divelab/Sys2Bench huggingface dataset:
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
Options:
A)18
B)27
C)25
D)21
E)17
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
Answer: C
Answer: C
Question: A person distributed 20% of his income to his 3 children each. He deposited 25% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income?
Options:
A)A)452000
B)B)562000
C)C)800000
D)D)400000
E)E)652000
Rationale: 3 children got = 3*20% = 60%
wife got = 25%
orphan house = 5%
total = 60+25+5 = 90%
remaining = 100-90 = 10%
10% = 40000
100% = 40000*100/10 = $400000
Answer is D
Answer: D
Question: A part of certain sum of money is invested at 9% 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)4:2
B)4:8
C)4:3
D)4:0
E)4:9
Rationale: 12:9
= 4:3
Answer: C
Answer: C
Question: In what time will a railway train 50 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)5 sec
B)4 sec
C)3 sec
D)6 sec
E)1 sec
Rationale: T = 50/36 * 18/5 = 5 sec
Answer: A
Answer: A
Question: With what number must 3.475817 be multiplied in order to obtain the number 34.75817?
Options:
A)100
B)1000
C)10,000
D)100,000
E)None of these
Rationale: Explanation: The decimal must be moved one places to the right. To do this, we must multiply by a number with one zeroes. The correct answer is 10 .The decimal must be moved one places to the right. To do this, we must multiply by a number with one zero. The correct answer is 10.
Answer : (E)
Answer: E
Question: The average of 11 results is 44, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
A)122
B)156
C)118
D)125
E)123
Rationale: 1 to 11 = 11 * 44 = 484
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 â€“ 484 = 122
Answer:A
Answer: A
Question: In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
Options:
A)10 students
B)20 students
C)30 students
D)40 students
E)50 students
Rationale: Let us write the fraction for each group of students
Group A: younger than 10: 50% = 50/100 = 1/2
Group B: 10 years old: 1/20
Group C: older that 10 but younger than 12: 1/10
Group D: 12 years or older: 70 students
The fraction for group A, B and C together is given by
1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator
= 13 / 20 , add numerators
The fraction for group D is given by
20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students
If X is the total number of students, then
7 / 20 of X = 70
or (7 / 20) ? X = 70
Solve for X
X = 70 ? (20 / 7) = 200
Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to
(1 / 20) of 200 = 10 students
correct answer A
Answer: A
Question: Pointing to an old man, Kailash said, "His son is my son's uncle." How is the old man related to Kailash ?
Options:
A)Brother
B)Uncle
C)Father
D)Grandfather
E)Sister
Rationale: Explanation:
Kailash's son's uncle — Kailash's brother. So. the old man's son is Kailash's brother
i.e., the old man is Kailash's father.
Answer: C
Answer: C
Question: An automobile parts supplier charges $20 per package of gaskets. When a customer orders more than 10 packages of gaskets, the supplier charges 4/5 the price for each package in excess of 10. During a certain week, the supplier sold 60 packages of gaskets. If 20 percent of the gaskets went to Company X, 15 percent to Company Y, and the rest to Company Z, what was the total amount, in dollars, that the parts supplier received in payment for the gaskets?
Options:
A)1005
B)1045
C)1075
D)1015
E)1096
Rationale: $25 per packet of gasket in case a customer orders less than 10
in case a customer orders > 10 price per gasket = 20*4/5=16
a certain week the supplier sold 60 gasket
1.he sold 20 % of the gaskets to X = 12 gaskets = 20*10 + 16 *2 = 200 + 32 = 232
2.he sold 15 % of the gaskets to Y = 9 gaskets = 20*9= 180
3.he sold remaining 65% to z =39 gaskets = 20*10 =200 + 16*29=684
thus ,total money earned
232+180+684 = 1096
Answer is E
Answer: E
Question: On what dates of April,2001 did Wednesday fall ?
Options:
A)1st,8th,15th,22nd,29th
B)2nd,9th,16th,23rd,30th
C)3rd,10th,17th,24th
D)4th,11th,18th,25th
E)None of these
Rationale: Solution
We shall find the day on 1st April,2001.
1st April,2001 =(2000 years + Period from 1.1.2001 to 1.4.2001)
Odd days in 1600 years =0
Odd days in 400 years =0
Jan. Feb. March April
(31 + 28 + 31 + 1) =91 days =0 odd days. Answer D
Answer: D
Question: In a simultaneous throw of 2 dice what is the probability of getting a total of 6?
