mathewhe/aqua_rat huggingface dataset:
Question: Mark drove for 1/2 of the trip, and Justin drove for 1/4 of the trip. Gina and Kaitlyn divided the
rest of the driving evenly between them. If the entire trip was 128 miles, how many miles did Kaitlyn
drive?
(A) 26 miles
(B) 16 miles
(C) 20 miles
(D) 18 miles
(E) 17 miles
Rationale: 1/2 x 128 = 64 miles Mark drove
1/4 x 128 = 32 miles Justin drove
64 + 32 = 96 miles driven
128 - 96 = 32 miles left
32 ÷ 2 = 16 miles driven by Kaitlyn
correct answer B
Answer: (B) 16 miles
Question: Jamboree and GMAT Club Contest Starts
QUESTION #10:
How many words (with or without meaning)F can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
(A)  660
(B)  600
(C)  500
(D)  300
(E)  240
Rationale: In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical. in this case,F if you think logically, A,B,C,D options are not divisible by 6!. 6 is total number of letters in the word SELFIE. Only option E is divisible by 6!. So correct answer is E that is 240
Answer: (E)  240
Question: An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?
(A) 25
(B) 35
(C) 150
(D) 210
(E) 300
Rationale: I get C. If I see this on the test, id prolly get to 210 and then guess A B or C.
OK so for the first position we have only 2 possibilities ( proj manager) 3 for the team leader so and 7!/3!4! for the consultants
2*3*35 --> 210
Now I dunno how to figure out the constraints quickly but I eventually figured it out. Obvs. we want to figure out the total ways in which the two ARE on the same team.
I did it by AB are the two and XYZFN are the rest
ABXO (O stands for the other 4) So the first is ABXY, Z,F,N 4 possible choices
The next is
ABYO (but notice we already had YX so there are only 3 possible choices)
ABZO
ABFO
ABNO No possible here we used them all up
So 4+3+2+1 = 10
SO now its 2*3*10 =60
So 210-60 = 150
ANS:C
Answer: (C) 150
Question: A cistern is normally filled in 14 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
(A) 33
(B) 88
(C) 40
(D) 99
(E) 112
Rationale: 1/14 - 1/x = 1/16
x = 112
Answer: E
Answer: (E) 112
Question: If the numbers representing volume and surface area of a cube are equal, then the length of the edge of the cube in terms of the unit of measurement will be
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Sol.
a3 = 6a2
⇒ a = 6.
Answer D
Answer: (D) 6
Question: Sachin Tendulkar bough a red ferrari with a strange 5 digit numbered plate.The water image of the number is 78633 more than my car number.All the digits of sachin's car number are distinct. What is the original number on sachin's number plate?
(A) 15468
(B) 10558
(C) 14298
(D) 10668
(E) 10968
Rationale: E
10968
Water image is 89601
Answer: (E) 10968
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 22 seconds
(B) 65 seconds
(C) 78 seconds
(D) 12 seconds
(E) 21 seconds
Rationale: Speed of the boat downstream
= 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m
= 60/5 = 12 seconds.
Answer:D
Answer: (D) 12 seconds
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x+4)(x+10)(2x-5) = 0?
(A) 1/12
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=-4,x=-10andx=5/2=2.5. So, three solutions present in our set of 12 distinct numbers, therefore P=3/12=1/4.
Answer: C.
Answer: (C) 1/4
Question: of polynomial for degree of x>+1 where f(x2)=f(x)2=f(f(x))
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Let f(x) = x2
f(x2)=[x2]2=x4
(f(x))2=[x2]2=x4
f(f(x))=f(x2)=[x2]2=x4
Only 1
ANSWER:B
Answer: (B) 1
Question: How many words can be formed by using all letters of the word “BIHAR”
(A) 120
(B) 240
(C) 150
(D) 160
(E) 140
Rationale: The word BIHAR contains 5 different letters.
Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120.
Answer A.
Answer: (A) 120
Question: The amount of principal Rs.4000 at compound interest at the ratio of 10% p.a. for 3 years is
(A) Rs.5342
(B) Rs.4325
(C) Rs.5324
(D) Rs.3425
(E) Rs.3525
Rationale: 5324
ANSWER:C
Answer: (C) Rs.5324
Question: A man can row a boat at 36 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 100 km upstream?
(A) 10/3
(B) 10/7
(C) 10/9
(D) 10/11
(E) 10/13
Rationale: Speed upstream = 36-6=30 kmph.
Time required to cover 100 km upstream = d/s = 100/30 = 10/3 hours. Answer:A
Answer: (A) 10/3
Question: A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?
