divelab/Sys2Bench huggingface dataset:
Question: A group of boy scouts and girls scouts is going on a rafting trip. 60% of the scouts arrived with signed permission slips. If 45% of the scouts were boy scouts and 50% of the boy scouts arrived with signed permission slips, then what percentage of the girl scouts arrived with signed permission slips? Round to the nearest percent.
Options:
A)64
B)68
C)72
D)76
E)80
Rationale: 45% were boy scouts so 55% (100-45=55) were girl scouts.
# of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed
(50% of 45% of the total going) + (?% of 55% of the total going) = 60% of the total going
We can let the "total going" = 1,000 arbitrarily since we only care about the percent (of girl scouts w/ permission signed)
.50*.45*1,000 + x*.55*1,000 = .60*1,000
225 + x*550 = 600
550x=375
x=375/550
x=.6818181818 which converts to a percent of 68.18181818% which rounds to 68%
B
Answer: B
Question: 5,9,18,31,52,__
Options:
A)79
B)80
C)86
D)82
E)83
Rationale: (9+5) +4 = 18
(16+9) +6 = 31
(28+16)+8 = 52
(48+28)+10 = 86
ANSWER:C
Answer: C
Question: An investment compounds annually at an interest rate of 10% What is the smallest investment period by which time the investment will more than triple in value?
Options:
A)n =log 3/log 1.1
B)11/10 ^n
C)(11/10)^n
D)1.1^n
E)1.2^n
Rationale: Assume initial amount is x
Annual Interest is 10% so after 1 year the amount will become x * (100+10)/100 => x*11/10
now we need to find n for x * (11/10)^n = 3x
or in other words or 3 =(11/10)^n or 3= (1.1^n)
log 3 =nlog 1.1 then n = log 3/log1.1
A
Answer: A
Question: The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
A)22
B)56
C)44
D)55
E)81
Rationale: 1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550 = 56
Answer: B
Answer: B
Question: A certain no. when divided by 140 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
Options:
A)2
B)4
C)7
D)8
E)11
Rationale: Explanation:
140 + 25 = 165/15 = 11 (Remainder)
E
Answer: E
Question: In how many different ways can the letters of the word VALUE be arranged in such a way that the vowels occupy only the odd positions?
Options:
A)10
B)12
C)18
D)24
E)32
Rationale: The 3 vowels can be arranged in three odd places in 3! ways.
The 2 consonants can be arranged in two even places in 2! ways.
The total number of arrangements in which vowels occupy odd positions = 3! Ã— 2! = 6 Ã— 2 = 12
The answer is B.
Answer: B
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
Options:
A)6 2/3%
B)6 2/9%
C)2 2/3%
D)6 5/3%
E)5 2/3%
Rationale: 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3%.Answer:A
Answer: A
Question: A cylinder of height h is 2/3 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
Options:
A)25%
B)50%
C)60%
D)80%
E)90%
Rationale: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 2/3
New cylinder 3/5
So 3/5/2/3 = 3/5*3/2 = 0.90 or 90%.
Answer E
Answer: E
Question: Fence X is twice as long as fence Y, and fence Y is 2 feet shorter than fence Z. If 3 feet were added to each fence, which of the following must be true?
I) Y is 3 feet shorter than X.
II) Y is 2 feet shorter than Z.
III) X is shorter than Z.
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: If X= 6
Y= 3
Z= 5
Then, after adding 3 feet to each:
X= 9
Y=6
Z=8
And the answer would be D, which is wrong.
Answer: D
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Options:
A)250
B)375
C)300
D)540
E)560
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
ANSWER B
Answer: B
Question: Food grains are to be sent to city from go down. Owner wants to reach the food grains at 11 O' Clock in the city. If a truck travels at a speed of 30km/hr then he will reach the city one hour earlier. If the truck travels at a speed of 20km/h then he will reach the city one hour late. Find the distance between the go down to city. Also with which speed the truck should travel in order to reach at exactly 11 'O clock.
Options:
A)24 kmph
B)25 kmph
C)26 kmph
D)27 kmph
E)28 kmph
Rationale: Let distance be x km and original time be t hr, when he travels at constant speed, say s kmph.