Options:
A)1/4
B)5/36
C)2/11
D)3/13
E)1/5
Rationale: n(S) = 6*6 = 36
E = {(1,5),(2,4),(3,3),(4,2),(5,1)}
Probability = 5/36
Answer is B
Answer: B
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Options:
A)12 cm
B)14 cm
C)18 cm
D)20 cm
E)22 cm
Rationale: 2(l + b) = 5
b 1
2l + 2b = 5b
3b = 2l
b = 2 l
3
Then, Area = 216 cm2
l x b = 216
l x 2 l = 216
3
l2 = 324
l = 18 cm.
C
Answer: C
Question: Find the least number of candidates in an examination so that the percentage of successful candidates should be 76.8%:
Options:
A)105
B)115
C)125
D)135
E)145
Rationale: suppose no. of total candidates are 'y' and successful are 'x'.
(x/y)*(100)=76.8 or x/y=0.768
or y=x/0.768
here we need minimum value of y, which is obtained by minimum value of x.
if put x=768 then y=1000
now we will try decrease value of x than we will find less value of y. so factorized 768 by 2 further.
if put x=384 then y=500
if put x=192 then y=250
if put x=96 then y=125(answer)
if put x=48 then y=62.5(not integer)
so ans is 125
ANSWER:C
Answer: C
Question: If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 166 m, what is its area?
Options:
A)1590
B)2535
C)2530
D)2515
E)2520
Rationale: length = breadth +23. Therefore,
4× breadth +2×23=166 m
⇒ breadth =30 m
length =30+23=53 m
Area =53×30=1590 m2
Answer is A.
Answer: A
Question: An article is bought for Rs.600 and sold for Rs.450, find the loss percent?
Options:
A)16%
B)18%
C)19 %
D)20%
E)25%
Rationale: 600 ---- 150
100 ---- ? => 16 2/3%
Answer: E
Answer: E
Question: A glass was filled with 10 ounces of water, and 0.02 ounce of the water evaporated each day during a 30-day period. What percent of the original amount of water evaporated during this period?
Options:
A)0.006%
B)0.06%
C)6%
D)2%
E)60%
Rationale: In 30 days 30*0.02=0.6 ounces of water evaporated, which is 0.6/10âˆ—100=6 of the original amount of water.
Answer: C.
Answer: C
Question: Two bullet train s 140 m and 180 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Options:
A)15.8 sec.
B)11.52 sec.
C)11.8 sec.
D)10.8 sec.
E)08.8 sec.
Rationale: Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.
Distance covered in crossing each other = (140 + 180) m = 320 m.
Required time = 320x9/250 = 11.52 sec.
ANSWER B
Answer: B
Question: M, N and O are inner angles in a triangle. If M= N+ O, what can't be the size of N?
Options:
A)90 DEGREES
B)60 DEGREES
C)960 DEGREES
D)960 DEGREES
E)9660 DEGREES
Rationale: Given M= N+ O, and M, N and O are inner angles in a triangle. Thus M+ N+ O= 180
N+ O + N+ O= 180 => 2(N+ O) = 180 => N+ O= 90. Thus beta will be less than 90.
Hence the answer is A.
Answer: A
Question: Mohan purchased 16 kgs of rice at the rate of Rs.26 per kg and 8 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.598
B)B)Rs.625
C)C)Rs.596
D)D)Rs.595
E)E)of these
Rationale: Explanation:
Price of 16 kgs of rice at Rs.26/kg = 16x26 = Rs.416
Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208
Therefore, Total amount = Rs.416+Rs.208 = Rs.624.
Answer: Option B
Answer: B
Question: Raj writes a number. He sees that the number of two digits exceeds four times the sum of its digits by 3. If the number is increased by 18, the results is the same as the number formed by reversing the digits. Find the next immediate prime greater than the number.
Options:
A)22
B)37
C)88
D)27
E)97
Rationale: Let the number be xy = 10x + y
10x + y = 4(x+y) + 3 ⇒⇒ 2x - y -1 -------(1)
Also 10x + y +18 = 10y +x , 9(y-x) = 18, y-x = 2 -------(2)
Solving we get x = 3, y = 5
The number is 35. So next immediate prime is 37
Answer:B
Answer: B
Question: Q' = 3Q - 3, what is the value of (5')' ?
Options:
A) 96
B) 108
C) 120
D) 132
E) 144
Rationale: (5')'=(3*5-3)'=12'=12*12-12=132
Answer D
Answer: D
Question: The Racing magic takes 90 seconds to circle the racing track once. The Charging bull makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?