(A) 7500
(B) 2776
(C) 2877
(D) 2667
(E) 2671
Rationale: P = (d * 1002) / R2
=> (48 * 100 * 100) / 8 * 8 = Rs.7500
Answer:A
Answer: (A) 7500
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
(A) 42, 33
(B) 42, 36
(C) 44, 33
(D) 44, 36
(E) 45, 38
Rationale: Explanation:
Let the marks secured by them be x and (x+9)
sum of their marks =x+(x+9)=2x+9
Given that (x+9) was 56% of the sum of their marks
=X+9=56/100(2X+9)
X=33
Then (x+9)=33+9=42
Hence their marks are 33 and 42
ANSWER IS A
Answer: (A) 42, 33
Question: In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ?
(A) 2/3
(B) 5/8
(C) 5/9
(D) 3/7
(E) 4/7
Rationale: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
B
Answer: (B) 5/8
Question: On dividing 190 by a number, the quotient is 9 and the remainder is 1. Find the divisor?
(A) A)12
(B) B)15
(C) C)16
(D) D)17
(E) E)21
Rationale: d = (D-R)/Q
= (190 - 1)/9
= 189/9 = 21
E)
Answer: (E) E)21
Question: The average mark of the students of a class in a particular exam is 90. If 2 students whose average mark in that exam is 45 are excluded, the average mark of the remaining will be 95. Find the number of students who wrote the exam?
(A) 10
(B) 40
(C) 20
(D) 30
(E) 25
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 90 x.
Total marks of (x - 2) students = 95(x - 2)
90x - (2 * 45) = 95(x - 2)
100 = 5x => x = 20
Answer: C
Answer: (C) 20
Question: The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly six elements each?
(A) 96
(B) 80
(C) 84
(D) 88
(E) 92
Rationale: nC2 = 36
=> n*(n-1)/2 = 36 by middle term factor and n cannot be negative
=> n = 9
nC3 = 9C6 = 9!/6!*(9-6)!= 9*8*7*6!/6!*3*2 =84
So, Answer is C.
Answer: (C) 84
Question: The length, breadth and height of a room are in the ratio 4 : 4 : 2. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
(A) (a) decrease by 37.5%
(B) (b) decrease by 13.64%
(C) (c) decrease by 15%
(D) (d) decrease by 18.75%
(E) (e) decrease by 30%
Rationale: Length (L) = 4
Breadth (B) = 4
Height (H) = 2
Total Area of Walls = 2(BH + LH) = 2*(4*2 + 4*2) = 2*(8+8) = 32
Then, Finally
Length (L) = 2*4 = 8
Breadth (B) = 4/2 = 2
Height (H) = 2/2 = 1
Total Area of Walls = 2(BH + LH) = 2*(2*1 + 8*1) = 2*(2+8) = 20
% change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area
i.e. % change in Area of four walls = (20-32)*100 /32=- 37.5% (Decrease)
Answer: Option A
Answer: (A) (a) decrease by 37.5%
Question: If Z= Y^2 + d W+ 9 does not cut the x-axis, then which of the following could be a possible value of d?
I. 0
II. -3
III. 9
(A) III only
(B) II only
(C) I and II only
(D) II and III only
(E) I and III only
Rationale: Here C is the answer as A and B statements will provide the discriminant to be negative thereby making the x axis cutting impossible.
Hence only 1 and 2
thus C
Answer: (C) I and II only
Question: The number of stamps that P and Q had were in the ratio of 7:4 respectively. After P gave Q 8 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 6:5. As a result of the gift, P had how many more stamps than Q?
(A) 4
(B) 8
(C) 12
(D) 16
(E) 20
Rationale: P started with 7k stamps and Q started with 4k stamps.
(7k-8)/(4k+8) = 6/5
35k - 24k = 48 + 40
11k = 88
k = 8
P has 7(8) - 8 = 48 stamps and Q has 4(8)+8 = 40 stamps.
The answer is B.
Answer: (B) 8
Question: How many positive even integers less than 100 contain digits 5 or 7?
(A) 10
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: Two digit numbers:
5 at tens place: 50,52,54,56,58
7 at tens place: 70,72,74,76,78
If 5 and 7 is at units place, the number cant be even
Total:5+5= 10
Answer A
Answer: (A) 10
Question: 3^b + 3^b + 3^b =
(A) 7^b
(B) 7^(b + 1)
(C) 7^(7b)
(D) 3^(b + 1)
(E) 49^B
Rationale: Easy one.