Clearly, x = st.
Now, x=30(t-1) and x=20(t+1). Solving these to simultaneous linear eqns, we get x=120 km and t=5 hr. So, distance between city and go-down=120km. To reach exactly at 11 o'clock, he must travel at speed s=x/t = 120/5 = 24 kmph
ANSWER:A
Answer: A
Question: The contents of a certain box consist of 14 apples and 20 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?
Options:
A)3
B)6
C)14
D)17
E)20
Rationale: The objective here is that 70% of the fruit in the box should be apples.
Now, there are 14 apples at start and there is no talk of removing any apples, so number of apples should remain 14 and they should constitute 70% of total fruit, so total fruit = 14/0.7 = 20
So we should have 20-14 = 6 oranges.
Right now, there are 20 oranges, so to get to 6 oranges, we should remove 20 - 6 = 14 oranges.
Answer C
Answer: C
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)3451
B)3467
C)3891
D)4601
E)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 box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
Options:
A)20/67
B)20/63
C)20/19
D)20/18
E)20/28
Rationale: Required probability
= (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126
= 20/63
Answer: B
Answer: B
Question: Dhoni spent 40 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Dhoni have left over?
Options:
A)30%
B)28%
C)32%
D)33%
E)34%
Rationale: Say Dhoni's earning last month was $100.
Dhoni spent 40 percent of his earning last month on rent --> $40 on rent;
20 percent less than what he spent on rent to purchase a new dishwasher --> $40*0.8=$32 on the dishwasher.
Left over amount 100 - (40 + 32) = $28
Answer: B
Answer: B
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.65 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)42
B)77
C)48
D)99
E)11
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.65 = 1.75 km = 1750 m.
Required time = 1750 * 3/125 = 42 sec.
Answer: A
Answer: A
Question: x is a positive integer less than 500. When x is divided by 5, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: the nubmer which when divided by 5 leaves remainder 1 should be of the form 7k+1
this number when divided by 3 leaves remainder 2.
so,
(7k+1)-2 should be divisible by 3 or 7k-1 should be divisible by 3.
we now put the values of k starting from 0 to find first number divisible by 3
we find 1st number at k= 1
thus smallest number will be 7(1)+1 = 8
now,
next number will be = 8+ lcm of 37
i.e 29
now we will find number of all such values less than 500 by using the formula for last term of an a.p
8+(n-1)21=500
n=24.42
or n= 24
Answer:- D
Answer: D
Question: If 0 < a < b and k = (3a + 5b)/b , which of the following must be true?
Options:
A)k < 2
B)k < 7
C)k > 3
D)k > 9
E)k > 11
Rationale: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
~~~~
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 since a < b, you get k = (3+10)/2 = 6.5, thus leaving the option B as the correct answer..
Answer: B
Question: If an investor puts $600 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?
Options:
A)$661.50
B)$663.50
C)$665.50
D)$667.50
E)$669.50
Rationale: 1.05*1.05*600=$661.50
The answer is A.
Answer: A
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,44,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:
Options:
A)0.23255
B)0.14544
C)0.25632
D)0.35466
E)0.63435
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 344000x
\therefore Required percentage = \inline \frac{800x}{344000}\times 100 = 0.23255
A
Answer: A
Question: By selling an article at $600, a profit of 25% is made. Find its cost price?
Options:
A)$580
B)$400
C)$480
D)$570
E)$330
Rationale: C
$480
SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = $480
Answer: C
Question: The average of the marks of 12 students in a class is 50. If the marks of each student are doubled, find the new average?
Options:
A)160
B)120
C)100
D)150
E)170
Rationale: Sum of the marks for the 12 students
= 12 * 50 = 600. The marks of each student are doubled, the sum also will be doubled.
The new sum =600 * 2 = 1200. So, the new average
= 1200/12 = 100.
Answer:C
Answer: C
Question: Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Thursday, what was the expected day when both the brothers were to return home and when did Rohit Return?
Options:
A)Wednesday, Sunday
B)Thursday, Monday
C)Sunday, Thursday
D)Monday, Friday
E)none
Rationale: Rajat returned on thursday -i.e. 3 days earlier
so actual day to return home is sunday.
