divelab/Sys2Bench huggingface dataset:
Question: The angles of a triangle are in the ratio 1 : 2 :3 . Find the measurement of the 3angles of triangle.
Options:
A)100°
B)110°
C)60°
D)180°
E)190°
Rationale: If the ratio of the three angles is 1:2:3, then the measures of these angles can be written as x, 2x and 3x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 2x + 3x = 180
Solve for x
6x = 180
x = 30
The measures of the three angles are
x = 30°
2x = 2 × 30 = 60°
3x = 3 × 30 = 90°
C
Answer: C
Question: A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of arc BDA when angle A is 35 degrees?
Options:
A)210
B)240
C)270
D)290
E)360
Rationale: An inscribed angle is an angle in a circle composed of two chords with a common endpoint, that is, an angle with its vertex on the circle. In this problem, all four lettered angles are inscribed angles.
An inscribed angle necessarily opens to intersect an arc (the technical word is to subtend an arc). The Inscribed Angle Theorem said that the measure of an inscribed angle is always half the measure of the arc it intersects, or subtends.
angle A = 35 degrees
Thus,
arc BCD = 70 degrees
A whole circle has 360 degrees of arc, so arc BDA should be the rest of the circle.
arc BDA = 360 - 70 = 290 degrees
Answer =(D)
Answer: D
Question: A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?
Options:
A)$148,000
B)$167,000
C)$156,000
D)$175,000
E)$144,000
Rationale: 6% x = 8,880 : x = selling price of house.
x = $148,000 : solve for x.
correct answer A
Answer: A
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
Options:
A)258
B)124
C)525
D)343
E)729
Rationale: The first ring can be worn in any of the 3 fingers (3 ways).
Similarly each of the remaining 5 rings also can be worn in 3 ways.
Hence total number of ways
=3×3×3×3×3×3=36=729
Ans: E
Answer: E
Question: A walks at 30 kmph and 30 hours after his start, B cycles after him at 48 kmph. How far from the start does B catch up with A?
Options:
A)1200km
B)1500km
C)2000km
D)2400km
E)3600km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 30 hours.
x/30 - x/48 = 30
x = 2400 km
Answer is D
Answer: D
Question: What is the value of x^2yz − xyz^2, if x = -1, y = 1, and z = 3?
Options:
A) 20
B) 24
C) 30
D) 12
E) 48
Rationale: 1*1*3 -(- 1*1*9)
=3+9 = 12
Ans: D
Answer: D
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 170kg then find the average weight of all the 7 rounds?
Options:
A)97.1 kgs
B)88.5 kgs
C)86.5 kgs
D)67.5 kgs
E)88.2 kgs
Rationale: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 170/7 = 97.1kgs
Answer:A
Answer: A
Question: If the mean of numbers 12, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 511, 1023 and x?
Options:
A)395
B)275
C)355
D)415
E)398.2
Rationale: The mean of numbers 12, x, 42, 78 and 104 is 62: 12+x+42+78+104=62*5 --> x=74;
So, the mean of 128, 255, 511, 1023 and x is (128+255+511+1023+74)/5=398.2.
Answer:E.
Answer: E
Question: A vessel contains a mixture of two milk M and N is the ratio 7 : 5. When 9 ltr of mixture are drawn off and the vessel is filled with B, the ratio of Mand N becomes 7 : 9. How many ltrof liquid M was contained by the can initially?
Options:
A)20ltr
B)21ltr
C)23ltr
D)24ltr
E)25ltr
Rationale: Suppose the can initially contains 7x and 5x of mixtures A and B respectively.
Quantity of M in mixture left = 7x -	7	x 9 ltr= 7x -	21 ltr.
12	4
Quantity of N in mixture left = 5x -	5	x 9 ltr = 5x -	15 ltr.
12	4
7x -	21
4
=	7
5x -	15 + 9
4
9
28x - 21	=	7
20x + 21	9
252x - 189 = 140x + 147
112x = 336
x = 3.