Options:
A)3
B)6
C)9
D)12
E)15
Rationale: Time taken by Racing magic to make one circle = 90 seconds
Time taken byCharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds
LCM of 90 and 90 seconds = 90 seconds
Time taken for them to meet at the starting point for the second time =2*90 sec=180 seconds = 3 mins
Answer A
Answer: A
Question: How many strings of 6 letters can be made using only the letters A, B, and C, or only the letters D, E, and F ?
Options:
A)2×3^6
B)3×2^6
C)3×3^6
D)2×2^6
E)6^6
Rationale: 3^6 + 3^6 = 2*3^6
ANS : A
Answer: A
Question: 10 men and 15 women together can complete a work in 7 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Options:
A)127 days
B)667 days
C)177 days
D)187 days
E)350 days
Rationale: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/7
15 women's 1 day work = (1/7 - 10/100) = 3/70
1 woman's 1 day work = 1/350
1 woman alone can complete the work in 350 days.
Answer:E
Answer: E
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 76% of the required amount. What is the net difference in the expenditure on that product?
Options:
A)12.5%
B)13%
C)5%
D)17%
E)19%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.76 x 1.25 = 0.95
Decrease in price = (0.05/1) × 100 = 5%
C)
Answer: C
Question: The simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on $4000 for 2 years at 10% per annum. The sum placed on simple interest is ?
Options:
A)$1250
B)$1300
C)$1750
D)$2015
E)$1452
Rationale: C.I. = 4000* (1 + 10/100)^2 - 4000 = 4000* 11/10 * 11/10 -4000 = $840
Sum = 420*100/3*8 = $1750
Answer is C
Answer: C
Question: In year Y imported machine tools accounted for 50 percent of total machine-tools sales in the United States, and Japanese imports accounted for 40 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
Options:
A)10x
B)12x
C)15x
D)17x
E)20x
Rationale: Sales of imported tools = 50% of the total sales = 0.50*{total} = {total}/2;
Sales of Japanese tools = 40% of the sales of imported tools = 0.40*{total}/4 = 4/10*{total}/4 = total}/10.
Since the sales of of Japanese tools was x, then {total}/10 = x --> {total} = 10x
Answer: A
Answer: A
Question: one prototyping machine can make 10 copies every 4 seconds. At this rate, How many copies
can the machine make in 6 min.?
Options:
A)900
B)600
C)360
D)240
E)150
Rationale: 10 copies--4 sec
10/4 copies--1 sec
(10/4)*6*60---1*6*60 sec
900 copies--6 min
ANSWER:A
Answer: A
Question: How many integers N are prime numbers in the range 200 < N < 220?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: To test a number N on whether it is a prime number , take square root(N) .
Consider as it is if it is a natural number. Otherwise, increase the sq. root to the next natural no.
Then divide given no. by all prime numbers BELOW the sq. root obtained.
If the no. is divisible by any of the prime numbers, then it is not a prime number; else it is.
Square root of 200 or 220 is less than 15
So, lets check if any number between 200 and 220 is not divisible by prime numbers 2,3,5,7,11(<15). That's it.
Out: 201, 202, 203, 204, 205, 206, 207, 208, 209, 210,
212, 213, 214, 215, 216, 217, 218, 219
Only 211 is a prime number in the given range
Correct Option : A
Answer: A
Question: In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 15P pots?
Options:
A)4/M
B)4M
C)900M
D)M/900
E)M/4
Rationale: The time it takes to wash 15P pots is 15M minutes which is 15M / 60 = M/4 hours.
The answer is E.
Answer: E
Question: What is the diffference between the place value and face value of 2 in the numeral 6328?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: place value of 2 = 2 * 10 = 20
face value of 2 = 2
20 - 2 = 18
E
Answer: E
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
Options:
A)8 PM
B)4 PM
C)7 PM
D)5 PM
E)2 PM
Rationale: 1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM
Answer: D
Answer: D
Question: 20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 9:10 in the morning?
Options:
A)32.
B)36.
C)42.
D)46.
E)50.
Rationale: @ 6:30 - 2
@ 7 - 4+7 =11
@ 7:30 - 2
@ 8 - 12
@ 8:30 - 2
@ 9 - 13
totals to 42=C
Answer: C
Question: The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 80 percent of the pollutant?