Rohit returned after days so thursday
ANSWER:C
Answer: C
Question: For numbers x, y, z, and w, if x is 50% greater than y, and z is 20% greater than w, is what percent greater or less than ?
Options:
A)20 % greater
B)20 % less
C)25 % greater
D)25 % less
E)50 % greater
Rationale: x = 1.5y
z = 1.2w
=> x/y = 1.5
z/w = 1.2
so x/y is greater by 0.3/1.2 * 100 = 25%
Answer - C
Answer: C
Question: If a + b - c = 2d, and if a - b + c =-4e, then a =
Options:
A)2(d + e)
B)d – e
C)(d + e)/2
D)d-2e
E)e-d
Rationale: Add both equations:
a + b - c = 2d
a - b + c =--4e
a+b-c+a-b+c=2d-e
2a=2d-4e
a=d-2e
Ans:D
Answer: D
Question: There are 12 pieces of radioactive metal A that look identical. 11 of the pieces give the same radiation count when measured, the 12th piece is a counterfeit and gives a different radiation level, which may be more or less than the other 11. We are given a radiation scale, which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different, which set has the higher level of radiation. What is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: First of all if you are down to just 3 pieces and you know that if the offending piece is less or more active, then it takes exactly 1 measurement to find out the offending piece. So you know you have to reduce the problem to three.
Now when you are down to either A or B after measurement 1, you need the next measurement to (a) reduce the problem set to 3 and (b) to know whether anser is more or less. Now you cannot compare a group of 4 to 4, as in the best case it will only reduce the problem to 4 elements which is not good enough.
If you have to choose a set of 3 to compare, you cannot pick any 3 on the same side from the same set (A or B) because if you do this, a quick check will show you that in every choice there is a case where you can only get down to 4 elements. Eg. If you weighed {1,2,3} v/s {5,9,10} and they were equal you're problem would only reduce to {4,6,7,8}
The easiest way to solve this then is to compare 3 to 3, and make sure each side has elements from both AB such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only. Which is why the sets {1,5,9} and {2,6,7} OR {A,B,C}{A,B,B}. The extra element from C is just taken to make the problem symmetric so to say, we have 8 elements and we make it 9, to compose 3 sets of 3 each.=B
Answer: B
Question: 10/21 of 3/5 of a number is greater than 4/7 of 1/5 of the same number by 36. What is half of that number?
Options:
A)105
B)180
C)210
D)240
E)315
Rationale: Let no. be x
10/21*3/5*x - 4/7*1/5*x =8
by further solving
30x/105- 4x/35=36
18x/105=36
x=210
we have to find x/2
=210/2=105
ANSWER:A
Answer: A
Question: How many seconds will a train 110 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Options:
A)28 sec
B)23 sec
C)24 sec
D)25 sec
E)26 sec
Rationale: D = 110 + 150 = 260
S = 36 * 5/18 = 10 mps
T = 260/10 = 26 sec
E
Answer: E
Question: United Telephone charges a base rate of $9.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?
Options:
A)2 minutes
B)10 minutes
C)20 minutes
D)40 minutes
E)60 minutes
Rationale: Lets take number of minutesx.
Given that, 9+0.25x=12+0.2x ->0.05x=2 -> x=60minutes
ANS E
Answer: E
Question: A satellite is composed of 24 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/8 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?
Options:
A)1/4
B)1/5
C)1/6
D)1/8
E)1/24
Rationale: Let x be the number of upgraded sensors on the satellite.
The number of non-upgraded sensors per unit is x/8.
The number of non-upgraded sensors on the whole satellite is 24(x/8) = 3x.
The fraction of sensors which have been upgraded is x / (x+3x) = x/4x = 1/4
The answer is A.
Answer: A
Question: If 10 typists can type 20 letters in 20 minutes, then how many letters will 40 typists working at the same rate complete in 1 hour?
Options:
A)220
B)210
C)200
D)240
E)260
Rationale: No. of letters typing by 10 typists in 20 minutes = 20
No. of letters typing by 10 typists in 60 minutes = 20*3 = 60
No. of letters typing by 40 typists in 60 minutes = 60/10*40 = 240
Answer : D
Answer: D
Question: There are two cars. One is 90 miles north of the other. Simultaneously, the car to the north is driven westward at 25 miles per hour and the other car is driven eastward at 35 miles per hour. How many miles apart are the cars after 2 hours?
