3600
C)2400
D)4900
E)5400
Rationale: By using the formula, t[n(n - 1) / 2], where t = no. of games between two teams and n = total no. of teams, we get: 4900
Option D.
Answer: D
Question: Trains A and B start simultaneously from stations 450 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 50 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?
Options:
A) 112
B) 133
C) 150
D) 167
E) 225
Rationale: Since we know the distance (450) and the combined rate (100), we plug it into the formula:
Distance = Rate * Time
450 = 100 * Time
We can solve for the time they will meet cause we added the rate of Train A and Train B together.
So the time will be 450/100 from dividing 100 on both sides to isolate Time in the equation above.
Time will be 4.5 hours so now you can plug that in for Train A’s distance.
Distance = Rate * Time
Distance = 50 * 4.5
Distance = 225 according to answer choice E.
Answer: E
Question: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
Options:
A)Rs. 21,000
B)Rs. 22,500
C)Rs. 25,300
D)Rs. 25,800
E)Rs. 26,800
Rationale: sell at 18700 he got a loss of 15% means, This 18700 is 85% not 100%.
To get 1% : 18700/85=220; Then 220 is 1%.
To get 100% : 220x100=22000.
To get 115% : 220x115=25300
answer :C
Answer: C
Question: A certain smoothie A is three-fifths blueberries and 40% raspberries by weight. Another smoothie B is three-quarters banana and one-quarter raspberries by weight. If the mixed smoothie of A and B is 30% raspberries by weight, how much weight of this mixture belongs to smoothie A?
Options:
A)10%
B)33.33%
C)45%
D)50%
E)66.66%
Rationale: A is 40% raspberries;
B is 25% raspberries.
A and B is 30% raspberries;
30% raspberries in the mixed smoothie of A and B come from 40% raspberries in A and 25% raspberries in B, thus:
0.3(A+B)=0.4A+0.25B --> 0.1A=0.05B --> A/B=1/2 --> A/(A+B)=1/3.
Answer: B.
Answer: B
Question: There are 600 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%?
Options:
A)100
B)200
C)250
D)300
E)400
Rationale: There are 594 managers and 6 others. The 6 others would compose 2% of the total number of people if there were 300 people in the room. Thus 300 managers must leave.
The answer is D.
Answer: D
Question: For which of the following does f(r)−f(s)=f(r−s) for all values of r and s?
Options:
A)f(a)=a^2
B)f(a)=a/2
C)f(a)=a+5
D)f(a)=2a−1
E)f(a)=|a|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. f(r) = r^2 and f(s) = s^2
so L.H.S = r^2 - s^2
and R.H.S = (r-s)^2 ==> r^2 + s^2 -2rs.
so L.H.S not equal to R.H.S
with option 2. f(r) = r/2 and f(s) = s/2
L.H.S = r/2 - s/2 ==> 1/2(r-s)
R.H.S = (r-s)/2
so L.H.S = R.H.S which is the correct answer.
B
Answer: B
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?
Options:
A)153
B)150
C)146
D)144
E)89
Rationale: Let x be the original 2-digit number.
If each digit is halved, then the sum of G and H is 3x/2.
Note the sum must be a multiple of 3 and less than 150.
Of these five choices, only 144 satisfies these two conditions.
The answer is D.
Answer: D
Question: Two goods trains each 625 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)40
B)45
C)48
D)60
E)44
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 625 + 625 = 1250 m.
Required time = 1250 * 6/125 = 60 sec.
Answer: Option D
Answer: D
Question: What is the ratio between perimeters of two squares one having 1.5 times the diagonal then the other?
Options:
A)3: 6
B)1.5: 1
C)3: 1.5
D)2: 1
E)3: 2
Rationale: d = 1.5d d = d
a√2 = 1.5d a√2 = d
a = 1.5d/√2 a = d/√2 => 1.5: 1
Answer: B
Answer: B
Question: A landlady has been paid $329,864 to her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to confirm that the money has been paid evenly by all 9 of her house rentors?
Options:
A)$1
B)$2
C)$3
D)$4
E)$6
Rationale: To find the least amount the landlady should add to her saving account to ensure that every rentor has paid evenly,
she needs to make the total divisible by 9
Simply add the individual digits of the total = 3+2+9+8+6+4 = 32
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Answer: D
Question: A company run by 20 men can produce 1000 pencils in a day. One-fifth of the pencils produced are defective and one-quarter of all pencils produced are rejected by quality control technician. If one-tenth of the nondefective pencils are rejected by mistake, and if all the pencils not rejected are sold, then what percent of the pencils sold by the company are defective?
