divelab/Sys2Bench huggingface dataset:
Question: In six successive games, a baseball team scored 4 runs once, 7 runs twice, and 10 runs three times.
What was the average (arithmetic mean) number of runs the team scored per game over the six-game period?
Options:
A)8
B)7
C)6
D)5
E)4
Rationale: 4 runs once (one game)
7 runs twice (two game)
10 runs three times (three games)
SO we have (4*1 + 7*2 + 10*3)/6 = 48/6 = 8.
ANS: A.
Answer: A
Question: A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?
Options:
A)2
B)3
C)6
D)12
E)14
Rationale: Explanation:
Since B and D are twins, so B = D.
Now, A = B + 3 and A = C - 3.
Thus, B + 3 = C - 3 D + 3 = C-3 C - D = 6.
Answer: C
Answer: C
Question: If 20% of a number = 200, then 120% of that number will be?
Options:
A)20
B)120
C)360
D)1200
E)820
Rationale: Let the number x. Then,
20% of x = 200
x = (200 * 100)/20 = 1000
120% of x = (120/100 *1000) = 1200.
ANSWER:D
Answer: D
Question: When positive integer x is divided by positive integer y, the remainder is 8. If x/y = 96.16, what is the value of y?
Options:
A)96
B)75
C)50
D)25
E)12
Rationale: by the definition of a remainder, the remainder here is equal to 8/y. the remainder in decimal form is given as .16
therefore, 8/y = .16
solve for y and get 50.
C
Answer: C
Question: The circumferences of two circles are 660 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?
Options:
A)2996 sq m
B)4774 sq m
C)4312 sq m
D)2768 sq m
E)2786 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 660 and 2∏l = 704
s = 660/2∏ and l = 704/2∏
Difference between the areas = ∏l^2 - ∏s^2
= ∏{330^2/∏^2 - 352^2/∏^2}
= 330^2/∏ - 352^2/∏
= (330 - 352)(330 + 352)/∏
= (22)(682)/(22/7)
=4774 sq m
Answer:B
Answer: B
Question: How many positive integers will divide evenly into 530?
Options:
A)8
B)12
C)16
D)18
E)20
Rationale: 520 = 10*13*4 = 8*5*13 = 2^3*5*13
We need to positive integers will divide evenly into 520 or simply the factors of 520
If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)
Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 18
Option D
Answer: D
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
Options:
A)230
B)881
C)711
D)622
E)211
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: A
Answer: A
Question: Ratio of two numbers x and y is 7:9. If x is increased by 20% and y is increased by 33 then the new ratio becomes 1:5. What is the ratio 2y:(x+4)
Options:
A)18:11
B)8:1
C)11:18
D)1:8
E)1:1
Rationale: Let:
x = 7n
y = 9n
8.4n/(9n+33) = 1/5
42n = 9n+33
n = 1
So, x =7; y=9
2y/(x+4) = 18/11
Answer = A
Answer: A
Question: In a certain company 20% of the men and 40% of the women attended the annual company picnic.If 45% of all the employees are men .What % of all the employee went to the picnic?
Options:
A)31%
B)34%
C)35%
D)36%
E)37%
Rationale: total men in company 45% means total women in company 55%(assume total people in company 100%)
no of men employees attended picnic=45x(20/100)=9
no of women employees attend picnic=55x(40/100)=22
total percentage of employees attend the picnic=9+22=31%
ANSWER:A
Answer: A
Question: 200,190,180,....,160,150,140
Insert the missing number
Options:
A)155
B)156
C)157
D)170
E)158
Rationale: Missing number : 170
Answer : D
Answer: D
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Options:
A)120
B)720
C)4320
D)2160
E)3570
Rationale: The word 'OPTICAL' contains 7 different letters.
when the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA)
Now, 5 letters can be arranged among themselves in 3!=6 ways.
Required number of ways =(120*6)=720.
Answer is B
Answer: B
Question: Two members of a certain club are selected to speak at the next club meeting. If there are 45 different possible selections of the 2 club members, how many members does the club have?