3*3^b = 3^(b+1)
Ans. D
Answer: (D) 3^(b + 1)
Question: A and B go around a circular track of length 150 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
(A) 30 sec
(B) 198 sec
(C) 178 sec
(D) 665 sec
(E) 276 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 150/ (36 * 5/18) , 150/ (54 * 5 /18) }
= LCM (15, 10) = 30 sec.
Answer:A
Answer: (A) 30 sec
Question: Donna, Chris, and Austin have a total of $93 in their wallets. Donna has $7 more than Chris. Austin has 3 times what Donna has. How much do they have in their wallets?
(A) D$20 C$13 Au$60
(B) D$40 C$23 Au$40
(C) D$60 C$33 Au$30
(D) D$80 C$43 Au$20
(E) D$90 C$53 Au$90
Rationale: Let the amount in Chris’s wallet be $x
Donna has $7 more than Chrish's wallet = $(x + 7)
Austin has 3 times than Donna's wallet = $3(x + 7)
According to the problem, Donna, chris, and Austin have a total of $93 in their wallets.
Therefore,
x + (x + 7) + 3(x + 7) = 93
x + x + 7 + 3x + 21 = 93
5x + 28 = 93
- 28 -28 (subtract 28 from both sides)
5x = 65
or, 5x/5 = 65/5 (Divide both sides by 5)
x = 13
Amount in Chris wallet = $x = $13
Amount in Donna's wallet = $(x + 7) = $(13 + 7) = $20
Amount in Austin 's wallet = $3(x + 7) = $3(13 + 7) = $3(20) = $ 60
Answer: Amount in Chris’s wallet: $13
Amount in Donna's wallet: $20
Amount in Austin's wallet: $60
correct answer A
Answer: (A) D$20 C$13 Au$60
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.80. How much was lent at 5%?
(A) 228
(B) 299
(C) 266
(D) 500
(E) 1000
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 80
5x/100 + 90 â€“ 6x/100 = 80
x/100 = 10
=> x = 1000
Answer:E
Answer: (E) 1000
Question: A grocer purchased 20 kg of rice at the rate of 15 per kg and 30 kg of rice at the rate of 13 per kg. At what price per kg should he sell the mixture to earn 331/3% profit on the cost price?
(A) 28.0
(B) 20.0
(C) 18.4
(D) 17.4
(E) None of these
Rationale: CP= 20 ×15 + 30 ×13 = 690
\ sp = 4⁄3 of 690 × 1⁄50 = 18.40
Answer C
Answer: (C) 18.4
Question: Weights of two friends Ram and Shyam are in the ratio 4:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?
(A) 19%
(B) 10%
(C) 21%
(D) 16%
(E) None
Rationale: Solution:
given ratio of Ram and Shayam's weight = 4:5
Hence, (x-15)/(15-10) = 4/5
Or, x = 19%.
Answer: Option A
Answer: (A) 19%
Question: The radius of a semi circle is 6.7 cm then its perimeter is?
(A) 32.75
(B) 32.45
(C) 22.45
(D) 34.45
(E) 32.15
Rationale: 36/7 r = 6.7 = 34.45
Answer:D
Answer: (D) 34.45
Question: The average weight of 8 person's increases by 3 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 60 kg
(B) 70 kg
(C) 80 kg
(D) 89 kg
(E) 95 kg
Rationale: Total weight increased = (8 x 3) kg = 24 kg.
Weight of new person = (65 + 24) kg = 89 kg.
D)
Answer: (D) 89 kg
Question: The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
(A) 82.5
(B) 52.9
(C) 52.2
(D) 52.5
(E) 52.7
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80 = 52.5
Answer:D
Answer: (D) 52.5
Question: 20 litres of mixture contains 40% alcohol and the rest water. If 8litres of water be mixed with it, the percentage of alcohol in the new mixture would be?
(A) 26.32%
(B) 35.14%
(C) 28.57%
(D) 25%
(E) 31.14%
Rationale: Alcohol in the 20litres of mix. = 40% of 20litres = (40*20/100) = 8litres
water in it = 20-8 = 12litres
new quantity of mix. = 20+8 = 28 litres
Quantity of alcohol in it = 8litres
Percentage of alcohol in new mix. = 8*100/28 = 50/3= 28.57%
Answer is C
Answer: (C) 28.57%
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 25 . The largest number is:
(A) 28
(B) 30
(C) 36
(D) 42
(E) 45
Rationale: Explanation:
Let the numbers be 4x, 5x and 6x. Therefore,
(4x+5x+6x)/3 = 25
15x = 75
x = 5
Largest number = 6x = 30.