Options:
A)4%
B)10%
C)8%
D)6%
E)2%
Rationale: We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 4 of every 100 that are sold (not rejected) and defective, which implies Answer A.
Answer: A
Question: A train 270 m long passed a pole in 27 sec. How long will it take to pass a platform 650 m long?
Options:
A)92 sec
B)89 sec
C)54 sec
D)27 sec
E)22 sec
Rationale: Speed = 270/27 = 10 m/sec.
Required time = (270 + 650)/10
= 92 sec.
Answer: A
Answer: A
Question: The measurement of a rectangular box with lid is 50cmx30cmx38cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
Options:
A)288
B)4500
C)7200
D)864
E)9640
Rationale: d=30, r=15;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*15*15*15= 4500πcm3 ANSWER:B
Answer: B
Question: 70% of the employees of a company are men. 50% of the men in the company speak French and 40% of the employees of the company speak French. What is % of the women in the company who do not speak French?
Options:
A)4%
B)10%
C)83.33%
D)90.33%
E)20%
Rationale: No of employees=100(say)
Men=70
Women=30
Men speaking french=0.5*70=35
Employees speaking french=0.4*100=40
Therefore women speaking French=40-35=5
And women not speaking French=30-5=25
% of women not speaking French=25/30*100=83.33%
Answer C
Answer: C
Question: Which of the following statements must be true?
I)The product of first 100 prime numbers is even
II)The sum of first 100 prime numbers is odd.
III)The sum of first five non-negative even numbers is divisible by both 4 and 5
Options:
A)I only
B)II only
C)I and II only
D)I and III only
E)I, II and III
Rationale: First look at some Odd & Even Rules:-
Multiplication
E x E = E
O x O = O
E x O = E = O x O
Addition
E + E = E
E + O = O = O + E
O + O = E
Now coming to the statements:-
I. The product of first 100 prime numbers is even
First 100 prime nos. includes 2 which is the ONLY even no. Hence, any no. multiplied by even no will give an Even No.
II. The sum of first 100 prime numbers is odd
We can figure this out through Cyclicity Rule. Ignore the First TWO Prime Nos. and let us start with 5, which is Odd.
O + O = E (Sum of two primes)
E + O = O (Even is carried over and added to 3rd prime)
O + O = E (Carry over and 4th prime)
E + O = O (5th prime)
O + O = E (6th prime)
Through Cyclicity, we can find out that the sum of any Even No of ODDS will always be EVEN. Since 98th no is Even, the answer will also be EVEN. Now, include the first two prime nos. i.e. 2 & 3.
E + 2(E) + 3(O) = O
Hence, the statement is TRUE.
III. The sum of first five non-negative even numbers is divisible by both 4 and 5
First five non negative even nos. = 0, 2, 4, 6 and 8
Sum = 20. Divisible by both 4 AND 5
Answer : E
Answer: E
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for three years?
Options:
A)29893
B)27773
C)29989
D)26100
E)29883
Rationale: Simple interest = (18000 * 3 * 15)/100 = Rs. 8100
Amount = P + I = 18000 + 8100 = Rs. 26100
Answer: D
Answer: D
Question: If P is a prime number greater than 3, find the remainder when P^2 + 13 is divided by 12.
Options:
A)6
B)1
C)0
D)2
E)7
Rationale: Every prime number greater than 3 can be written 6N+1 or 6N-1.
If P = 6N+1, then P^2 + 13 = 36N^2 + 12N + 1 + 13 = 36N^2 + 12N + 12 + 2
If P = 6N-1, then P^2 + 13 = 36N^2 - 12N + 1 + 13 = 36N^2 - 12N + 12 + 2
When divided by 12, it must leave a remainder of 2.
The answer is D.
Answer: D
Question: Ashok opened a shop investing Rs.60,000 and Madhuri joined him after 2 months investing Rs.90,000. They get a profit of Rs. 1,08,000 after one year. The share of Madhuri is
Options:
A)Rs.35,000
B)Rs.30,000
C)Rs.60,000
D)Rs.45,000
E)None of the above
Rationale: 60000*12:90000*10=4:5
5/9(108000)=60000
ANSWER:C
Answer: C
Question: If 945*s is a perfect square then s can be which of the following numbers?
