mathewhe/aqua_rat huggingface dataset:
Question: If the average of 42, 87, 36, 78, 99, 22, and x is 59, what is x?
(A) 49
(B) 42
(C) 59
(D) 78
(E) 44
Rationale: The answer is 49, because:
(42+87+36+78+99+22+x)/7=59
(42+87+36+78+99+22+x)/7 *7 = 59*7
(42+87+36+78+99+22+x)= 413
(42+87+36+78+99+22+x)-364 = 413-364
x = 49,
so the correct answer is A, 49.
Answer: (A) 49
Question: Harold works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 2 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
(A) 1/3
(B) 2/5
(C) 1/4
(D) 1/2
(E) 4/7
Rationale: The time from beginning of March to the end of September is 7 months.
If x is the average monthly tip for all months other than August then his August month tip will be 2*x
His total tip for the 7 months = 6*(average tip for the months other than August) + 2x
=8x
August tips as a fraction of total tips = 2x/8x =1/4. So C
Answer: (C) 1/4
Question: How many odd numbers between 10 and 1200 are the squares of integers?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: The numbers are the squares of 5, 7, 9,...,33 which includes 15 numbers.
The answer is D.
Answer: (D) 15
Question: Given an integer x, let f(x) be the sum of the digits of x. Compute the number of positive
integers less than 1000 where f(x) = 2.
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: We do casework on the number of digits:
(a) The number has 1 digit. The only valid number is 2.
(b) The number has 2 digits. The only valid numbers are 11 and 20.
(c) The number has 3 digits. The only valid numbers are 101, 110, and 200.
This gives us 6 numbers.
correct answer C
Answer: (C) 6
Question: John has 6 people in his group of friends. How many different ways can he invite one or more of them to his house?
(A) 56
(B) 97
(C) 63
(D) 65
(E) 71
Rationale: John can select one or more of his group of 6
=> Required number of ways = 2^6 – 1= 63.
C
Answer: (C) 63
Question: If u and v are negative integers, which of the following statements must be true?
I. (-u)^v is positive.
II. (-u)^(-v) is positive.
III. u^(-v) is positive.
(A) None
(B) II only
(C) I and II
(D) I and III
(E) I, II and III
Rationale: Let's u = -2 and v = -3
I. (-u)^v = (2)^(-3) = 1/(2^3) --> Positive
II. (-u)^(-v) is positive. = 2^3 --> Positive
III. u^(-v) is positive. = -2^3 --> Negative
Answer: C
Answer: (C) I and II
Question: You have 59 cubic blocks. What is the minimum number that needs to be taken away in order to construct a solid cube with none left over?
(A) 27
(B) 43
(C) 11
(D) 32
(E) 45
Rationale: D
32
The next cube number below 64(4 ×4 ×4) is 27(3 ×3 ×3).
In order to construct a solid cube, therefore, with none left over,
59 – 27 = 32 blocks need to be taken away.
Answer: (D) 32
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
(A) 5/54
(B) 5/12
(C) 5/17
(D) 5/18
(E) 5/14
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
Answer: B
Answer: (B) 5/12
Question: An amount of Rs. 3000 becomes Rs. 3500 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?
(A) Rs. 4500.
(B) Rs. 3800
(C) Rs. 3700.
(D) Rs. 2500.
(E) Rs. 3500.
Rationale: A = P(1 + TR/100)
=> 3500 = 3000[1 + (4 * R)/100]
=> R = 4.16%
Now R = 5.16%
=> A = 3000[1 + (4 * 5.16)/100] = Rs. 3500.
ANSWER:E
Answer: (E) Rs. 3500.
Question: For each color copy, Print Shop X charges $1.20 and Print Shop Y charges $1.70. How much greater is the charge for 40 color copies at Print Shop Y than at Print Shop X?
(A) $14
(B) $16
(C) $18
(D) $20
(E) $22
Rationale: The difference in the two prices is $1.70 - $1.20 = $0.50 for each color copy.
Each color copy will cost an extra $0.50 at Print Shop Y.
40*$0.50 = $20
The answer is D.
Answer: (D) $20
Question: A can finish a work in 9 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
(A) 6
(B) 3
(C) 5.5
(D) 7
(E) 8
Rationale: B's 10 day's work = ( 1 x 10 ) = 2 .
15 3
Remaining work = ( 1 - 2 ) = 1 .
3 3
Now, 1 work is done by A in 1 day.
9
Therefore 1 work is done by A in ( 9 x 1 ) = 3 days.