Options:
A)5
B)6
C)7
D)8
E)10
Rationale: Method-1
Total No. of Selection of r out of n objects are defined by nCr = n! / [(r!)(n-r)!]
i.e. If total member = n
then nC2 = n! / [(2!)(n-2)!] = 45
i.e. n*(n-1)*n-2!/ [(2!)n-2!] = 45
i.e. n*(n-1) = 90
(for Positive Values of n)
therefore, n*(n-1) = 90
i.e. n= 10
Answer: Option E
Answer: E
Question: From among the 35 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
A)1360
B)1260
C)1060
D)1190
E)1460
Rationale: There are 35 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 35 ways. When one person is appointed as leader, we are left with 35 students. Out of these 34 teachers, we can select one class representative. So, a class representative can be selected in 34 ways. Hence, the number of ways in which a leader and class representative can be selected = 35 x 34 = 1190
ANSWER:D
Answer: D
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 70 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
Options:
A)22
B)10
C)25
D)99
E)21
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 70) = 90(x - 5)
100 = 10x => x = 10.Answer: B
Answer: B
Question: Seats for Maths, Physics and Biology are in the ratio of 4 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
Options:
A)2 : 3 : 4
B)6 : 7 : 8
C)8 : 15 : 20
D)Cannot be determined
E)None of these
Rationale: Reqd ratio 4 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100
= 4 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 8 : 15 : 20
Answer C
Answer: C
Question: A 5" cube is painted in all its faces and then it is cut down into 1" blocks. How many 1" blocks
are there even without a single face being painted?
Options:
A)16 blocks
B)20 blocks
C)27 blocks
D)36 blocks
E)64 blocks
Rationale: The unpainted blocks are the interior blocks.
These blocks form a 3" cube on the inside.
The number of unpainted blocks is 3*3*3 = 27 blocks.
The answer is C.
Answer: C
Question: At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $5 on candy, how much did John spend at the supermarket?
Options:
A) $75
B) $80
C) $90
D) $120
E) $180
Rationale: Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T.
We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $5 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have:
(1/2)T + (1/3)T + (1/10)T + 5 = T
To get rid of the fractions we can multiply the entire equation by 30, and we obtain:
15T + 10T + 3T + 150 = 30T
28T + 150 = 30T
150 = 2T
T = 75
John spent $7 at the supermarket.
Answer: A
Answer: A
Question: In how many ways can the letters of the word TATTOO be arranged?
Options:
A)1206
B)1348
C)2520
D)60
E)3478
Rationale: TATTOO has 6 words, but T is repeated three times and O is repeated two times. Thus ways
= 6! / 3!2! = 60 ways
D
Answer: D
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 45 years. What will be the age of the B ten years hence?
Options:
A)22
B)77
C)26
D)96
E)90
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 45 => b + c = 90 --- (2)
From (1) and (2), we cannot find b.
Answer: E
Answer: E
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
Options:
A)1134
B)1234
C)1257
D)1259
E)1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: E
Question: A club with a total membership of 30 has formed 3 committees, M, S and R, which have 8, 10 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
Options:
A)5
B)7
C)8
D)10
E)12
Rationale: As no member of committee M is on either of the other 2 committees then 30-M=30-8=22 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees
General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 22-10=12 is the greatest possible number of members in the club who are on none of the committees.
Answer: E.
Answer: E
Question: If x^2+4x+3 is odd, then which one of the following could be the value of x.
Options:
A)3
B)4
C)5
D)6
E)9
Rationale: for any x, 4x+3->odd
so x^2 should be even, means x should be even;
only ans we have 4 as even.
ANSWER:B
Answer: B
Question: Which is the following is divisible by 11
Options:
A)A)109
B)B)4825
C)C)4805
D)D)4905
E)E)4906
Rationale: Explanation:
Sum of first 'n' natural numbers = 1(1 + 1)/2
Sum of first 9 natural numbers = 1(1 + 1)//2 = 1 x 1= 1
Sum of first 99 natural numbers = 11(11 + 1)//2 = 11 x 10 = 110
110 - 1 = 109
Answer: Option A
Answer: A
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)76 sec
B)16 sec
C)15 sec
D)17 sec
E)19 sec
Rationale: Speed = 63 * 5/18
= 35/2 m/sec
Time taken
= 280 * 2/35
= 16 sec
Answer: B
Answer: B
Question: A cycle is bought for Rs.840 and sold for Rs.1220, find the gain percent?
