mathewhe/aqua_rat huggingface dataset:
Question: What is the next number of the following sequence
5, 25, 61, 113,?
(A) 118
(B) 181
(C) 132
(D) 144
(E) 121
Rationale: 5, 25, 61, 113, x
1^2 + 2^2 = 5
3^2 + 4^2 = 25
5^2 + 6^2 = 61
7^2 + 8^2 = 113
9^2 + 10^2 = x ====> x = 181
ANSWER:B
Answer: (B) 181
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?
(A) 350
(B) 300
(C) 400
(D) 450
(E) 500
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 A
Answer: (A) 350
Question: The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?
(A) 0.03
(B) 0.04
(C) 0.048
(D) 0.05
(E) 0.12
Rationale: Probability of Brand A defective is x
Probability of Brand B defective is 0.06 which 6/100. Which tells you there are 2 defective piece in a lot of 33, for 35 lot it is approx - 2.12
Probability of Brand C defective is 0.08 which 8/100. Which tells you there are 2 defective piece in a lot of 25
Total = 40 + 25 + 25 = 100
Probability of having defective piece in a lot of 100 ( All brands ) = 0.053
Hence 5.3 defective piece out 100 lot.
So 40x + 2.12 + 2 = 5.3
x = 0.03
ANSWER :Opt A.
Answer: (A) 0.03
Question: Victor gets 80 % marks in examinations. If these are 240 marks, find the maximum marks.
(A) 334
(B) 300
(C) 376
(D) 288
(E) 271
Rationale: Let the maximum marks be m
Then 80 % of m = 240
⇒ 80/100 × m = 240
⇒ m = (240 × 100)/80
⇒ m = 24000/80
⇒ m = 300
Therefore, maximum marks in the examinations are 300
Answer:B
Answer: (B) 300
Question: Mr. Smith calculated the average of 10 three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 59.4. The difference between the unit digit and hundreds digit of that number is :
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Since the average increased by 59.4 and there were a total of 10 numbers, it means the incorrect number was 297 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 594
99c - 99a = 99(c - a) = 594
594 = 99*6 = 99(c - a)
So c - a = 6
Answer (D)
Answer: (D) 6
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 128 m
(B) 125 m
(C) 198 m
(D) 276 m
(E) 279 m
Rationale: D = 90 * 5/18 * 5
=125 m
Answer: B
Answer: (B) 125 m
Question: John has taken four (8) tests that have an average of 82. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?
(A) 87
(B) 90
(C) 92
(D) 107
(E) 97
Rationale: 87-82=5*8=40 points
2*87=174
174+40=214 points to be scored in the 2 tests.
Avg of 2 tests = 214/2=107
Answer: D
Traditional Method:
Total scored till now 82*8=656
Total score to avg 87 in 10 tests = 87*10=870
Total to be scored on 2 tests = 870-656=214
Avg on 2 tests = 214/2 = 107
Answer D
Answer: (D) 107
Question: If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 13.2
II. 12.3
III. 9.3
(A) I only
(B) I and II only
(C) II only
(D) III only
(E) I and III only
Rationale: Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
12.3 and 13.2 lies in the range of 2SD from mean
Answer: Option D
Answer: (D) III only
Question: If Shreehari walks in the speed of 4.5 km/hr from his house, in what time will he reach his school which is 750 m long from his house?
(A) 5
(B) 30
(C) 10
(D) 12
(E) 15
Rationale: Speed = 4.5 * 5/18 = 1.25 m/sec
Time taken = 750/1.25 = 600 sec ie. 10 mins.
Answer:C
Answer: (C) 10
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 60 other employees of Company K, how many employees does Company K have?
(A)  240
(B)  180
(C)  190
(D)  200
(E)  400
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 60
so 25% of x = 60
x = 240
Therefore there a total of 240 employees in the company K
Correct answer - A
Answer: (A)  240
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 40
(B) 45
(C) 48
(D) 51
(E) 44
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer: Option C
Answer: (C) 48
Question: How many minutes does it take Sharuk to type 25 words if he types at the rate of 5 words per minute?