ANSWER B
Answer: (B) 30
Question: The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
(A) 448
(B) 488
(C) 542
(D) 548
(E) 560
Rationale: Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8
= 548.
answer :D
Answer: (D) 548
Question: Calculate the standard deviation of each data set {10,10,10,10,10}
(A) 8.05
(B) 9
(C) 10
(D) 15
(E) 15.5
Rationale: Standard Deviation Data set A
= √[ ( (9-10)2+(10-10)2+(11-10)2+(7-10)2+(13-10)2 )/5 ] = 2
Standard Deviation Data set B
= √[ ( (10-10)2+(10-10)2+(10-10)2+(10-10)2+(10-10)2 )/5 ] = 0
Standard Deviation Data set C
= √[ ( (1-10)2+(1-10)2+(10-10)2+(19-10)2+(19-10)2 )/5 ] = 8.05
Option A
Answer: (A) 8.05
Question: If x is a positive even number, then each of the following is odd EXCEPT
(A) (x + 3)(x + 5)
(B) x^2 + 5
(C) x^2 + 6x + 9
(D) 3x^2 + 4
(E) 5(x + 3)
Rationale: lets see the choices..
A. (x + 3)(x + 5)
We have two terms with x and each is added with a odd number..
each bracket becomes odd and Odd*Odd=Odd
B. x^2 + 5
here we are adding an Odd number to even.. so E + O=O
C. x^2 + 6x + 9
here we are again adding an Odd number to even.. so E +E + O=O
D. 3x^2 + 4
here we are adding an Even number to even.. so E + E=E..
so this is our answer
E. 5(x + 3)
again O*O=O
ANSWER:D
Answer: (D) 3x^2 + 4
Question: A rectangular box of volume x has width, depth and height in the ratio of 5:1:2 (in that order). What is the width as a function of x?
(A) (4x/12)^(1/2)
(B) (10x/4)^(1/2)
(C) (5x)^(1/2)
(D) (2x/5)^(1/2)
(E) (4x/3)^(1/2)
Rationale: We are given width = 5, depth = 1, height = 2
Then Volume x = Width x Depth x Height = 5*1*2 = 10
i.e. x = 10
i.e. The correct option should result in 5 (the width) on substituting the value of x=10
Checking options with x=10
A) (4x/12)^(1/2) = (4*10/12)^(1/2) = (40/12)^(1/2) INCORRECT ANSWER
B) (10x/4)^(1/2) = (10*10/4)^(1/2) = 25^(1/2) = 5 CORRECT ANSWER
C) (5x)^(1/2) = (5*10)^(1/2) = 50^(1/2) INCORRECT ANSWER
D) (2x/5)^(1/2) = (2*10/5)^(1/2) = 4^(1/2) = 2 INCORRECT ANSWER
E) (4x/3)^(1/2) = (4*10/3)^(1/2) = 40/3^(1/2) INCORRECT ANSWER
Answer: Option B
Answer: (B) (10x/4)^(1/2)
Question: A man has a job, which requires him to work 8 straight days and rest on the ninth day. If he started work on Monday, find the day of the week on which he gets his 12th rest day.
(A) Thursday
(B) Wednesday
(C) Tuesday
(D) Friday
(E) None
Rationale: Explanation :
The man get his 1st rest on the ninth day,
So he will get his 12th rest on : 12x9 = 108th day
The first day is monday so 108th(15x7 + 3) day will be same as 3rd day which will be Wednesday.
Answer : B
Answer: (B) Wednesday
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
(A) 9:1
(B) 9:9
(C) 9:7
(D) 9:5
(E) 9:2
Rationale: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1 Answer:A
Answer: (A) 9:1
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 35%?
(A) 228
(B) 480
(C) 267
(D) 416
(E) 276
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.224
SP = CP - Loss = 640 - 224 = Rs.416
Answer: D
Answer: (D) 416
Question: What is the smallest positive integer x for which x3+5xx3+5x has a value more than 80?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 4^3 + 5*4 = 64 + 20 = 84
That's pretty close to 80 already so I can cancel D and E since they'll be more than 80. B just needs to be checked just in case so...
3^3 + 5*3 = 27 + 15 = not close to 80.
Therefore, 4 (C) is the smallest positive integer x for which x^3 + 5x has a value more than 80.ANSWER:C
Answer: (C) 4
Question: The cash realised on selling a 14% stock is Rs.109.25, brokerage being 1/4% is
(A) 123
(B) 109
(C) 100
(D) 156
(E) 240
Rationale: Explanation:
Cash realised= Rs. (109.25 - 0.25)
= Rs. 109.
Answer: B
Answer: (B) 109
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.24200. What is the share of X in the profit?