Options:
A)70%
B)45%
C)48%
D)30%
E)40%
Rationale: Explanation:
840 ---- 380
100 ---- ? => 45%
Answer: B
Answer: B
Question: The average of 35 students in a class is 17 years. The average age of 25 students is 15. What is the average age of remaining 10 students?
Options:
A)26 years
B)27 years
C)28 years
D)29 years
E)30 years
Rationale: Sum of the ages of 14 students
= (17 * 35) - (15 * 21) = 595 - 315 = 280
Required average = (280/10) = 28 years.
Answer:C
Answer: C
Question: In what ratio should rice at Rs.9.30 per Kg be mixed with rice at Rs. 10.80 per Kg so that the mixture
be worth Rs.10 per Kg ?
Options:
A)7 : 8
B)8 : 7
C)6 : 7
D)7 : 6
E)None of these
Rationale: Explanation :
By the rule of alligation, we have
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
9.3 10.80
Mean Price
10
10.8-10 = .8 10 - 9.3 = .7
Required ratio = .8 : .7 = 8 : 7.
Answer : Option B
Answer: B
Question: What will be the difference between simple and compound interest @25% per annum on a sum of $3600 after 2 years?
Options:
A)$150
B)$220
C)$225
D)$182
E)$189
Rationale: S.I. = 3600*25*2/100 = $1800
C.I. = 3600 * (1 + 25/100)^2 - 3600 = $2025
Difference = 2025-1800 = $225
Answer is C
Answer: C
Question: Tina and Rebecca had the same number of candies. Tina gave Rebecca 24 candies so that now Rebecca has five times as many candies as Tina has. Rebecca has how many candies initially?
Options:
A)36
B)48
C)54
D)36
E)60
Rationale: T = R
T - 24 ;R + 24
R + 24 = 5 ( T - 24 )
R + 24 =5T - 120
R - 5T = - 144
We knowR = T, so
R - 5T = - 144
Or, R - 5R = -144
Or, - 4R = - 144
Or, R = 36( This is the initital no of Candies Rebecca had)
Answer : D
Answer: D
Question: There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure m in inches of the width of the foil covered prism?
Options:
A)4
B)6
C)8
D)9
E)10
Rationale: If the width is w, then length and height would be w/2.
So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)
=> w = 2*4 m= 8 in.
Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes
= 8 +2 =10
Ans E.
Answer: E
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)09
B)10
C)05
D)02
E)06
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer:B
Answer: B
Question: Suppose 12 points lie on a circle. How many cyclic quadrilaterals can be made by using these points?
Options:
A)440
B)454
C)495
D)486
E)None
Rationale: For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495. Therefore, we can draw 495 quadrilaterals.
Answer C
Answer: C
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)277
B)888
C)228
D)860
E)911
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer:D
Answer: D
Question: A train crosses a platform of 130 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150
B)887
C)167
D)197
E)230
Rationale: Length of the train be ‘X’
X + 130/15 = X + 250/20
20X + 2600 = 15X + 3750
5x=1150
X = 230m
Answer: E
Answer: E
Question: The total monthly income of four men and two women is 46,000. If every woman earns 500 more than a man then what is the monthly income of a woman?
Options:
A)7,500
B)8,000
C)9,000
D)6,500
E)None of these
Rationale: 4M + 2W = 46000;
Again, W = M + 500
or, M = W – 500
∴ (W – 500) + 2W = 46000
or, 6W = 46000 + 2000 = 48000
∴ W = 8000
Answer B
Answer: B
Question: A sun is divided among X, Y and Z in such a way that for each three rupees X gets, Y gets two rupees and Z gets 80 paisa. If the share of Y is RS. 55, what is the total amount of X and Y?
Options:
A)120
B)124.5
C)104.5
D)114.5
E)100
Rationale: x:y:z = 300:200:80
15:10:4
10 --- 55
19 --- ? => 104.5
Answer: C
Answer: C
Question: The grade point average of one third of the classroom is 30; the grade point average of the rest is 33. What is the grade point average of the whole class?
