mathewhe/aqua_rat huggingface dataset:
Question: A shopkeeper labels the price of articles 20% above the cost price. If he allows 31.20 off on a bill of 312, find his profit per cent on the article?
(A) 8
(B) 12 1⁄3
(C) 11 2⁄3
(D) 8 1⁄3
(E) None of these
Rationale: Let the CP = 100 Marked price = 120
Discount = 312⁄31.2 × 1⁄100 = 10% = 12
SP = 120 – 12 = 108 Profit% = 108 – 100 = 8%
Answer A
Answer: (A) 8
Question: A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?
(A) 22
(B) 21
(C) 77
(D) 88
(E) 66
Rationale: 20 15 5
25 20 8
500 + 300 + 40 = 840/40 = 21
Answer: B
Answer: (B) 21
Question: 3x^2-6x+3 = 0 Find the above equation find the value of x
(A) 0
(B) 1
(C) 3
(D) 4
(E) 5
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: (B) 1
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) 7 kmph
(B) 9 kmph
(C) 3 kmph
(D) 8 kmph
(E) 2 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: There are two groups of students in the sixth grade. There are 45 students in group A, and 55 students in group B. If, on a particular day, 20% of the students in group A forget their homework, and 40% of the students in group B forget their homework, then what percentage of the sixth graders forgot their homework?
(A) 23%
(B) 25%
(C) 29%
(D) 31%
(E) 36%
Rationale: Number of students in group A = 45
students who forget homework in group A = 20 % of 45 = 9 students
Number of students in group B = 55
students who forget homework in group B = 40 % of 55 = 22 students
Total number of students = 45 + 55 = 100
students who forgot homework = 9 + 22 = 31 students
percentage of students who forget homework = 31/100 * 100 = 31%
Answer: D
Answer: (D) 31%
Question: Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many different ways can this be done?
(A) 6!*7!
(B) 136!*7!
(C) 356!*7!
(D) 366!*7!
(E) 566!*7!
Rationale: Yes, the solution given above is correct. Think of it this way:
There are 7 men: Mr. A, Mr. B .....
and 7 women: Ms. A, Ms. B ....
14 seats around a circular table.
You seat the 7 women such that no two of them are together so they occupy 7 non-adjacent places in 6! ways. For the first woman who sits, each seat is identical. Once she sits, each seat becomes unique and when the next woman sits, she sits in a position relative to the first woman (e.g. 1 seat away on left, 3 seats away on right etc)
The 7 men have 7 unique seats to occupy. Each of the 7 seats are unique because they have a fixed relative position (e.g. between Ms. A and Ms. B or between Ms. C and Ms. B etc...). So the men can sit in 7! ways.
Total 6!*7! ways.
ANS:A
Answer: (A) 6!*7!
Question: Find the odd man out
4, 9,16, 36, 64, 144
(A) 144
(B) 16
(C) 9
(D) 36
(E) 4
Rationale: 9 is square of 3 which is odd number where as all others are squares of even numbers.
ANSWER:C
Answer: (C) 9
Question: 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 140kg then find the average weight of all the 7 rounds?
(A) 98.5 kgs
(B) 80 kgs
(C) 76.5 kgs
(D) 67.5 kgs
(E) 58.2 kgs
Rationale: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 140/7 = 80 kgs
Answer:B
Answer: (B) 80 kgs
Question: Let C be defined as the sum of all prime numbers between 0 and 30. What is C/3
(A) 155
(B) 129
(C) 61
(D) 47
(E) 43
Rationale: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19 , 23 , 29
Sum,C = 129
C/3 = 43
Answer E
Answer: (E) 43
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 950 grams. Find the profit percent.
(A) 100/18%
(B) 100/17%
(C) 100/16%
(D) 100/19%
(E) 100/13%
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 950
100 + g / 100 + 0 = 1000 / 950
100+g = 20/19*100
g = 100/19 %
ANSWER: D
Answer: (D) 100/19%
Question: What distance will be covered by a bus moving at 36 kmph in 30 seconds?
(A) 287
(B) 600
(C) 289
(D) 300
(E) 207
Rationale: 36 kmph = 36 * 5/18
= 10 mps
D = Speed * time = 10 * 30
= 300 m.
Answer:D
Answer: (D) 300
Question: Rs.8000 become Rs.11256 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 6 YEARS
(B) 7
(C) 5
(D) 3
(E) 4
Rationale: Explanation:
11256 = 8000(21/20)N
(21/20)7 = (21/20)N => N = 7
Answer: Option B
Answer: (B) 7
Question: In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: 14n/60 must be an integer. => 7n/30 must be an integer. Hence n must be a multiple of 2*3*5.