B
Answer: (B) 3
Question: The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than A
(A) A)11
(B) B)12
(C) C)13
(D) D)14
(E) E)15
Rationale: Explanation:
Given that A+B = 11 + B + C
=> A – C = 11 + B – B = 11
=> C is younger than A by 11 years
Answer: Option A
Answer: (A) A)11
Question: A 140 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
(A) 228
(B) 108
(C) 84
(D) 188
(E) 211
Rationale: S = 140/6 * 18/5 = 84kmph
Answer: C
Answer: (C) 84
Question: A car moves at 80 km/hr. What is the speed of the car in meters per second ?
(A) 20 2/9m sec
(B) 22 2/9m sec
(C) 24 2/9m sec
(D) 26 2/9m sec
(E) 28 2/9m sec
Rationale: Explanation:
Speed=(80∗5/18)m/sec
=200/9m/sec
=22 2/9msec
Option B
Answer: (B) 22 2/9m sec
Question: If n is the smallest integer such that 432 times n is the square of an integer, what is the value of n?
(A) 2
(B) 3
(C) 6
(D) 12
(E) 24
Rationale: The prime factorization of a square has to have even powers of all its prime factors. If the original number has a factor, say of 7, then when it’s squared, the square will have a factor of 7^2. Another way to say that is: any positive integer all of whose prime factors have even powers must be a perfect square of some other integer. Look at the prime factorization of 432
432 = (2^4)*(3^3)
The factor of 2 already has an even power —- that’s all set. The factor of 3 currently has an odd power. If n = 3, then 432*n would have an even power of 2 and an even power of 3; therefore, it would be a perfect square. Thus, n = 3 is a choice that makes 432*n a perfect square.
Answer: B.
Answer: (B) 3
Question: If 15% of A is the same as 20% of B, then A : B is :
(A) 3 : 4
(B) 4 : 3
(C) 17 : 16
(D) 16 : 17
(E) 1:2
Rationale: 15% of A I= 20 % of B
15A/100 = 20B/100
=4/3 = 4:3
ANSWER:B
Answer: (B) 4 : 3
Question: A man saves Rs 300 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
(A) Rs 962
(B) Rs 962.01
(C) Rs 662.02
(D) Rs 993.03
(E) None of these
Rationale: Explanation:
=[300(21/20Ã—21/20Ã—21/20)+300(21/20Ã—21/20)+300(21/20)]=993.03
Option D
Answer: (D) Rs 993.03
Question: In May Mrs Lee's earnings were 70 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
(A) 64%
(B) 68%
(C) 72%
(D) 74%
(E) 83%
Rationale: Let in May Lee family's total income =100
in May Mrs Lee's income =70
in May rest of the family's income = 30
In june Mrs Lees income = 70*120/100 = 84
In june Total income = 84+ 30 = 114
% of Mrs Lee's income =84/114 =73.68
(D)
Answer: (D) 74%
Question: The average of 45 results is 8. The average of first 22 of them is 15 and that of last 22 is 20. Find the 23 result?
(A) 600
(B) 470
(C) 750
(D) 650
(E) 560
Rationale: 23th result = sum of 45results - sum of 44 results
8*45-15*22+20*22 = 360-330+440 = 470
Answer is B
Answer: (B) 470
Question: If the area of circle is 616 sq cm then its circumference?
(A) 78 m
(B) 88 m
(C) 75 m
(D) 70 m
(E) 80 m
Rationale: Area of Circle = ∏r2
= 22/7(r2) = 616
= r2 = (616)(7/22)
= r = 14
Circumference = 2∏r = (2)(22/7)(14)
= 88 m
Answer: B
Answer: (B) 88 m
Question: A certain computer manufacturing firm last year produced 82 percent of its computers using parts made by its subsidiary company. If the remaining 10,890 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether?
(A) 60000
(B) 60100
(C) 60500
(D) 72000
(E) 74000
Rationale: 82% parts used of subsidary company, so 18% parts used of other companies.
Now, 18% parts = 10,890 computers
So, 1% parts = 10,890/18
Or, 100% parts = 60,500 computers.
Hence answer is (C)
Answer: (C) 60500
Question: A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage.
(A) 20%
(B) 21%
(C) 21.33%
(D) 22.109%
(E) 23%
Rationale: Lets say the indicated weight is x for $10
but the trader actually get 1.1x for $10
now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1
so profit % = (12.1-10)/ 10 = 0.21 = 21%
ANSWER:B
Answer: (B) 21%
Question: In N is a positive integer less than 200, and 18N/60 is an integer, then N has how many different positive prime factors?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: (A).
18n/60 must be an integer. => 3n/10 must be an integer. Hence n must be a multiple of 2*5.