(A) 3
(B) 5
(C) 8
(D) 15
(E) 7
Rationale: time*rate=job --> time*5=25 --> time=25/5=5.
Answer: B.
Answer: (B) 5
Question: 96% of the population of a village is 23040. The total population of the village is?
(A) 24000
(B) 25000
(C) 15000
(D) 1750
(E) 2589
Rationale: Explanation:
X * (96/100) = 23040
X = 240 * 100
X = 24000
A
Answer: (A) 24000
Question: The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability C that Tommy CANNOT form a triangle from the 3 sticks?
(A) 11/32
(B) 13/32
(C) 15/32
(D) 17/32
(E) 19/32
Rationale: In order to form a triangle, the sum of two sides must be greater than the third side.
So we can choose the combination of numbers which will NOT result in a triangle.
Favorable outcomes:
1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or
1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!
1,3,4 (4=1+3): 6 ways of arriving at this
2,2,4 (4=2+2): 3 ways of arriving at this
1,1,3 (3>1+1): 3 ways of arriving at this
1,2,3 (3=1+2): 6 ways of arriving at this
1,1,2 (2+1+1): 3 ways of arriving at this
Overall favourable outcomes: 30
Total outcomes: 4*4*4 = 64 (4 ways of choosing a stick from each of the 3 bags)
Probability C that a triangle is not formed = 30/64 = 15/32
C is the correct option here.
Answer: (C) 15/32
Question: I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 75 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
(A) 8715
(B) 0152
(C) 3581
(D) 5625
(E) 9126
Rationale: D
5625
n^1
75 * 75 = 5625 (sum of first 75 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).
Answer: (D) 5625
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Interest on Loans and Transport	Bonus	Fuel	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
The total amount of interest on loans paid by the company during the given period is approximately what percent of the total amount of salary paid during this period?
(A) A)0.5%
(B) B)1.5%
(C) C)1.25%
(D) D)3%
(E) E)1%
Rationale: Required percentage
=	(288 + 342 + 324 + 336 + 420)
=	[	17	x 100	]	%
1710
~= 1%.
Answer : E
Answer: (E) E)1%
Question: Paul and John are in a relay race. Paul runs the first leg of the course in 22 seconds. Ben runs the second leg of the course in 53 seconds. What was the average time they took to run a leg of the course?
(A) 36.5
(B) 37.5
(C) 38.5
(D) 39.5
(E) 40.5
Rationale: (22 seconds +53 seconds)/2= 37.5 seconds
Correct option is: B
Answer: (B) 37.5
Question: How many two-digit numbers are there such that all two digits are different and the first digit is not zero?
(A) 50
(B) 64
(C) 72
(D) 79
(E) 81
Rationale: All two digits are different and first digit is not zero.
So first digit can be filled in 9 ways.
And, second digit can be filled in 8 ways.
Total ways = 9*8
= 72
Hence option (C).
Answer: (C) 72
Question: A child want to buy 5 new toys. If there are 15 toys that satisfy the child's criteria,in how many different ways can the child select the 5 new toys if the order of selection doesn't matter.
(A) 210
(B) 1365
(C) 3003
(D) 5005
(E) 3030
Rationale: The number of ways of choosing 5 toys out of 15 are counted by = 15C5 ways = 3003
Answer: Option C
Answer: (C) 3003
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 288
(B) 277
(C) 245
(D) 266
(E) 261
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time
= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x)
= 750 => x = 245 m.
Answer: C
Answer: (C) 245
Question: what is the next term of this series6,10,9,15,12...?
(A) 9
(B) 20
(C) 11
(D) 12
(E) 15
Rationale: 3&2=6;
5*2=10;
3*3=9;
3*5=15
3*4=12
5*4=20.