Options:
A)$500,000
B)$100,000
C)$50,000
D)$10,000
E)$5,000
Rationale: Cost to remove 90% - Cost to remove 80% = 100,000*90/(100 - 90) - 100,000*80/(100 - 80) = 9*100,000 - 4*100,000 = 5*100,000 =500,000
Answer: A
Answer: A
Question: If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
Options:
A)None
B)I only
C)II only
D)III only
E)I and III
Rationale: There are other possibilities here: 3 might be a factor of y, and might therefore cancel in the fraction, leaving us with a prime that comes from the factors of x. For example, if x = 10, and y = 6, then 3x/y = 5. So we can see that none of I, II, or III need to be true
ANSWER:A
Answer: A
Question: A and B together can complete work in 10 days. A alone starts working and leaves it after working for 6 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?
Options:
A)4
B)8
C)5
D)6
E)30
Rationale: Explanation:
(A+B) one day work =1/10
now A does half of the work in 6 days so A can complete the whole work in 12 days
A’s one day work =1/12
B’s one day work=1/10 - 1/12= 2/120= 1/60
B alone can complete the work in 60 days so half of the work in 30 days
Answer: Option E
Answer: E
Question: Find the odd man out
2, 5, 10, 17, 26, 37, 50, 64
Options:
A)50
B)26
C)64
D)27
E)17
Rationale: Difference is series of ODD numbers
2+3 = 5
5+5 =10
10+7=17
17+9=26
26+11=37
37+13=50
50+15=65
ANSWER:C
Answer: C
Question: The speeds of three motor bikes are in the ratio 12 : 4 : 2. The ratio between the time taken by them to travel the same distance is :
Options:
A)1 : 3 : 4
B)1 : 3 : 6
C)1 : 2 : 6
D)1 : 3 : 5
E)1 : 4 : 6
Rationale: Ratio of time taken :
1/12 :1/4 : 1/2 = 1 : 3 : 6
ANSWER:B
Answer: B
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 40. He was allowed to drop his lowest score. After doing so, his average test score improved to 45. What is the lowest test score that was dropped?
Options:
A)20
B)25
C)55
D)65
E)80
Rationale: The arithmetic mean of 4 equally weighted tests was 40. So what we can assume is that we have 4 test scores, each 40.
He dropped his lowest score and the avg went to 45. This means that the lowest score was not 40 and other three scores had given the lowest score 5 each to make it up to 40 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 40.
So the lowest score = 40 - 15 = 25
Answer (B)
Answer: B
Question: If x+|x|+y=4 and x+|y|-y=6 what is x+y=?
Options:
A)11
B)-1
C)3
D)5
E)13
Rationale: If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0.
If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases).
Answer: C.
Adding both eqn we get 2x +IxI+IyI = 13
Now considering X <0 and y>0
2x-x +y = 13
we get x+y =11
Hence answer should be A
Answer: A
Question: Bob is about to hang his 8 shirts in the wardrobe. He has four different styles of shirt, two identical ones of each particular style. How many different arrangements are possible if no two identical shirts are next to one another?
Options:
A)764
B)864
C)964
D)1064
E)None of these
Rationale: Explanation :
Total number of 8-perms of 8 shirts, recognising identical pairs, is:=8!2!4=2520In order to find the number of perms with no adjacency we subtract from this the number of perms with 4 pairs adjacent, 3 pairs adjacent, 2 pairs adjacent and 1 pair adjacent.The following four intermediate results aid explanation of the final calculation :Let the shirts be called A, A, B, B, C, C, D, D and let {A,.....} be the set of 8-perms that have only the styles named in the argument list adjacent to each other. So, for instance, {B,D} is the set of perms that contain BB and DD but not AA and CC. Let s{A,....} be the number of perms in {A,...}(i) s{A,B,C,D} = 24. This is because we can imagine each pair as one object and simply permute the four twin objects amongst themselves in 4! ways to give {A,B,C,D}.(ii) s{A,B,C} = 36. To see this we first permute the 5 objects AA, BB, CC, D, D. This can be done in5!2!=60 ways but includes {A,B,C,D}. Hence s{A,B,C} =5!2!−24(iii) s{A,B}=84. As before, we first permute the 6 objects AA, BB, C, C, D, D. This can be done in 6!/(2!)^2 ways but includes {A,B,C}, {A,B,D} and {A,B,C,D}.Hence s{A,B} =6!2!2–2×36−24(iv) s{A}=246. This time we start by permuting the 7 objects AA, B, B, C, C, D, D in7!2!3ways and then removing from it the subsets {A,B}, {A,C}, {A,D}, {A,B,C}, {A,B,D}, {A,C,D} and {A,B,C,D}. Hence s{A}=7!2!3−3×36−3×84–24Assembling the total number of perms with some adjacency:There are 4C4 subsets of type (i) ie {A,B,C,D}Total number of 8-perms of this type is 24.There are 4C3 subsets of type (ii) ie {A,B,C} {A,B,D} {A,C,D} {B,C,D}Total number of 8-perms of this type is 4×36=144There are 4C2 subsets of type (iii) ie {A,B} {A,C} {A,D} {B,C} {B,D} {C,D}Total number of 8-perms of this type is 6×84=504Finally there are 4C1 subsets of type (iv) ie {A} {B} {C} {D}Total number of 8-perms of this type=4×246=984Therefore, number of perms with some adjacency is 24+144+504+984=1656Number of perms with no adjacency is 2520−1656= 864
Answer : B
Answer: B
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
Options:
A)128.9 m
B)127.5 m
C)812.9 m
D)127.7 m
E)712.7 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs
= (900 * 700)/800
= 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5)
= 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C
= (600 * 212.5)/1000 = 127.5 m.