Options:
A)21
B)35
C)54
D)105
E)150
Rationale: For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 945 are 3 *3 *3 *5 * 7
1) 21 = 3 * 7
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 105 = 3 * 5 * 7
5) 150 = 2 * 3 * 5 * 5
So only answer choice D completes the pairing of 3, 5 and 7. It adds a "3", a "5", and a "7" to the prime factors of 945 (3*3*3*5*7) and makes it a perfect square.
Answer: D
Question: A swimmer can swim in still water at 4 km/h. If the speed of the water current is 1 km/h, how many hours will the swimmer take to swim against the current for 6 km?
Options:
A)1.2
B)1.4
C)1.6
D)1.8
E)2
Rationale: The swimmer can swim against the current at a speed of 4-1 = 3 km/h.
The time it will take is 6/3 = 2 hours.
The answer is E.
Answer: E
Question: P = {22, 24, 26, 28, 30, 32}
Q = {2, 24, 25, 26, 27, 28}
R = {4, 7, 10, 13, 16, 19}
If p is the standard deviation of set P, q is the standard deviation of set Q, and r is the standard deviation of set R, which of the following must be true?
Options:
A)p<q<r
B)p<r<q
C)q<r<p
D)q<p<r
E)r<q<p
Rationale: P has difference by 2.
Q has difference of 22 between 2 and 24 and for other numbers we have difference by 1.
R has difference 3.
We need to take the SD as per the difference.
So Q > R > P. Option B has this set
ANSWER:B
Answer: B
Question: A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?
Options:
A)24
B)46
C)67
D)28
E)29
Rationale: 2/7 - 1/x = 1/4
x = 28
Answer: D
Answer: D
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
Options:
A)3/7
B)4/7
C)5/7
D)5/11
E)6/11
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
B)
Answer: B
Question: A 14 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
A)12
B)20
C)88
D)77
E)4
Rationale: 1: 2/5 = 5: 2
2/7 * 14 = 4
Answer: E
Answer: E
Question: 30 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?
Options:
A)12 days
B)11 days
C)10 days
D)16 days
E)13 days
Rationale: C
10 days
Total work to be done = 30 * 40 = 1200
Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (20 * 40) = 1200
40P = 400 => P = 10 days
Answer: C
Question: What is the probability of flipping a fair coin four times and the coin landing on heads on at least two flips?
Options:
A)1/16
B)15/16
C)9/16
D)11/16
E)7/16
Rationale: There are totally 16 outcomes
Chances of all being heads is 1/16
Chances of 3 heads is = 4c34c3 ways = 4/16
Chances of 2 heads is 4c24c2 ways = 6/16
hence 1/16+4/16+6/16=11/161/16+4/16+6/16=11/16
Ans: "D"
Answer: D
Question: There are total 15 people. 7 speaks French and 8 speaks Spanish 3 do not speak any language. Which part of total people speaks both languages.
Options:
A)3/4
B)1/5
C)1/6
D)3/8
E)1/3
Rationale: If x no of people speak both languages then
15 = 8+7-x+3
x=3
so part of total people speaks both languages = 3/15 =1/5
ANSWER:B
Answer: B
Question: The ages of two persons differ by 16 years. If 6 years ago , the elder one be 3 times as old as the younger one, find their present ages .
Options:
A)10 years and 18 years
B)18 years and 26 years
C)20 years and 28 years
D)14 years and 30 years
E)16 years and 25 years
Rationale: Explanation :
Sol. Let the age of the younger person be xx years
Then , age of the elder person = (x+16)(x+16) years
âˆ´âˆ´ 3(xâˆ’6)=(x+16âˆ’6)3(x-6)=(x+16-6)
â‡” 3x âˆ’18=x+10â‡” 3x -18=x+10
â‡” 2x=28â‡” 2x=28
â‡” x=14â‡” x=14
Hence, their present age are 14 years and 30 years .
ANSWER IS D
Answer: D
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
Options:
A)20%
B)30%
C)32%
D)73%
E)84%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 ---20 => 20%
Answer:A
Answer: A
Question: Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 40 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?