So, the can contained 21ltr of M
B
Answer: B
Question: Tom and Beth each drove from Smallville to Crown City by different routes. Tom drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than Tom to complete the trip. How many miles per hour was Beth's average speed on this trip?
Options:
A) 24
B) 30
C) 48
D) 54
E) 75
Rationale: Speed = Distance/Time
Distance for Tom = Speed * Time = 40 * 1/2 = 20 miles
Distance for Beth = Distance for Tom +5 = 20+5 = 25 miles
Time taken by Beth = Time taken by Tom + (1/3 hour) = 1/2+1/3 = 5/6
Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour
Hence, B is the answer.
Answer: B
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is
Options:
A)12 kg
B)60 kg
C)72 kg
D)96 kg
E)None
Rationale: Solution
Volume of water displaced	= (3 x 2 x 0.01)m3
= 0.06m3.
Mass of man	=Volume of water displaced ×Density of water
= (0.06×1000) kg
= 60 kg.
Answer B
Answer: B
Question: The ration between the present ages of P and Q is 1:2. If Q is 8 years older than P, what will be the ratio of the ages of P and Q after 8 years?
Options:
A)1:2
B)1:3
C)2:3
D)5:7
E)4:9
Rationale: Let P's and Q's age be x and 2x
2x-x = 8
x = 8
Required ratio = (x+8):(2x+8) = 16:24 = 2:3
Answer is C
Answer: C
Question: The sum of three numbers is 98. If the ratio between first and second be 2 : 3 and that between second and third be 5 : 8, then the second number is?
Options:
A)30
B)20
C)58
D)48
E)68
Rationale: Let the numbers be X, Y and Z. Then,
X + Y + Z = 98, X/Y = 2/3 and Y/Z = 5/8
Therefore, X = 2Y/3 and Z = 8Y/5. So, 2Y/3 + Y + 8Y/5 = 98.
49Y/15 = 98
Y = 30.
ANSWER:A
Answer: A
Question: The last time Parag bought Diwali cards, he found that the four types of cards that he liked were priced Rs.2.50, Rs.3.50, Rs.3.00 and Rs.5.00 each. As Rahul wanted 50 cards, he took ten each of two kinds and fifteen each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How many notes did paragl give?
Options:
A)10
B)12
C)15
D)11
E)18
Rationale: Explanation :
Let the four cards be a, b ,c and d. 'x' be the number of notes.
Then, according to the question,
=>10a + 10b + 15c + 15d = 10*x.
=> a +b + 1.5(c+d) = x . -----------------------------(i)
Since, a + b = 2.50+3.50 =6.
And,
=> c + d = 3+5 =8
Putting these values in (i), we get :-
=> 6 + 1.5 * 8 = x.
=> x = 18 .
Answer : E
Answer: E
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 30, how many more dollars, in terms of x, will it cost per person?
Options:
A) x/6
B) x/12
C) x/15
D) 3x/40
E) 3x/80
Rationale: Just plugging in values
X= 300
Cost per person if we consider 10 = 30
Cost per person if we consider 30 = 10
Difference between costs is 20 dollars.
Plugging in the value of x into the answer choices, let's see which one yields a result of 20. And that is C.
Answer: C
Question: In a series of three football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 3 draws in the series?
Options:
A)24/576
B)125/864
C)1/25
D)1/64
E)1/5
Rationale: Since the probability of a draw is 1/4, then the probability of 3 draws in 3 matches is (1/4)^3=1/64.
Answer: D.
Answer: D
Question: A sales executive receives an annual bonus if he meets a certain target. This year, the salesman has so far sold 1/4 of last year's quota. If this year's quota is reduced by 20 percent from last year, how much target percentage of this year's target does he still need to complete to get bonus?
Options:
A)15/25
B)4/20
C)3/4
D)15/20
E)9/10
Rationale: We have 1/5 and 20% which is 1/5. Let's pick some smart numbers.
Assume last year's quota to be 25.