=> n has 2 different prime integers .
Answer: (A) 2
Question: A Bus travels first half distance between two places with a speed of 40 kmph and the rest half distance with a speed of 60 kmph. The average speed of the Bus is ?
(A) 48 kmph
(B) 78 kmph
(C) 28 kmph
(D) 18 kmph
(E) 98 kmph
Rationale: Explanation:
we know that speed = distance traveled/time taken
let the total distance traveled by the car is 2x km.
then time taken by it to cover first half is hour.
and for second half is hour.
Then average speed= total distance travelled / total time taken.
i.e.
=>
= 48 kmph.
Answer: A
Answer: (A) 48 kmph
Question: Mary works in a restaurant a maximum of 40 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?
(A) 300
(B) 420
(C) 360
(D) 320
(E) 400
Rationale: Mary receives $8(20)=$160 for the first 20 hours.
For the 20 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(20)=$200.
The total amount is $160+$200 = $360
Answer C 360.
Answer: (C) 360
Question: Of the four numbers, whose average is 75, the first is one-fourth of the sum of the last three. The first number is ?
(A) 60
(B) 29
(C) 11
(D) 48
(E) 10
Rationale: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 75 or x = (75 * 4) / 5 = 60
Answer: A
Answer: (A) 60
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
(A) 12 ½ years
(B) 62 ½ years
(C) 18 ½ years
(D) 72 ½ years
(E) 12 ½ years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
600 ---- 12 ½ years
Answer:A
Answer: (A) 12 ½ years
Question: If |a+b|=|a-b|, then a*b must be equal to:
(A) 1
(B) -1
(C) 0
(D) 2
(E) -2
Rationale: so, let b≠0b≠0
Distance of aa from bb, equals the distance of aa from -bb
Draw this on a number line, aa must equal zero
same logic holds for a≠0a≠0
So either aa or bb = 0, ab=0ab=0
or just solve using our normal absolute value method, two cases:
(a+b)=(a−b)(a+b)=(a−b)
b=0
−(a+b)=(a−b)−(a+b)=(a−b)
−a−b=a−b−a−b=a−b
a=0
so ab=0
ANSWER:C
Answer: (C) 0
Question: The arithmetic mean of the 9 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 4?
(A) 2 + s + a
(B) 22 + a
(C) 2s
(D) 2a + 2
(E) 2 + a
Rationale: (9s+36)/9=s+4=a
(9s+54)/9=s+6=2+a
E
Answer: (E) 2 + a
Question: A type Q machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type Q machines and 3 type B machines working together and independently to complete the job?
(A) 1/5
(B) 29/35
(C) 5/6
(D) 35/29
(E) 35/12
Rationale: now D should be the answer.
Q need 5 hours to complete
and B needs 7 hours to compete
so 2Q + 3B will complete 2/5 + 3/7 or 29/35 portion of the job in 1 hour
so the whole job will take 35/29 hours....=D
Answer: (D) 35/29
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
(A) 70,000
(B) 60,000
(C) 80,000
(D) 90,000
(E) 10,000
Rationale: C
80,000.
The distance traveled by each tyre:
4/5 * 1, 00, 000km = 80,000 km.
Answer: (C) 80,000
Question: Pam and Cathy begin running at the same time on a straight path. Pam runs at 10 miles per hour, and Cathy runs at 8 miles per hour. After 45 minutes, Pam stops to stretch. If it takes Pam 30 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pam to catch up to Cathy assuming Pam resumes running at 10 miles per hour?
(A) 30 minutes
(B) 40 minutes
(C) 45 minutes
(D) 60 minutes
(E) 75 minutes
Rationale: After 45 mins
Pam would have covered 45/60 * 10 mph = 7.5 miles
Cathy would have covered 45/60 * 8 mph = 6 miles
Pam does 30 minutes of stretching .. so after 75 mins
Pam would still be at 7.5 miles
Cathy would have covered 75/60 * 8 = 10 miles.
So after 75 mins Cathy is 2.5 miles ahead.
ANSWER:E
Answer: (E) 75 minutes
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
(A) 25200.
(B) 26200
(C) 28000
(D) 29000
(E) 30000
Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
=7 x 6 x 5/3 x 2 x 1 x	4 x 3	/2 x 1
= 210.
Number of groups, each having 3 consonants and 2 vowels = 210.
Each group contains 5 letters.
Number of ways of arranging
5 letters among themselves	= 5!
= 5 x 4 x 3 x 2 x 1
= 120.
Required number of ways = (210 x 120) = 25200.