=> n has 3 different prime integers and cannot have more than 3 different prime integers because 2*3*5*7=210 > 200 ANSWER:B
Answer: (B) 3
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
(A) 432
(B) 672
(C) 278
(D) 266
(E) 261
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer: A
Answer: (A) 432
Question: Month	Average Price
per Dozen
April $1.26
May $1.20
June $1.08
The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a General store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
(A) 1.4
(B) 1.3
(C) 1.2
(D) 1.1
(E) 1.16
Rationale: Say x dozen eggs were sold in May.
Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.
Total x+2x/3+4x/3=3x dozen eggs were sold in three months.
Total sales: 2x/3*1.26+x*1.2+4x/3*1.08=$3.48x. The average price per dozen 3.48x/3x=$1.16.
E
Answer: (E) 1.16
Question: If A : B= 1 : 2 and B : C = 3 : 4, then A : B : C is:
(A) 9:6:4
(B) 1:2:3
(C) 3:6:9
(D) 12:25:87
(E) 3:5:7
Rationale: A:B=1:2, B:C=3:4, A:B:C=3Ã—3:3Ã—2:1Ã—4
â‡’ 9:6:4
Answer: A.
Answer: (A) 9:6:4
Question: A college has classes from 10:00 AM until 1:55 PM. In this duration, there are five periods. If 5 minutes are provided between each period to leave one class and enter the next class, how many minutes long is each period?
(A) 38 min
(B) 41 min
(C) 40 min
(D) 42 min
(E) 43 min
Rationale: The total time is 235 minutes.
There are four breaks of five minutes between the classes for a total of 20 minutes.
The total class time is 215 minutes.
215 / 5 classes = 43 minutes per class
The answer is E.
Answer: (E) 43 min
Question: The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income is
(A) 70
(B) 72
(C) 75
(D) 78
(E) None of the above
Rationale: Income of 6 months = (6 × 85) – debt
= 510 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 780
Average monthly income = 780 ÷ 10 = 78
Answer D
Answer: (D) 78
Question: Which of the following is always odd?
(A) Sum of two odd numbers
(B) Diff. of two odd numbers
(C) Prod. of two odd numbers
(D) none of these
(E) Cannot be determined
Rationale: Solution
Product of two numbers is always odd.
Answer C
Answer: (C) Prod. of two odd numbers
Question: Statement: Concerns have risen about air pollution in Indian cities. A recent report by the World Health Organization (WHO) states that of the 20 most polluted cities in the world, 13 are in India.
Action:
I. Pollution committee should immediately take certain measures to control the pollution levels in India.
II. Licenses of polluting industries should be cancelled and owners should be put behind the bars.
(A) Only I follows
(B) Only II follows
(C) Either I or II follows
(D) Neither I nor II follows
(E) Both I and II follow
Rationale: Explanation: Only one follows. The given statement describes the problem and the actions mention the solutions for the same. Second option is to be avoided because it is a negative and harsh approach. As listed in tips and tricks section also Options which are negative in nature and provide harsh solutions should be avoided.
ANSWER IS A
Answer: (A) Only I follows
Question: There are 7 red cups and 5 blue cups on a shelf. If 4 cups are selected at random from the shelf, what is the probability that all 4 cups selected are blue cups?
(A) 1/80
(B) 1/88
(C) 1/90
(D) 1/95
(E) 1/99
Rationale: The number of ways of choosing 4 cups from the shelf is 12C4 = 495.
The number of ways of choosing 4 blue cups is 5C4 = 5.
P(4 blue cups) = 5/495=1/99.
The answer is E.
Answer: (E) 1/99
Question: What is the area of a triangle with the following vertices L(1, 3), M(3, 1), and N(3, 5) ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: There is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem.
Though if you make a diagram minimum simple calculations will be needed:
Answer: B.
Answer: (B) 4
Question: John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 150% of John's weight. Which of these 5 people weighs the least?
(A) John
(B) Susan
(C) Sam
(D) Mark
(E) Lynn
Rationale: John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;
Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;
Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;
Lynn weighs 150% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);
As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.5*J)=0.75*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight ismore than 50%of that of John.
Answer: B.
Answer: (B) Susan
Question: If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss.
(A) $ 50
(B) $ 58
(C) $ 52
(D) $ 60
(E) $ 12
Rationale: Cost of 20 lollipops = $90
Sold each lollipop for $2
So he sold 20 lollipops for $(20 × 2) = $40
Loss = $(90 – 40) = $50
Therefore, loss = $ 50.