ANSWER:B
Answer: (B) 20
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
(A) 1 : 2
(B) 3 : 4
(C) 2:5
(D) 5:7
(E) 7:9
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
B
Answer: (B) 3 : 4
Question: If g(x) = ax^5 + bx^3 + 2, and g(5) = 10, then g(–5) =?
(A)  – 10
(B)  – 8
(C)  – 6
(D)  0
(E)  4
Rationale: g(5) = 10
or, 5^5 a + 5^3 b + 2 = 10
or, 5^5 a + 5^3 b = 8
g(-5) = -5^5 a - 5^3 b + 2 = - (5^5 a + 5^3 b) + 2 = - 8 + 2 = - 6 = (C)
Answer: (C)  – 6
Question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 21
(B) 20
(C) 17
(D) 12
(E) 18
Rationale: 1: 2/5 = 5: 2
2/7 * 70 = 20
Answer: B
Answer: (B) 20
Question: Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
(A) 1444
(B) 1440
(C) 1443
(D) 1432
(E) 1435
Rationale: In the word, "MATERIAL" there are three vowels A, I, E.
If all the vowels are together, the arrangement is MTRL'AAEI'.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways of arranging the above letters = 5! * 4!/2!
= (120 * 24)/2 = 1440 ways.
Answer:B
Answer: (B) 1440
Question: 12+6=792
10+2=110
1+9=9
2+7=16
11+4=??
Solve it?
(A) 100
(B) 120
(C) 190
(D) 160
(E) 154
Rationale: x+y=x[y+(x-1)]=x^2+xy-x
12+6=12[6+(12-1)]=792
10+2=10[2+(10-1)]=110
1+9=1[9+(1-1)]=9
2+7=2[7+(2-1)]=16
11+4=11[4+(11-1)]=154
Answer :E
Answer: (E) 154
Question: If 20 typists can type 50 letters in 30 minutes, then how many letters will 40 typists working at the same rate complete in 1 hour?
(A) 400
(B) 500
(C) 350
(D) 250
(E) 200
Rationale: No. of letters typing by 20 typists in 30 minutes = 50
No. of letters typing by 20 typists in 60 minutes = 50*2 = 100
No. of letters typing by 40 typists in 60 minutes = 100/10*40 = 400
Answer : A
Answer: (A) 400
Question: Ages of two sisters differ by 9 years. If 5 years ago, the elder one was twice as old the younger one, find their present age
(A) 12,28
(B) 14,23
(C) 16,32
(D) 18,34
(E) 19,32
Rationale: Explanation:
Let the age of younger sister be x,
Then elder sister's age is (x+9)
=> 2(x-5) = (x+9-5) [5 years before]
=> 2x-10 = x+4
=> x = 14.
So older sister's age is x + 9 = 23
Answer: Option B
Answer: (B) 14,23
Question: Analyze the number square carefully and find out what number fits in place of question mark.
35	20	14
27	12	18
6	4	?
(A) 6
(B) 12
(C) 24
(D) 36
(E) 8
Rationale: 20 fits in place of question mark.
This is because (number in first column) / (number in second column) * 8 = number in third column.
Here (left number / middle number) * 8 = right number
(6 / 4) * 8 = 6*2= 12
B
Answer: (B) 12
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
(A) 20
(B) 22
(C) 30
(D) 10
(E) 9
Rationale: C = 1/4 - 1/12 â€“ 1/18 = 1/9 => 9 days
ANSWER E
Answer: (E) 9
Question: To reach her destination, Jeanette must drive 90 miles. If she drives 5 miles every 6 minutes, how much time will it take her to reach her destination?
(A) 2 hours and 2 minutes
(B) 1 hours and 48 minutes
(C) 2 hours and 10 minutes
(D) 2 hours and 12 minutes
(E) 2 hours and 15 minutes
Rationale: 6 minute for 5 miles how much for 90? minutes for 1(6/5) mile multiplied by 90 miles.