Options:
A)120
B)130
C)140
D)150
E)160
Rationale: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:
The right triangle will have a base of 90 and a height of 120. The hidden pattern here is a 3/4/5 right triangle (the 90 lines up with the '3' and the 120 lines up with the '4'). In this way, you can deduce that each side is '30 times' bigger than it's corresponding side:
3/4/5 becomes
90/120/150
Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...
Final Answer: D
Answer: D
Question: Recipe requires 15mins to cook. you have 7 mins hourglass and a 11 mins hourglass with you. how will you measure 15 mins using them?
Options:
A)15 mins
B)12 mins
C)13 mins
D)17 mins
E)20 mins
Rationale: Correct Answer : A
Put up both hour glasses. time starts when 7 min hourglass turns empty. and 11 min hourglass will run for 4 min. now flip 11 min hour glass upside down as soon as it runs empty. it will be empty in another 11 mins. and time is up. so 4+11= 15 mins
Answer: A
Question: At what rate percent per annum will a sum of money double in 2 years.
Options:
A)34%
B)50%
C)11.5%
D)20%
E)21.5%
Rationale: Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 2)]% = 50% per annum. Answer: B
Answer: B
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Options:
A)20
B)22
C)27
D)28
E)30
Rationale: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
Short cut method:
a:b = 2:3
c:d = 3:4
1.Cross multiplication with both ratios
a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1
2. If 10 is added both the number means 10 * 3 = 30 and 10 * 4 = 40,
Then 30 ~ 40 = 10
===> 1 -----> 10
===> 2 -----> 20
A
Answer: A
Question: Positive integer y is 50 percent of 25 percent of positive integer x, and y percent of x equals 100. What is the value of y?
Options:
A) 50
B) 125
C) 200
D) 1,000
E) 2,000
Rationale: y = 50% of 25 % 0f x
= x/8
and
y/100 of x = 100
y /100 *8y =100
y = 125
Answer - B
Answer: B
Question: Three balls are to be tossed in a row. How many different sequences are possible if red and blue always follow one-another in each toss ?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Consider red and blue as one. But, in this arrangement they can be tossed in two different combinations.
Red first and Blue second or blue first and red second. Total we have (R and B) and third color = 2 arrangements to do. Total arrangements= 2*2= 4
B is the answer
Answer: B
Question: A train 210 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40 sec
B)50 sec
C)44 sec
D)49 sec
E)28 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 210 + 140 = 350 m
Required time = 350 * 2/25 = 28 sec
Answer:E
Answer: E
Question: If 70% of an equal to 40% of b, then ratio between a and b is?
Options:
A)4: 7
B)4: 9
C)4: 2
D)4: 1
E)4: 5
Rationale: Explanation:
70 a = 40 b
a: b = 4: 7
Answer:A
Answer: A
Question: If 2/a + 3/a + 5/a is an integer, which of the following must also be an integer?
Options:
A)12/a
B)3/a
C)6/a
D)10/a
E)15/a
Rationale: 2/a + 3/a + 5/a
=10/a
Answer D
Answer: D
Question: The value of x + x(xx) when x = 2 is:
Options:
A)36
B)16
C)18
D)64
E)10
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: E
Question: Two partners investede Rs. 1250 and Rs. 850 respectively in a business. They distributed 60% of the profit equally and decide to distribute the remaining 40% as the ratio of their capitals. If one partner received Rs. 30 more than the other, find the total profit?