This year's quota = 20% reduction from 25 = 20
Sold so far = 1/5 * 25 = 5
Remaining = 20-5 = 15
Required = 15/25
Answer (A).
Answer: A
Question: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is :
Options:
A)334
B)378
C)377
D)400
E)288
Rationale: Explanation:
Let the numbers be x and y.
Then, xy = 9375 and x/y = 15.
=>
=> y = 25
=> x = 15y = 15 x 25 = 375.
Sum of the numbers = 375 + 25 = 400.
Answer: D) 400
Answer: D
Question: In a deck of cards there are 52 cards numbered from 1 to 13. There are 4 cards of each number in the deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it?
Options:
A)1/4.
B)4/17.
C)5/29
D)4/13
E)1/3
Rationale: P(10) = (4+12) / (52+12)
= 16/64
= 1/4.
Answer:A
Answer: A
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 12 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)477
B)396
C)279
D)276
E)291
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 12 + 21 = 33
T = 12
D = 33 * 12 = 396.Answer: B
Answer: B
Question: Look at this series: 0.6, 0.3, ____, 0.075, 0.0375, ... What number should fill the blank?
Options:
A)0.015
B)1.15
C)0.15
D)0.25
E)0.35
Rationale: This is a simple multiplication series. Each number is multiple by 1/2.
Answer: C
Answer: C
Question: A tap can fill a tank in 6 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?
Options:
A)1 hr 20 min
B)2 hr
C)3 hr
D)4 hr
E)5 hr 50 min
Rationale: Explanation:
1 tap can fill the tank in 6 hours.
Therefore
1 tap can fill half tank in 3 hours.
3 taps can fill the tank in 6/3 hour = 2 hours.
Therefore
3 taps can fill half tank in 2/2 hour =60 minutes = 1hour.
Total time taken=4 hours
Answer: Option D
Answer: D
Question: Find out the C.I on Rs.2000 at 4% p.a. compound half-yearly for 1 1/2 years.
Options:
A)A)Rs.420.20
B)B)Rs.319.06
C)C)Rs.306.04
D)D)Rs.294.75
E)E)Rs.295.75
Rationale: A = 2000(51/50)3
= 2122.41
2000
-----------
122.41
ANSWER:C
Answer: C
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 31 kmph. Of how many minutes does the train stop per hour?
Options:
A)18.6
B)27
C)12
D)121
E)28
Rationale: Explanation:
T = 14/45 * 60 = 18.6
Answer: Option A
Answer: A
Question: A small beaker is 1/2 filled with salt water. Another beaker, which has five times the capacity of the small beaker, is 1/3 filled with fresh water. After dumping all of the salt water from the small beaker into the large beaker, to what fraction of its capacity will the large beaker be filled?
Options:
A)7/10
B)11/20
C)13/30
D)17/30
E)19/30
Rationale: 1/2 of the small beaker is 1/10 of the large beaker.
1/10 + 1/3 = 13/30
The answer is C.
Answer: C
Question: A man walks at a speed of 4 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
Options:
A)2 4/2 hours
B)2 hours
C)2 1/6 hours
D)2 1/1 hours
E)2 1/2 hours
Rationale: Required time
= (5 1/4)/4 + (5 1/4)/7
= 2 hours.
Answer:B
Answer: B
Question: Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4,
find P (E|F) and P(F|E)
Options:
A)1/4
B)1/5
C)1/7
D)2/5
E)2/9
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1
P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4.
A
Answer: A
Question: A group of 6 members to be made from 8 boys and 6 girls. How many ways of forming group provided that there will be exactly 3 boys?
Options:
A)1110
B)1120
C)1130
D)1140
E)1150
Rationale: 3 boys out of 8 boys & 3 girls out of 6 girls bcz total 6 member of a group where exactly 3 boys.