Answer:A
Answer: (A) $ 50
Question: A man buys an article for $100. and sells it for $120. Find the gain percent?
(A) 10%
(B) 15%
(C) 25%
(D) 20%
(E) 30%
Rationale: C.P. = $100
S.P. = $120
Gain = $20
Gain% = 20/100 *100 = 20%
Answer is D
Answer: (D) 20%
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:
(A) Rs. 3100
(B) Rs. 6240
(C) Rs. 6500
(D) Rs. 9600
(E) Rs. 9000
Rationale: Explanation:
To obtain Rs. 10, investment = Rs. 96.
To obtain Rs. 650, investment = Rs. 96	/10 *650=Rs. 6240.
ANSWER IS B
Answer: (B) Rs. 6240
Question: A car covers a distance of 624 km in 3 hours. Find its speed?
(A) 104 kmph
(B) 194 kmph
(C) 208 kmph
(D) 174 kmph
(E) 101 kmph
Rationale: 624/3
=208 kmph
Answer:C
Answer: (C) 208 kmph
Question: In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 4%.what is population of after 2 year.
(A) 140
(B) 141
(C) 142
(D) 143
(E) 147
Rationale: next year total population=[150^2+90^2]^.5=174.92=175
man decreased by 4% so total man =150*.96=144
women will be= 175-144=31
so population after two years= [135^2+31^2]^.5=147.30=147
so population after two year= 147
ANSWER:E
Answer: (E) 147
Question: Arjun and Sajal are friends . each has some money. If Arun gives Rs. 30 to Sajal, the Sajal will have twice the money left with Arjun. But, if Sajal gives Rs. 10 to Arjun, the Arjun will have thrice as much as is left with Sajal. How much money does Sajal have?
(A) Rs 34
(B) Rs 35
(C) Rs 36
(D) Rs 37
(E) Rs 38
Rationale: If arun had x rs , and sejal had y rs, then
2*(x-30) = y+30 or 2x-60= y+30 or y= 2x-90
and
x+10 = 3*(y-10)= 3*(2x-90-10)=6x-300
or
5x=310
x= 310/5 = 62 Rs with Arjun
y= 2x-90 = Rs 34 with Sajal
ANSWER:A
Answer: (A) Rs 34
Question: If x^2 – 3x = 18, then one possible value of x – 4 =
(A) -9
(B) -5
(C) -3
(D) -1
(E) 2
Rationale: x^2 – 3x = 18
i.e. x^2 – 3x - 18 = 0
i.e. x^2 –6x + 3x - 18 = 0
i.e. (x-6)(x+3) = 0
i.e. x = 6 or -3
i.e. x-4 = 6-4 or -3-4
i.e. x-4 = 2 or -7
Answer: Option E
Answer: (E) 2
Question: In a class, there are 24 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?
(A) 6
(B) 12
(C) 18
(D) 16
(E) 26
Rationale: Explanation:
Let the number of boys be x. Then, (3/4)x = 24 or x = 24 x(4/3) = 32.
If total number of students is y, then (2/3) y = 32 or y = 32 x (3/2) = 48.
Therefore Number of girls in the class = (48 - 32) = 16.
Answer: D
Answer: (D) 16
Question: In a certain company 20% of the men and 40% of the women attended the annual company picnic.If 30% of all the employees are men .What % of all the employee went to the picnic?
(A) 33%
(B) 34%
(C) 35%
(D) 36%
(E) 37%
Rationale: total men in company 30% means total women in company 70%(assume total people in company 100%)
no of men employees attended picnic=30x(20/100)=6
no of women employees attended picnic=70x(40/100)=28
total percentage of employees attended the picnic=6+28=34%
ANSWER:B
Answer: (B) 34%
Question: If |x| = 4x - 2, then x = ?
(A) 1
(B) 2
(C) 1 and 1/2
(D) -1/2
(E) -1
Rationale: Answer:
Approach:
Substituted option A i.e x=2. Inequality satisfied.
B
Answer: (B) 2
Question: How many even 4-digit numbers can be formed, so that the numbers are divisible by 4 and no two digits are repeated?
(A) 336
(B) 784
(C) 1120
(D) 1804
(E) 1936
Rationale: Number is divisible by 4 if the last two digits form a number divisible by 4.
Therefore last two digits can be:
00;
04;
08;
12
16;
...
96.
Basically multiples of 4 in the range 0-96, inclusive. Multiples of 4 in a range 0-96, inclusive are last multiple in the range − first multiple in the range4+1=25last multiple in the range − first multiple in the range4+1=25
But 3 numbers out of these 25 are not formed with distinct digits: 00, 44, and 88. Hence the numbers we are looking for can have only 22 endings.