Options:
A)80 lakh
B)50 lakh
C)40 lakh
D)64 lakh
E)None of these
Rationale: Let the incomes of two companies A and B be 5x and 8x respectively.
From the question,
5x+40/8x=5/4 ⇒ 20x + 160 = 40x
∴ x = 8
∴ Income of company B = 8x = 64 lakh
Answer D
Answer: D
Question: The dimensions of a rectangular solid are 4 inches, 5 inches, and 10 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?
Options:
A) 10:17
B) 2:5
C) 10:19
D) 25:7
E) 32:25
Rationale: Answer: C.
Answer: C
Question: Dimitri weighs 2x-x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of y pounds. Which of the following represents Allen’s weight?
Options:
A)y - x/2
B)2x - y/2
C)(y - x)/2
D)y - 2x
E)2x - y
Rationale: These type of multi-variable story problems are usually perfect for TESTing VALUES.
Here, we're told that Dimitri weighs 2X-X or X pounds more than Allen weighs and that they weight a combined TOTAL of Y pounds.
IF....
Dimitri = 30
Allen = 20
X = 10
Y = 50
We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.
Answer A: 50 - (10/2) = 45 NOT a match
Answer B: 20 - (50/2) = -5 NOT a match
Answer C: (50-10)/2 = 20 This IS a match
Answer D: 50 - 20 = 30 NOT a match
Answer E: 20 - 50 = -30 NOT a match
Final Answer:
C
Answer: C
Question: In how many ways can the letters of the word MECHANIC be arranged?
Options:
A)2580
B)2500
C)20160
D)2520
E)3420
Rationale: MECHANIC has 8 words, but C is repeated two times. Thus ways = 8! / 2! = 20160 ways
C
Answer: C
Question: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/2, then what is the value of abc/def ?
Options:
A) 27/4
B) 27/8
C) 3/4
D) 3/8
E) 1/4
Rationale: Say a = 3. Then:
a/b = 1/3 --> b = 9;
b/c = 2 --> c = 9/2;
c/d = 1/2 --> d = 9;
d/e = 3 --> e = 3;
e/f = 1/2 --> f = 6.
abc/def = (3*9*9/2)/(9*3*6) = 3/4.
Answer: C.
Answer: C
Question: A and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work ?
Options:
A)4 days
B)5 days
C)6 days
D)7 days
E)8 days
Rationale: Explanation:
(A+B)'s 1 day work = 1/4
A's 1 day work = 1/12
B's 1 day work =
(1/4−1/12)=3−1/12=1/6
So B alone can complete the work in 6 days
Option C
Answer: C
Question: How many seconds will a 100 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)11 sec
B)6 sec
C)77 sec
D)14 sec
E)12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 100 * 3/50
= 6 sec.
Answer: B
Answer: B
Question: A person has his own coach & whenever he goes to railway station he takes his coach. One day he was supposed to reach the railway station at 5 O'clock. But he finished his work early and reached at 3 O'clock. Then he rung up his residence and asked to send the coach immediately. He came to know that the coach has left just now to the railway station. He thought that he should not waste his time and started moving towards his residence at the speed of 3miles/hr. On the way, he gets the coach and reaches home at 6 o'clock. How far is his residence from railway station.
Options:
A)17 miles
B)18 miles
C)19 miles
D)16 miles
E)15 miles
Rationale: He walked for 1.5 hrs and coach travelled in one side for 1.5 hrs instead of 2 hrs to save 0.5 hrs one side journey of coach.
So Coach speed is 3 times speed of man i.e. 9 mph.
Total distance of stn from Home = 1.5( 3+9) = 1.5*12= 18 miles
ANSWER:B
Answer: B
Question: The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
Options:
A)2.98 min
B)5.28 min
C)1.97 min
D)2.88 min
E)2.77 min
Rationale: Clearly, the two will meet when they are 726 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 726 m apart, they take (100/825 * 726/1000) hrs
= (242/2750 * 60) min
= 5.28 min.
Answer: B
Answer: B
Question: What should come in place of the question mark (‘?) in the following equation?
18 2⁄5 of 150.8 + ? = 8697.32 – 3058.16
Options:
A)2764.44
B)2864.34
C)1864.44
D)2684.44
E)None of these
Rationale: ? = 8697.32 – 3058.16 – 92⁄5 × 150.8
= 5639.16 – 2774.72 = 2864.44
Answer E
Answer: E