8C3*6C3= 8!/(5!3!) * 6!/(3!3!)= 56*20=1120
ANSWER:B
Answer: B
Question: A certain no. when divided by 80 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
Options:
A)2
B)4
C)7
D)8
E)9
Rationale: Explanation:
80 + 25 = 105/15 = 7(Remainder)
C
Answer: C
Question: Seats for Maths, Physics and Biology are in the ratio of 9 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
Options:
A)18 : 15 : 20
B)6 : 7 : 8
C)6 : 8 : 9
D)Cannot be determined
E)None of these
Rationale: Reqd ratio 9 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100
= 9 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 18 : 15 : 20
Answer A
Answer: A
Question: An urn contains 5 black and 3 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
Options:
A)1/5
B)3/7
C)2/5
D)5/14
E)2/7
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 5/8
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 4 black balls and three white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 4/7
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 5/8 × 4/7 = 5/14
D
Answer: D
Question: John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes.
Options:
A)24
B)12
C)7
D)6
E)5
Rationale: 5 different colours = 5 single colours = 5 different clients
There are 7 clients to go
The use of the factorial is the easiest way to solve this kind of problem for me.
A B C D E (different colour)
C C N N N (2 colour coding + 3 colour non chosen)
5!/2!3!= 10
15 codings can be done with 5 different colours
Ans E
Answer: E
Question: A wolf eats 5 Kg of meat in 2 days. A baby tiger eats 3 Kg of meat in 4 days. How much meat can the two combined eat in three days?
Options:
A)10.5
B)9.75
C)8.25
D)7.15
E)6.0
Rationale: 3/2*5+3/4*3=9.75 kg
B
Answer: B
Question: In how many ways can a team of 5 be chosen out of a batch of 8 players?
Options:
A)45
B)56
C)32
D)50
E)61
Rationale: required number of ways = 8C5 = 56
Answer is B
Answer: B
Question: All factors of a positive integer X are multiplied and the product obtained is X^3. If X is greater than 1, how many factors does X have?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: The question can be done in seconds if you understand the properties of factors of a number. Note that every distinct factor of a number which is not a perfect square has a complementary factor.
For example,
Factors of 6: 1, 2, 3, 6
1 has a complementary factor 6 such that 1*6 = 6 (the original number)
2 has a complementary factor 3 such that 2*3 = 6 (the original number)
So if you have a number, n, which is not a perfect square, and start multiplying its factors, you will get n to a certain power. the power will half of the number of factors. For example, 6 has 4 factors and when you multiply all 4 factors, you get 6^2 (2 is half of 4).
So if you know that the product of all factors is X^3, it means there must have been twice the number of factors i.e. 3*2 = 6 factors.
E)
Answer: E
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
Options:
A)432
B)277
C)269
D)2656
E)290
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer: A
Answer: A
Question: The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 12 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: To get 40 points as end of season we need another 28 points or more from remaining 15 matches:
Option A= 6*3+9*1=27
Option B=7*3 + 8*1=29
hence option B-7
Answer: B
Question: 5, 11, 17, 25, 33, 43, ?
Options:
A)44
B)26
C)58
D)59
E)53
Rationale: E
53
The sequence is +6, +6, +8, +8, +10, ....
Answer: E
Question: A letter lock consists of three rings each marked with thirteen different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?
Options:
A)1773
B)2196
C)2153
D)1683
E)1673
Rationale: Since each ring consists of thirteen different letters, the total number of attempts possible with the three rings is
= 13*13*13 = 2197. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 2197 - 1
= 2196.
Answer: B
Answer: B
Question: Victor gets 95 % marks in examinations. If these are 285 marks, find the maximum marks.
Options:
A)334
B)500
C)376
D)288
E)300
Rationale: Let the maximum marks be m
Then 95 % of m = 285
⇒ 95/100 × m = 285
⇒ m = (285 × 100)/95
⇒ m = 28500/95
⇒ m = 300
Therefore, maximum marks in the examinations are 300.
Answer:E
Answer: E
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3669
Options:
A)3669
B)9654
C)5945
D)7963
E)8216
Rationale: The product of first two digits in a number equals the last two digits, except in 3669. Hence, it is the odd one.
The answer is 3669.