Answer: A
Answer: (A) 25200.
Question: Alex deposited x dollars into a new account that earned 10 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
(A) w/(1+1.08)
(B) w/(1.08+1.16)
(C) w/(1.16+1.24)
(D) w/(1.10+1.10^2)
(E) w/(1.08^2+1.08^2)
Rationale: Account at the end of the first year would be 1.10x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.10x+x) dollars. Account at the end of the second year would be (1.10x+x)*1.10=w --> x(1.10^2+1.10)=w --> x=w/(1.10+1.10^2).
Answer: D.
Answer: (D) w/(1.10+1.10^2)
Question: If UVW= 1 , WXY = 0 , and UWX = 0, which of the following must be zero?
(A) U
(B) V
(C) W
(D) X
(E) Y
Rationale: UVW= 1 which means neither U / V/ W is 0
W x XY = 0 , we know W is not 0 from above hence either X or Y must be 0.
X x U x W = 0, we know from first expression that U and W are not 0 hence X =0.
OPTION D
Answer: (D) X
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
(A) 50
(B) 120
(C) 100
(D) 60
(E) 40
Rationale: Explanation:
Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer:C
Answer: (C) 100
Question: 1398 x 1398 = ?
(A) 1624404
(B) 1851404
(C) 1951404
(D) 1954404
(E) None of these
Rationale: Explanation :
1398 x 1398
= (1398)2
= (1400 - 2)2
= 14002 - (2 × 1400 × 2) + 22
= 1960000 - 5600 + 4
= 1954404. Answer : Option D
Answer: (D) 1954404
Question: Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $100, what was the final price of the sweater?
(A) $25.75
(B) $52.5
(C) $15.75
(D) $ 45.75
(E) $18.75
Rationale: The price with 30% off
100 - 30% of 100 = 100 - (30 / 100) *100 = 70
The price with another 25% off
70 - 25% of 70 = 70 - (25/100)* 70 = $52.5
correct answer B
Answer: (B) $52.5
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 45, 55, 60, then the average marks of all the students is:
(A) 53.33
(B) 54.68
(C) 52.97
(D) 56
(E) None of these
Rationale: Explanation:
Required average = (55 × 45 + 60 × 55 + 45 × 60/55 + 60 + 45)
= (2475 + 3300 + 2700/160)
= 8475/160
= 52.97
Answer: C
Answer: (C) 52.97
Question: The annual income of Puja, Hema and Jaya taken together is Rs. 46,000. Puja spends 70 % of income, Hema spends 80 % of her income and Jaya spends 92 % of her income. If their annual savings are 15 : 11 : 10, find the annual saving of Puja?
(A) 10, 000 /-
(B) 12, 000 /-
(C) 17, 500 / -
(D) 25, 000 /-
(E) NONE OF THE ABOVE
Rationale: EXPLANATION:
Suppose income of Puja, Hema and Jaya are Rs A, Rs B and Rs C.
Annual income given is Rs 46, 000
If 70 % income is spent by Puja, then that means she saves 30 % (0.3). Similarly, Hema saves 20 % (0.2) and Jaya saves 8 % (0.08)
Given ratio of their annual savings are 15 : 11 : 10
(0.3A)/15	=	(0.2B)/11	=	(0.08C)/10	=	A/50	=	B/55	=	C/125
=	A/10	=	B/11	=	C/25	=	(A + B + C)/(10+11+25)	=	46000/46----(Since, A+B+C=46000)
=1000
From this equation, we can
A = 1000 x 10 = 10,000
B = 1000 x 11 = 11,000
C = 1000 x 25 = 25000
ANSWER IS A
Answer: (A) 10, 000 /-
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 30 . The largest number is:
(A) 28
(B) 32
(C) 36
(D) 42
(E) 45
Rationale: Explanation:
Let the numbers be 4x, 5x and 6x. Therefore,
(4x+5x+6x)/3 = 30
15x = 90
x = 6
Largest number = 6x = 36.
ANSWER C
Answer: (C) 36
Question: A local restaurant recently renovated its dining space, purchasing new tables and chairs to use in addition to the original tables and chairs. The new tables each seat six customers, while the original tables each seat four customers. Altogether, the restaurant now has 40 tables and is capable of seating 208 customers. How many more new tables than original tables does the restaurant have?
(A) 8
(B) 12
(C) 16
(D) 20
(E) 24
Rationale: If all the tables seated 4, the number of customers could be 4*40 = 160.
208-160 = 48, so 48/2 = 24 tables must be new tables seating 6 people.
The number of tables seating 4 people is 40-24 = 16.