6*90/5= 108> 1 hours 48 min answer is B
Answer: (B) 1 hours and 48 minutes
Question: If the number of 194,n70, where n represents the hundreds digit, is a multiple of 9, then the value of n could be which of the following?
(A) 6
(B) 5
(C) 4
(D) 2
(E) 1
Rationale: Divisibility rule of 9: The sum of the digits must be divisible by 9
i.e 1+9+4+n+7+0 = multiple of 9
or, 21 + n = multiple of 9.
If n=6, 21 + n =27,which is a multiple of 9.
Hence answer is A.
Answer: (A) 6
Question: How many two letter words are formed using the letters of the word BOOK?
(A) 12
(B) 10
(C) 6
(D) 3
(E) 9
Rationale: The number of letters in the given word is four.
The number of TWO letter words that can be formed using these four letters is 4P2 = 4 * 3 = 12.
Answer:A
Answer: (A) 12
Question: A gambler bought $4,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?
(A) $2,040
(B) $2,120
(C) $1,960
(D) $3,120
(E) $1,400
Rationale: In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.
So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost.
Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $4,000-$880=$3,120.
Answer: D
Answer: (D) $3,120
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
(A) 16 days
(B) 34 days
(C) 10 days
(D) 16 days
(E) 15 days
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x
=10 days
Answer: C
Answer: (C) 10 days
Question: The temperature of a certain cup of coffee 2 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*2^(-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
(A) 65
(B) 60.003662
(C) 80.2
(D) 85
(E) 90
Rationale: First, we have to find a.
We know that after t=2 minutes the temperature F=120 degrees.
Hence:
120 = 120*(2^-2a)+60
60 = 120*(2^-2a)
60/120 = 2^-2a
1/2 = 2^-2a
2^-1 = 2^-2a
-1 = -2a
1/2 = a
Now we need to find F after t=30 minutes:
F = 120*(2^-1/2*30)+60
F = 120* (2^-15) +60
F = 120* (1/2^15) +60
F = 120*1/32768 +60
F = 0.003662+60 = 60.003662
Answer B!
Answer: (B) 60.003662
Question: Statement: Put thechild in school at the age of 5. Assumptions: At that age the child reaches appropriate level of development and is ready to learn. The schools do not admit children after 6years of age.
(A) Only assumption I is implicit
(B) Only assumption II is implicit
(C) Either I or II is implicit
(D) Neither I nor II is implicit
(E) Both I and II are implicit
Rationale: Since the statement talks of putting the child in school at the age of 5, it means that the child is mentally prepared for the same at this age. So, I is implicit. But nothing about admission after 6 years of age is mentioned in the statement. So, II is not implicit.
A
Answer: (A) Only assumption I is implicit
Question: A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number M is
(A) 74
(B) M=75
(C) M=175
(D) M=680
(E) 690
Rationale: I solved this question by plugging in numbers from the answer choices.
A.) 74
Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5.
B.) 75
I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7.
15-7 = 8 so I know the correct answer isB
Answer: (B) M=75
Question: On what dates of April, 2001 did Wednesday fall?
(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: EXPLANATION
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.
Total number of odd days = (0 + 0 + 0) = 0
On 1st April, 2001 it was Sunday.
In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.
Answer D
Answer: (D) 4th, 11th, 18th, 25th
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 $8 on candy, how much did John spend at the supermarket?
(A)  $60
(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 $8 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 + 8 = T
To get rid of the fractions we can multiply the entire equation by 30, and we obtain:
15T + 10T + 3T + 240 = 30T
28T + 240 = 30T
240 = 2T
T = 120
John spent $90 at the supermarket.
Answer: D
Answer: (D)  $120
Question: The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 58
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
(A) 51
(B) 88
(C) 90
(D) 96
(E) 162
Rationale: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics
No. of total students = 58 + (35-15) + (40-10-12) = 58+20+18 = 96
Hence, Answer will be D.