ANSWER:A
Answer: A
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:
Options:
A)20
B)80
C)100
D)200
E)250
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
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)Rs.4538
B)Rs.4518
C)Rs.4518
D)Rs.4530
E)Rs.4517
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs.4530
Answer: D
Answer: D
Question: Uncle Bruce is baking chocolate chip cookies. He has 40 ounces of dough (with no chocolate) and 20 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 25% chocolate?
Options:
A)8.5
B)9.5
C)10.5
D)6.7
E)6.5
Rationale: First, you must find the total weight of the mixture given that 80% of it will be dough.
75%*Total = 40 => (75/100)Total=40 => Total=4000/75=> Total=53.33oz,
From there, you must find 25% of the total 53.33 oz of the mixture.
25%*Total => (25/100)(53.33)= 13.33 oz choclate used,
Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 20-13.3 = 6.7 oz chocolate left over.
Answer : D
Answer: D
Question: A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 7 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
Options:
A)18
B)23
C)38
D)53
E)68
Rationale: There is one post for each length of chain, plus one final post at the end.
The length of the fence in feet is 7.5x + 0.5, where each is the number of chain lengths.
The length of the fence is an integer when x = 1,3,5,7,...
The length of the fence could be 8, 23, 38, 53, 68,...
The answer is A.
Answer: A
Question: y = 248 - 198x
Which of the following values of x gives the greatest value of y in the equation above?
Options:
A) 200
B) 100
C) 0.5
D) -5
E) 4
Rationale: Clearly, the negative value of x will result in maximum value of y.
Don't even look at the rest of the answer choices as only one negative value is being present.
Answer is D
Answer: D
Question: A number when divided by 45, gives 30 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 15
Options:
A)A)0
B)B)3
C)C)4
D)D)6
E)E)7
Rationale: Explanation:
P ÷ 45 = 30
=> P = 30 * 45 = 1350
P / 15 = 1350 / 15 = 90, remainder = 0
Answer: Option A
Answer: A
Question: If 525/999=0.525, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?
Options:
A)-1
B)0
C)3
D)4
E)5
Rationale: 0.[u]125[/u = 0.525525525.....
Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.
Answer E
Answer: E
Question: Car Dealership X, the total profit from sales increased by 8 percent over the previous years, while the number of cars sold decreased by 8 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.
Options:
A)17.39%
B)20%
C)22%
D)23%
E)25%
Rationale: Let Profit be x and cars sold be y
Originally Profit/Car = x/y
Now it is 1.08x / 0.92 y = 108/92 (x/y)
Increase in profit per car = ((16/92) (x/y)) / (x/y) * 100 = 17.39%
Answer = A
Answer: A
Question: A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 9 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?
Options:
A)14
B)45
C)54
D)65
E)32
Rationale: Just check the answers and reverse the numbers until you get 9.
32 - 23 = 9
Answer E
Answer: E
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.964 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
Options:
A)22200
B)31897
C)38799
D)40000
E)42782
Rationale: P(11/10)^4 - P(6/5)^2 = 964
P = 40000
Answer: D
Answer: D
Question: How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
Options:
A)26
B)50
C)100
D)1000
E)90
Rationale: 1 million distinct 3 digit initials are needed.
Let the number of required alphabets in the language be ‘n’.
Therefore, using ‘n’ alphabets we can form n * n * n = n3 distinct 3 digit initials.
Note distinct initials is different from initials where the digits are different.
For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.
This n3 different initials = 1 million
i.e. n3 = 106 (1 million = 106)
=> n3 = (102)3 => n = 102 = 100
Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.
Option C
Answer: C
Question: The perimeters of two squares are 44 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .
Options:
A)22 cm
B)24 cm
C)26 cm
D)30 cm
E)29 cm
Rationale: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 44/4 = 11 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 11*11 - 8*8
= 57 cm
So side of third square = 7.5 [because area of square = side*side]
Perimeter = 4*Side = 4*7.5 = 30 cm
Answer: Option D
Answer: D