The number of new tables is 24-16 = 8 more than the number of old tables.
The answer is A.
Answer: (A) 8
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
(A) 814
(B) 820
(C) 840
(D) 844
(E) 548
Rationale: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles =1517 x 902/(41^2)= 814.
ANSWER:A
Answer: (A) 814
Question: In a consumer survey, 90% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: pick 100 and x= all set with exactly two items
90=30+50+20 -(X)-10
X=0
so the answer is 0+5/100= 5%
Answer A
Answer: (A) 5
Question: Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is
(A) 1
(B) 3
(C) 4
(D) 0
(E) 2
Rationale: 4 points are possible in which 1 point is the incentre of the circle and other 3 are excentres
ANSWER:C
Answer: (C) 4
Question: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 2 years would be
(A) (1.5)^4
(B) 4(1.5)
(C) (1.05)^2
(D) 1 + (0.05)^4
(E) 1 + 4(0.05)
Rationale: f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 2 years would be
1(1.05)^2
1.05^2
C. (1.05)^2
Answer: (C) (1.05)^2
Question: If f=(10^10)-47, what is the sum of all the digit of f?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 80
Rationale: Start small and check for any pattern:
10^2 - 47 = 53 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits
10^3 - 47 = 953 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits
...extrapolate
10^10 - 47 -> number of digits = 10; number of 9s = 8; 53 will be the last 2 digits
f= 9*8 + 5 + 3 = 80.
Answer (E).
Answer: (E) 80
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 6 kmph
(B) 9 kmph
(C) 3 kmph
(D) 8 kmph
(E) 1 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2)
= 34 kmph
Speed upstream = d/t = 45/(2 1/2)
= 18 kmph
The speed of the stream = (34 - 18)/2
= 8 kmph
Answer:D
Answer: (D) 8 kmph
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 138 m length?
(A) 82.1 sec.
(B) 12.4 sec
(C) 19.1 sec.
(D) 17.1 sec.
(E) 42.1 sec.
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 138 = 248 m.
Required time = 248/20 = 12.4 sec.
Answer: B
Answer: (B) 12.4 sec
Question: There are 44 students in a hostel, due to the administration, 15 new students has joined. The expense of the mess increase by Rs. 33 per day. While the average expenditure per head diminished by Rs. 3, what was the original expenditure of the mess ?
(A) Rs. 618
(B) Rs. 612
(C) Rs. 622
(D) Rs. 616
(E) Rs. 630
Rationale: Explanation:
Let the average expenditure per head be Rs. p
Now, the expenditure of the mess for old students is Rs. 44p
After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3
Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33
Therefore, 59(p-3) = 44p + 33
59p - 177 = 44p + 33
15p = 210
=> p = 14
Thus, the expenditure of the mess for old students is Rs. 44p = 44 x 14 = Rs. 616.
Answer: D
Answer: (D) Rs. 616
Question: A truck carrying cans of paint contains P stacks. Each stack contains P/4 cases, and each case contains 12 cans. How many cans of paint are contained in 7 trucks?
(A) P^2/21
(B) P^2/336
(C) 336
(D) 21/P^2
(E) 21P^2
Rationale: There are 12 cans in each case.
There are 3P cans in each stack.
There are 3P^2 cans in each truck.
There are 21P^2 cans in 7 trucks.
The answer is E.
Answer: (E) 21P^2
Question: Look at this series: 97, 97, 97, 81, 81, 81, 65, 65, 65 ... What number should come next?
(A) 45
(B) 33
(C) 43
(D) 38
(E) 36
Rationale: Explanation:
In this series, each number is repeated, then 16 is subtracted to arrive at the next number.
Answer: Option B
Answer: (B) 33
Question: 1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 1/5 , 1/2 , 1/3
1/5*2 , 1/2*2 ,1/3*2
1/5*3 , 1/2*3 ,1/3*3
1/5*4 , 1/2*4 ,1/3*4
so
1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,2
ANSWER:B
Answer: (B) 2
Question: In a clothing store, there are six different colored neckties ( orange, yellow, green, blue, and indigo) and five different colored shirts ( orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color?
(A) 719/720
(B) 1/120
(C) 2/233
(D) 3/543
(E) 1/720
Rationale: 5 ties and 5 shirts...
red tie can take any of 5 shirts..
orange can take any of the remaining 4 shirts
yellow any of remaining 3..
and so on till last indigo chooses the 1 remaining..
Total ways= 5*4*3*2*1= 120
out of this 120, ONLY 1 way will have same colour tie and shirt..
prob = 1/120
B
Answer: (B) 1/120