Options:
A)44
B)41
C)38
D)35
E)32
Rationale: Let n=total students in class
total points for 1/3 class=30n/3=10n
total points for 2/3 class=33*2n/3=22n
total points for whole class=10n+22n=32n
32n total class points/n total students=32 grade point average for total class
Answer : E
Answer: E
Question: Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 8 seconds, the speed of each train (in km/hr) is
Options:
A)42
B)36
C)28
D)20
E)54
Rationale: Explanation:
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/8 = 30 m/s
Speed of each train = v = 30/2 = 15 m/s
= 15×36/10 km/hr = 54 km/hr
Answer: Option E
Answer: E
Question: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit and remaining 50% at 30% profit. Find his % profit on total.
Options:
A)23%
B)25%
C)26%
D)28%
E)35%
Rationale: If the total quantity was 100
Then 40X 20% + 50 X30%= 23
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'A' is the answer
Answer: A
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)15 a.m
B)10 a.m
C)12 a.m
D)02 a.m
E)05 a.m
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer:B
Answer: B
Question: two branch of tree bird sit in way if one bird of the first branch goes to second branch there ratio become equal and if bird from second branch goes to first branch ratio become double than first. what are there ratio in sitting ?
Options:
A)7:5
B)6:5
C)8:5
D)5:7
E)5:8
Rationale: if birds on 1st branch=x, 2nd branch=y
Ist condition, x-1=y+1, x-y=2 ---(i) &
2nd condition, x+1=2(y-1), x-2y=-3 ---(ii)
Solving (i) & (ii), x=7, y=5
ANSWER:A
Answer: A
Question: The value of x.320 Ã· 2 Ã· 3 = X
Options:
A)53.33
B)46.33
C)15.36
D)15.45
E)15.48
Rationale: 320Ã·2Ã·3
=320Ã—1/2Ã—1/3
=160/3
=53.33
CORRECT ANSWER : A
Answer: A
Question: In a race with 30 runners where 3 trophies will be given to the top 5 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
A)5^3 ways
B)8^9 ways
C)7^8 ways
D)8^7 ways
E)8^6 ways
Rationale: 5 people can be prized with 3 distinct prizes in 5^3 ways
ANSWER:A
Answer: A
Question: How many keyboards do you need if you have to place 1024 keys into keyboards that each hold 32 keys?
Options:
A)A)28
B)B)30
C)C)32
D)D)34
E)E)None of the above
Rationale: Sol.
1024 keys of 32 each
= 1024 / 32
= 32
Answer : C
Answer: C
Question: In certain year in Country C, x sets of twins and y sets of triplets were born. If there were z total babies born in Country C in this year, and x and y were both greater than 0, which of the following represents the fraction R of all babies born who were NOT part of a set of twins or triplets?
Options:
A)z - 2x - 3y
B)(2x+3y)/z
C)(x+y)/z
D)1 - (2x+3y)/z
E)1 - (x+y)/z
Rationale: X set of twins implies 2x babies of twin category.
Y set of triplets means 3y babies of triplet category.
Let K be the babies other than twin or triplet category.
Total babies = z = 2x+3y+k.
or K=Z-(2x+3y)
=> Fraction of babies other than twin or triplet categories = K/Z = Z-(2x+3y)/Z.
R= 1- (2x+3y)/Z. Hence answer is D.
Answer: D
Question: What positive number, when squared, is equal to the cube of the positive square root of 16?
Options:
A)64
B)32
C)8
D)4
E)2
Rationale: Let the positive number be x
x^2 = ((16)^(1/2))^3
=>x^2 = 4^3 = 64
=> x = 8
Answer C
Answer: C
Question: 0.002 x 0.5 = ?
Options:
A)0.1
B)0.0001
C)0.01
D)1.0
E)0.001
Rationale: 2 x 5 = 10.
Sum of decimal places = 4
0.002 x 0.5 = 0.001
Answer is E.
Answer: E
Question: How many different values of positive integer x, for which |x+6|<x, are there?