If there is 0 in the ending (04, 08, 20, 40, 60, 80 - total 6 such numbers), then the first and second digit can take 8 and 7 choices each = 56 choices total. As there are 6 numbers with 0 in ending, hence total 6*56=336.
If there is no 0 in the ending (total 22 - 6 with zero = 16 such numbers), then the first digit can take 7 choices (10 - 2 digits in the ending and zero, so total 3 digits = 7, as 4-digit number can not start with zero) and the second digit can take 7 choices too (10 digits - 3 digits we've already used) = 7*7=49 choices total. As there are 16 numbers without zero in ending, hence total 16*49=784.
TOTAL: 336+784=1120
Answer: C.
Answer: (C) 1120
Question: A retailer bought a coat at wholesale and marked it up 90% to its initial price of $76. By how many more dollars does he need to increase the price to achieve a 100% markup?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Let x be the wholesale price.
Then 1.9x= 76 and x = 76/1.9 = 40.
To achieve a 100% markup, the price needs to be $80.
The retailer needs to increase the price by $4 more.
The answer is B.
Answer: (B) 4
Question: If an object travels at ten feet per second, how many feet does it travel in two hours?
(A) 60000
(B) 30000
(C) 18000
(D) 72000
(E) 22200
Rationale: If an object travels at 10 feet per second it covers 10x60 feet in one minute, and 10x60x2x60 feet in two hour.
Answer = 72000 Answer: D
Answer: (D) 72000
Question: what is the least number. which should be added to 0.0568 to make it a perfect square?
(A) 0.0004
(B) 0.0009
(C) 0.0002
(D) 0.0003
(E) 0.0008
Rationale: 0.0568+0.0008=0.0576
(0.24)^2
ANSWER:E
Answer: (E) 0.0008
Question: If M and N are positive integers and M = 15N - 1, what is the remainder when M is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: This question asks what IS...(the answer), so we know that the answer will be consistent. As such, we can TEST VALUES to quickly get the solution.
We're told that M and N are POSITIVE INTEGERS and M = 15N - 1. We're asked for the REMAINDER when M is divided by 5.
IF....
N = 1
M = 14
14/5 = 2 remainder 4
Final Answer:
E
Answer: (E) 4
Question: The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 30∘, the temperature of Friday was :
(A) 40∘
(B) 39∘
(C) 38∘
(D) 30∘
(E) None of these
Rationale: Explanation:
M+T+W+Th=(4×38)=152
Monday temparature is 30. So T+W+Th=(152-30)=122
T+W+Th+F=(4×40)=160
F = (160-122)=38∘
Correct Option: C
Answer: (C) 38∘
Question: Fred and Sam are standing 40 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 4 miles per hour and Sam walks at a constant speed of 4 miles per hour, how many miles has Sam walked when they meet?
(A) 5
(B) 9
(C) 20
(D) 30
(E) 45
Rationale: relative distance =40 miles
relative speed =4+4 =8 miles per hour
time taken =40/8=5 hours
distance travelled by sam =4*5=20 miles=C
Answer: (C) 20
Question: What day of the week will 22 Apr 2222 be?
(A) Monday
(B) Tuesday
(C) Sunday
(D) Thursday
(E) Saturday
Rationale: Explanation:
22 Apr 2222 = (2221 years + period from 1-Jan-2222 to 22-Apr-2222)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2200
= Number of odd days in 200 years
= 5 x 2 = 10 = 3
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
Number of odd days in the period 2201-2221
= 16 normal years + 5 leap years
= 16 x 1 + 5 x 2 = 16 + 10 = 26 = 5 odd days
Number of days from 1-Jan-2222 to 22 Apr 2222
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 22(Apr) = 112
112 days = 0 odd day
Total number of odd days = (0 + 3 + 5 + 0) = 8 = 1 odd day
1 odd days = Monday
Hence 22 Apr 2222 is Monday.
Answer: Option A
Answer: (A) Monday
Question: If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of s^2 – r^2 – q^2?
(A) -20
(B) 0
(C) 8
(D) 12
(E) 16
Rationale: s > r > q are consecutive even integers
Testing for s2−r2−q2
I: For s = 0, r = -2, q = -4,
s2−r2−q2=−20
II: For s = 2, r = 0, q = -2
s2−r2−q2=0
III: For s = 4, r = 2, q = 0
s2−r2−q2=12
Step II & Step III have consecutive representation of values of s, r, q. No other combination is possible.