Options:
A)393.75
B)393.78
C)393.72
D)393.71
E)393.77
Rationale: Let the total profit be Rs.x
60% of the profit = \inline \frac{60}{100}\times x=Rs.\frac{3x}{5}
from this part of the profit each gets = Rs.\inline \frac{3x}{10}
40% of the profit = \inline \frac{40}{100}\times x=Rs.\frac{2x}{5}
Now, this amount of Rs.\inline \frac{2x}{5} has been divided in the ratio of capitals 1250 : 850 = 25 :17
\inline \therefore Share on first capital = \inline (\frac{2x}{5}\times \frac{25}{42})=Rs.\frac{5x}{21}
Share on second capital = \inline (\frac{2x}{5}\times \frac{17}{42})=Rs.\frac{17x}{105}
Total money received by 1st investor = \inline [\frac{3x}{10}+\frac{5x}{21}]= Rs.\frac{113x}{210}
Total money received by 2nd investor = \inline [\frac{113x}{210}+\frac{97x}{210}]=Rs.\frac{97x}{210}
\inline \therefore x = 393.75
Hence total profit = Rs. 393.75
Answer:A
Answer: A
Question: What is the largest integer n such that 2^n is a factor of 20^8 ?
Options:
A)1
B)2
C)4
D)8
E)16
Rationale: 20^8=(2^2∗5)^8=2^16 5^8 Therefore the largest integer n such that 2^n is a factor of 2^165^8 is 16.
Answer: E.
Answer: E
Question: The difference between a number and its two-fifth is 510. What is 30% of that number?
Options:
A)158
B)200
C)255
D)400
E)280
Rationale: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
10% of 850 = 255.
Answer:C
Answer: C
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
Options:
A)28888
B)38000
C)28880
D)27752
E)11222
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: B
Answer: B
Question: How many arrangements of the letters of the word GRADES can be made, without changing the place of the vowels in the word?
Options:
A)36
B)25
C)45
D)66
E)24
Rationale: A,E fixed. Consonants can be arrangements in 4P4 = 4! = 24 ways
Option 'E'
Answer: E
Question: The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places?
Options:
A)Rs.20043.94
B)Rs.20043.99
C)Rs.20043.95
D)Rs.20043.98
E)Rs.20043.91
Rationale: Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer:A
Answer: A
Question: How many zeros does 500! end with?
Options:
A)201
B)240
C)124
D)125
E)180
Rationale: According to above 500! has 500/5+500/25+500/125=100+20+4=124 trailing zeros.
Answer: C.
Answer: C
Question: If the sides of a triangle are 36 cm, 34 cm and 20 cm, what is its area?
Options:
A)320 cm2
B)360 cm2
C)340 cm2
D)310 cm2
E)300 cm2
Rationale: The triangle with sides 36 cm, 34 cm and 20 cm is right angled, where the hypotenuse is 36 cm.
Area of the triangle
= 1/2 * 34 * 20
= 340 cm2
Answer: C
Answer: C
Question: Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is?
Options:
A)8 km
B)7 km
C)5 km
D)6 km
E)4 km
Rationale: dist travelled at 4 kmph speed = 2/3
dist at 5 kmph speed = (1-2/3)d=(1/3)d
tot time = 1 hr 24 min =(64+24) min=84/60hr=>21/15 hr
time = dist/speed
21/15=2/3/4d+1/3/5d
d=6 km
ANSWER D
Answer: D
Question: The length of the bridge, which a train 170 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)388
B)267
C)205
D)288
E)261
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (170 + X)/30 = 25/2 ==> 2(170 + X) = 750 ==> X = 205 m.
Answer: C
Answer: C
Question: The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 3 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be English teachers?
Options:
A)2/3
B)1/3
C)2/9
D)1/12
E)1/24
Rationale: Probability of first member an English teacher = 3/10
Probability of second member an English teacher = 2/10
Probability of both being english teacher = 3/9 x 2/8 =3/5(D)
Answer: D
Question: An object travels at fifteen feet per minute. How many feet does it travel in 24 minutes and 40 seconds?
Options:
A)220
B)156
C)370
D)420
E)519
Rationale: Convert speed from feet/minute into feet/seconds.
15 feet / mn = 15 feet / 60 sec
In 24 minutes 40 seconds, there are
24*60 + 40 = 1480 seconds
We now multiply speed by time to find distance
1480*15/60 = 370 feet
correct answer C
Answer: C
Question: What is the are of an equilateral triangle of side 16 cm?
Options:
A)64√3
B)64√5
C)64√9
D)64√2
E)64√1
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16
= 64√3 cm2;
Answer:A
Answer: A