Options:
A)0
B)2
C)3
D)8
E)16
Rationale: Answer D
I opted to put the random value option.
i used 0 , 6 , -6 and the the extreme of 20 and -20..
i was able to solve it in 1:09
D
Answer: D
Question: In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?
Options:
A)46.5 kg
B)54 kg
C)65 kg
D)66.5 kg
E)76.5 kg
Rationale: Let Mike's weight be X kg.
According to Mike, 65 < X < 72.
According to Mike's brother, 60 < X < 70.
According to Mike's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
D
Answer: D
Question: A trailer carries 3, 4 and 5 crates on a trip. Each crate weighs no less than 120 kg. What is the maximum weight of the crates on a single trip?
Options:
A)1250
B)625
C)600
D)7500
E)375
Rationale: Max No. of crates=5.
Max Weight=120Kg
Max. weight carried = 5*120=600Kg=C
Answer: C
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
Options:
A)81:121
B)81:126
C)81:189
D)81:176
E)81:117
Rationale: Ratio of the sides
= ³√729 : ³√1331 = 9 : 11
Ratio of surface areas
= 92 : 112 =81:121
Answer:A
Answer: A
Question: If 0 < m < 1 < n< 6, which of the following must be less than 1? I.m/n II. mn III. n - m
Options:
A)I only
B)III only
C)II,III only
D)II only
E)I,II only
Rationale: n > 1. So, option II, III is not possible.
So, Option I is correct.
Answer : A
Answer: A
Question: A and B undertake to do a piece of work for $500. A alone can do it in 5days while B alone can do it in 10days. With the help of C, they finish it in 2days. Find the share of C?
Options:
A)$200
B)$150
C)$300
D)$25
E)$100
Rationale: C's 1day work = (1/2)-(1/5 + 1/10) = 1/5
A:B:C= 1/5 : 1/10: 1/5 = 2:1:2
B's share = 500*2/5 = $200
Answer is A
Answer: A
Question: Light glows for every 13 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am.
Options:
A)380 times
B)381 times
C)382 times
D)392 times
E)482 times
Rationale: Time difference is 1hr,22min,49sec=4969sec. So, light glows floor(4969/13)=382 times.
ANSWER:C
Answer: C
Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
Options:
A)240 meters
B)360 meters
C)420 meters
D)600 meters
E)Cannot be determined
Rationale: Explanation:
Length of the platform = speed of train * extra time taken to cross the platform.
Length of platform = 72 kmph * 12 seconds
Convert 72 kmph into m/sec
1 kmph = 518518 m/s (This can be easily derived. But if you can remember this conversion, it saves a good 30 seconds).
∴ 72 kmph = 518∗72518∗72 = 20 m/sec
Therefore, length of the platform = 20 m/s * 12 sec = 240 meters.
Correct answer: A
Answer: A
Question: 120 is what percent of 40?
.
Options:
A)0.2%
B)2%
C)5%
D)300%
E)500%
Rationale: 120= x*40/100
x = 300%
Ans; D
Answer: D
Question: In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket in c hours, and the hot-water leak alone would fill the same bucket in h hours, where c < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it took t hours to fill the bucket, which of the following must be true?
I. c < t < h
II. 0 < t < h
III. (c/2) < t < (h/2)
Options:
A)a) I only
B)b) II only
C)c) III only
D)d) I and II
E)e) II and III
Rationale: I picked numbers for this problem
C = 2 hours
H = 3 hours
C<H
2 people working together formula is
1/C + 1/H = 1/t
1/2 + 1/3 = 1/t
t = 6/5 = 1.2
Substitute the values of C, H and t in the 3 choices given below
Only 2, 3 are valid.Therefore E is the best answer
Answer: E
Question: The average age of a group of 10 students was 20. The average age increased by 3 years when two new students joined the group. What is the average age of the two new students who joined the group?
Options:
A)22 years
B)30 years
C)38 years
D)44 years
E)None of these
Rationale: The total age of 10 students with average 20 = 200
The total age of 12 students with average 23 = 276
The total age of 2 new students = 76
Their average =38
Correct Option C
Answer: C