(A) Rs.14400
(B) Rs.26400
(C) Rs.12000
(D) Rs.12500
(E) Rs.13200
Rationale: Ratio of the investment=21000:17500=210:175
=42:35=6:5
Share of X in the profit=(24200×6)/11=
=13200
ANSWER:E
Answer: (E) Rs.13200
Question: How many terminating zeroes W does 200! have?
(A)  40
(B)  48
(C)  49
(D)  55
(E)  64
Rationale: You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.C
Answer: (C)  49
Question: P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
(A) 10 days
(B) 14 days
(C) 15 days
(D) 9 days
(E) 5 days
Rationale: Explanation :
Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1
Ie, the work will be done in 15 days
Answer :C
Answer: (C) 15 days
Question: 30 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?
(A) 30
(B) 32
(C) 45
(D) Data inadequate
(E) None of these
Rationale: Capacity of the tank = 30 Ã— 13.5= 405 litres
When the capacity of each bucket = 9 litres, then the required no. of buckets
=405â„9 = 45
Answer C
Answer: (C) 45
Question: Surekha started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajesh joined him with an amount of Rs. 35,000. In 2001, Surekha invested another additional amount of Rs.10,000 and Jay joined them with an amount of Rs.35,000. What will be Rajesh's share in the profit of Rs.1,20,000 earned at the end of 3 years from the start of the business in 1999?
(A) Rs 40000
(B) Rs 50000
(C) Rs 70000
(D) Rs 75000
(E) None
Rationale: Surekha:Rajesh:Jay= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajesh's share =Rs.(120000×2/6) = Rs.40000.
Answer A
Answer: (A) Rs 40000
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
(A) 10.7 km/hr
(B) 10.8 km/hr
(C) 17.8 km/hr
(D) 10.5 km/hr
(E) 30.8 km/hr
Rationale: Total distance traveled = 10 + 12 = 22 km /hr.
Total time taken = 10/12 + 12/10 = 61/30 hrs.
Average speed = 22 * 30/61 = 10.8 km/hr.
Answer:B
Answer: (B) 10.8 km/hr
Question: A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
(A) 2.4 km
(B) 2.9 km
(C) 3.4 km
(D) 4.4 km
(E) 5.6 km
Rationale: Explanation:
Speed in still water = 5 kmph
Speed of the current = 1 kmph
Speed downstream = (5+1) = 6 kmph
Speed upstream = (5-1) = 4 kmph
Let the required distance be x km
Total time taken = 1 hour
⇒ x/6+x/4=1
⇒2x+3x=12
⇒5x=12
⇒x=2.4 km
Answer: Option A
Answer: (A) 2.4 km
Question: On Monday, Lou drives his vehicle with 27-inch tires, averaging x miles per hour. On Tuesday, Lou switches the tires on his vehicle to 30-inch tires yet drives to work at the same average speed as on Monday. What is the percent change from Monday to Tuesday in the average number of revolutions that Lou's tires make per second?
(A) Decrease by 14.3%
(B) Decrease by 10%
(C) Increase by 14.3%
(D) Increase by 12.5%
(E) Cannot be determined with the given information.
Rationale: 270 the LCM
On Tuesday 270/30 =9
On Monday 270/27 = 10
Therefore, 9-10/10 = -10% decrease
Answer is B
Answer: (B) Decrease by 10%
Question: If x = a!, which of these following values of a is the least possible value (in this list) for which the last 10 digits of the integer x will all be zero?
(A) 16
(B) 27
(C) 38
(D) 44
(E) 63
Rationale: 2*5 will give one 0 at the end. We need 2^10*5^10 to get 10 zeroes at the end.
There are many 2's, so we need to find the first 10 appearances of 5.
These multiples of 5 are: 5, 10, 15, 20, 5*5, 30, 35, 40, 45...which gives us 10.
To have at least 10 zeroes at the end, a => 45.
The answer is E.
Answer: (E) 63
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 3 days?
(A) 2/5
(B) 1/6
(C) 1/4
(D) 1/9
(E) 2/6
Rationale: B
1/6
A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 3 days = 3 (1/18) = 1/6.
Answer: (B) 1/6
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 4 receives how many more dollars per hour than an employee with a salary grade of 1?
(A) $0.75
(B) $1.00
(C) $1.25
(D) $1.50
(E) $1.75
Rationale: Salary grade of 4 is p(4)=9.50+0.25(4–1)=9.50+0.25*3;
Salary grade of 1 is p(1)=9.50 + 0.25(1–1)=9.50;
p(4)-p(1)=9.50+0.25*4-9.50=0.75.
Answer: A.
Answer: (A) $0.75
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 337
(B) 278
(C) 287
(D) 270
(E) 191
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: (D) 270