Answer: (D) 96
Question: How many words can be formed by using all the letters of the word “DAUGHTER” so that vowels always come together & vowels are never together?
(A) 2310
(B) 4510
(C) 5231
(D) 2351
(E) 4320
Rationale: Given word contains 8 different letters
When the vowels AUE are always together we may suppose
them to form an entity ,treated as one letter
then the letter to be arranged are DAHTR(AUE)
these 6 letters can be arranged in 6p6 = 6!
= 720 ways
The vowels in the group (AUE) may be arranged in 3! = 6 ways
Required number of words = 760 * 6 =4320
Ans: E
Answer: (E) 4320
Question: How many possible ways are there to select 3 stocks at random from 7 stocks?
(A) 26
(B) 29
(C) 32
(D) 35
(E) 38
Rationale: 7C3 = 35
The answer is D.
Answer: (D) 35
Question: If Raj walks at 12.5 km/hr instead of 10 km/hr, he would have walked 6 km more. The actual distance traveled by him during this period is?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 24
Rationale: Let the actual distance traveled is 'x' km
Then by given conditions, we have
x/10 = (x+6)/12.5
12.5x = 10x + 60
x = 24 km
Ans- E
Answer: (E) 24
Question: If the population of a certain country increases at the rate of one person every 30 seconds, by how many persons does the population increase in 10 minutes?
(A) 20
(B) 30
(C) 15
(D) 10
(E) 80
Rationale: Answer = 2 * 10 = 20
Answer = A
Answer: (A) 20
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 45 m
(B) 60 m
(C) 57 m
(D) 69 m
(E) 78 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: (B) 60 m
Question: The maximum number of students among them 1230 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
(A) 91
(B) 10
(C) 1001
(D) 1911
(E) None of these
Rationale: Explanation:
Required number of students = H.C.F of 1230 and 920 = 10. Answer: B
Answer: (B) 10
Question: A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds. What is the length of the train in meters?
(A) 400 meters
(B) 1111 meters
(C) 160 meters
(D) 850 meters
(E) None of these
Rationale: Train overtakes a bike means that we are talking about total length of the train. (train's head is close to bike when it started and its tail crosses the bike when it overtakes the bike)
Relative speed= 100-64= 36Km/h = 36000 m/h
time= 85 seconds
Distance= speed*time
36000* 85/3600= 850 meters.
D is the answer.
Answer: (D) 850 meters
Question: The ratio of the incomes of Lakshmi and Latha is 5:4 and the ratio of their expenditure is 4:3. If at the end of the year, each saves $6000 then the income of Lakshmi is?
(A) $26000
(B) $20000
(C) $23000
(D) $25000
(E) $22000
Rationale: Let the income of Lakshmi and Latha be $5x and $4x
Let their expenditures be $4y and $3y
5x-4y = 6000-------1)
4x-3y = 6000-------2)
From 1) and 2)
x = 6000
Lakshmi's income = 5x = 5*5000 = $25000
Answer is D
Answer: (D) $25000
Question: If daily wages of a man is four times to that of a woman, how many men should work for 20 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
(A) 10
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Explanation :
Wages of 1 woman for 1 day = 21600/40Ã—30
Wages of 1 man for 1 day = 21600Ã—4/40Ã—30
Wages of 1 man for 20 days = 21600Ã—4Ã—20/40Ã—30
Number of men = 14400/(21600Ã—4Ã—20/40Ã—30)=144/(216Ã—80/40Ã—30)=10
Answer : Option A
Answer: (A) 10
Question: One half of a two digit number exceeds its one third by 7. What is the sum of the digits of the number?
(A) A)3
(B) B)5
(C) C)7
(D) D)9
(E) E)10
Rationale: x/2 – x/3 = 7 => x =46
4 + 6 = 10
ANSWER:E
Answer: (E) E)10