8 cannot be the answer as for value of s = 6 & above, the resultant would be greater than 12
Answer = C
Answer: (C) 8
Question: A bag contains 5 white balls, 4 black balls, and 3 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
(A) 0.25
(B) 0.15
(C) 0.35
(D) 0.45
(E) 0.4
Rationale: Each ball has an equal probability of being the third ball drawn.
P(3rd ball is red) = 3/12 = 0.25
The answer is A.
Answer: (A) 0.25
Question: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 2/5 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?
(A) 4/5
(B) 8/15
(C) 11/15
(D) 9/20
(E) 13/20
Rationale: (1/2)X = (1/4)Y
(1/4)Y + (2/5)Y = (13/20)Y
The answer is E.
Answer: (E) 13/20
Question: A certain team consists of 4 professors and 5 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)
(A) 74
(B) 85
(C) 96
(D) 107
(E) 118
Rationale: The total number of ways to form a group of 3 from 9 people is 9C3 = 84
The number of ways to form a group without a professor is 5C3 = 10
The total number of ways to form a valid group is 84 - 10 = 74.
The answer is A.
Answer: (A) 74
Question: An plane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of ?
(A) 100
(B) 720
(C) 1100
(D) 940
(E) 860
Rationale: We know
Distance = speed * time
= 240 * 5
= 1200 km
Now to cover 1200 km in 5/3 hrs ,
speed = distance / time
= 1200 / (5/3)
= 720 KMPH
Ans- B
Answer: (B) 720
Question: The sector of a circle has radius of 21 cm and central angle 270o. Find its perimeter?
(A) 145 cm
(B) 135 cm
(C) 121 cm
(D) 141 cm
(E) 151 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (270/360 * 2 * 22/7 * 21) + 2(21)
= 99 + 42 = 141 cm
Answer: D
Answer: (D) 141 cm
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
(A) 2221
(B) 2882
(C) 3600
(D) 2882
(E) 1271
Rationale: P = 144(100/5)2 => P = 3600.Answer: C
Answer: (C) 3600
Question: In a certain country vehicle number plates come in a certain format - XXX - XXXX . The first 3 places are filled with letters of an alphabet and the next 4 spaces are filled with numbers starting from 0001. What is the maximum number of vehicle number plates that we can have.
(A) 175742424
(B) 175742425
(C) 175742434
(D) 175742444
(E) 100000000
Rationale: The first set of XXX can be filled with letters only.
So the number of ways is 26*26*26 (Since there are 26 letters in an alphabet and we can use any letter in all 3 places, since repetition is allowed)
The second set of XXXX can be filled with numbers ranging from 0,1,2,3,4,5,6,7,8,9
Number of ways by which we can have letters in this is 10 * 10 * 10 * 10 since we can have any number at any place, since repetition is allowed
= (10*10*10*10) - 1 (we are subtracting 1 since one of the numbers can be 0000 which is not allowed since numbers start with 0001)
Total number of vehicles can be
=26*26*26 * (10000-1)
=175742424
Answer: A
Answer: (A) 175742424
Question: At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ?
(A) 20
(B) 45
(C) 55
(D) 90
(E) 95
Rationale: number of handshakes = 10C2= 10*9/2 = 45
ANSWER:B
Answer: (B) 45
Question: A 600 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) 800
(B) 700
(C) 360
(D) 370
(E) 380
Rationale: Speed = 600/18 = 100/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 100/3
=> x = 1300 m.
L=1300-600 =700m
Answer: Option B
Answer: (B) 700
Question: For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^3 -S(n+1).in addition ,S2=1.then which of the following must be true.
(A) a)S4 +S3 +1=0
(B) b)(S1)^2 +S4 +2=0
(C) c) ifS1=-1thenS4 is also equal to-1.
(D) d) ifS4 =-7thenS1=-2.
(E) e) ifS1 =-3thenS4=-7
Rationale: Since all the answers include S4, let's start from there.
S4=S2^2-S3
S3=S1^2-S2
Substituting S3 into the first equation we get:
S4=S2^2-(S1^2-S2)
Since S2=1
S4=1-(S1^2-1)
S4=2-S1^2
We need S1^2 in order to calculate S4.
E) provides S1 and from there we can calculate S4:
S4=2-(-3)^2
S4=-7
Correct.
As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer.
For example:
If S4=-7 then S1=3 :
if we substitute S4 with - 7 we get:
-7=2-S1^2
S1^2=9
now S1 can be +/-3 !!
D
Answer: (D) d) ifS4 =-7thenS1=-2.