Answer: B
Answer: B
Question: If the area of a circle decreases by 25%, then the radius of a circle decreases by
Options:
A)13%
B)18%
C)36%
D)64%
E)None of these
Rationale: If area of a circle decreased by x % then the radius of a circle decreases by
(100−10√100−x)%=(100−10√100−25)%
= (100−10√75)%
= 100 - 87 = 13%
Answer A
Answer: A
Question: A and B complete a work in 50 days. A alone can do it in 40 days. If both together can do the work in how many days?
Options:
A)1.075 days
B)0.185 days
C)0.065 days
D)0.045 days
E)0.0775 days
Rationale: 1/50 + 1/40 = 0.045 days
ANSWER:D
Answer: D
Question: Three dice are thrown together, Find the probability of getting a total of atmost 6?
Options:
A)1/3
B)1/8
C)3/13
D)2/25
E)5/54
Rationale: Three different dice are thrown at the same time.
Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.
Number of events of getting a total of atmost 6 = 20
i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1), (1, 2, 2), (1, 1, 4), (1, 4, 1), (4, 1, 1), (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1) and (2, 2, 2).
Therefore, probability of getting a total of atmost 6
P(E) = Number of favorable outcomes/Total number of possible outcome
= 20/216
= 5/54
Answer: E
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Options:
A)287
B)350
C)828
D)277
E)122
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: B
Answer: B
Question: Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8 : 5 ?
Options:
A)3: 4
B)4 : 3
C)9 : 7
D)7 : 9
E)8 : 1
Rationale: Explanation:
Let Cost Price(CP) of 1 litre spirit be Rs.1
Quantity of spirit in 1 litre mixture from vessel A =5/7
Cost Price(CP) of 1 litre mixture from vessel A = Rs. =5/7
Quantity of spirit in 1 litre mixture from vessel B =7/13
Cost Price(CP) of 1 litre mixture from vessel B =Rs. =7/13
Quantity of spirit to be obtained in 1 litre mixture from vessel C =8/13
Cost Price(CP) of 1 litre mixture from vessel C(Mean Price) = Rs. =8/13
=> Mixture from Vessel A : Mixture from Vessel B
=1/13:9/91 =7:9
Answer IS D
Answer: D
Question: Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 4,500, how much money did investors B and C earn in total?
Options:
A)$4,000
B)$4,900
C)$5,600
D)$9,500
E)$13,500
Rationale: Let profit for A = 5x
profit for B = 7x
profit for C = 8x
Investor A earned = 34500
5x = 4500=>x=900
Total profit for B and C = 7x+ 8x = 15x
Therefore , 15x = 15*900 = 13,500
Answer E
Answer: E
Question: The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 15000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is
Options:
A)Rs. 7000
B)Rs. 8000
C)Rs. 8800
D)Rs. 9000
E)None
Rationale: Answer
Average salary
= 8000 + 5000 + 15000 + 7000 + 9000 / 5
= Rs. 8800
Correct Option: C
Answer: C
Question: x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 9 will be equal to:
Options:
A)3
B)6
C)1/9
D)1/3
E)9
Rationale: Explanation :
Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.
.'. x = 9/y^2
=> x =9 /9^2 = 1/9
Answer : C
Answer: C