mathewhe/aqua_rat huggingface dataset:
Question: Area of a square is 1/2 hectare. The diagonal of the square is?
(A) 250 meter
(B) 100 meter
(C) 50√ 2 meter
(D) 50 meter
(E) 35 meter
Rationale: Area = 1/2 hectare = 10000 / 2 m2
= 5000 m2
Again Area = 1/2 x (Diagonal)2
So 1/2 x (Diagonal)2 = 5000m2
Diagonal2= 10000
Diagonal = 100
Answer : B
Answer: (B) 100 meter
Question: A box contains 9 apples, 8 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: P(choosing a red apple 5 times in a row) = 8/9*7/8*6/7*5/6*4/5 = 4/9 < 0.5
The answer is C.
Answer: (C) 5
Question: How much time will a train of length 400 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) 40 sec
(B) 50 sec
(C) 60 sec
(D) 70 sec
(E) 80 sec
Rationale: The distance to be covered = Sum of their lengths = 400 + 300 = 700 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 700/10 = 70 sec.
ANSWER:D
Answer: (D) 70 sec
Question: If k is a non-negative integer and 21^k is a divisor of 435,961 then 7^k - k^7 =
(A) 0
(B) 1
(C) 42
(D) 118
(E) 242
Rationale: 4+3+5+9+6+1 = 28, so this number is not divisible by 3 and thus not divisible by 21.
Therefore, k=0
7^k - k^7 =1-0=1
The answer is B.
Answer: (B) 1
Question: The Simplastic language has only 2 unique values and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic?
(A) 9
(B) 12
(C) 36
(D) 72
(E) 108
Rationale: The nouns havefixed structureC-V-C-V-C. Now,each Ccan take 3 values (let's say X, Y or Z) andeach Vcan take 2 values (let's say A or E), so there will be 3*2*3*2*3=108 nouns possible.
Answer: E.
It's basically the same if it were how many different 5-digit numbers are possible with the following structure odd-even-odd-even-odd, where odd numbers can be only 1, 3 or 5 and even numbers only 2 and 4.
It's natural to think that a noun can have for example two same vowels (X-A-Y-A-Z) or 3 same consonants (X-A-X-A-X), so if this was not the case then this would be explicitly mentioned.answer is E
Answer: (E) 108
Question: What distance will be covered by a city bus moving at 72 kmph in 30 seconds?
(A) 200 m
(B) 300 m
(C) 600 m
(D) 500 m
(E) 400 m
Rationale: 72 kmph = 72 * 5/18 = 20 mps
Dist = Speed * time = 20 * 30 = 600 m.
ANSWER C
Answer: (C) 600 m
Question: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 25 p coins are there?
(A) 155
(B) 100
(C) 125
(D) 150
(E) 120
Rationale: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
Then, sum of their values = (25 x/100) + (20 x/100) + (15 x/100)
= 60 x /100
30 = 60 x / 100
x = 50 = 25 p coin
Hence, the number of 5 p coins = (3 * 50) = 150.
Ans - D
Answer: (D) 150
Question: What is the square root of 3,969?
(A) A)18
(B) B)9
(C) C)45
(D) D)63
(E) E)81
Rationale: A square root of a number is a number times itself equals the original number.
Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).
63*63=3,969
3969 divided by x = 63
x=63
(D)63
Answer: (D) D)63
Question: Which No. Replace in Question mark?
4,02,42,82,23,63,?
(A) 04
(B) 05
(C) 06
(D) 07
(E) 08
Rationale: 4*(4+0)=4
4*(4+1)=20 i.e 02
4*(4+2)=24 i.e 42
4*(4+3)=28 i.e 82
4*(4+4)=32 i.e 23
4*(4+5)=36 i.e 63
hence
4*(4+6)=40... i.e.ans:04
ANSWER:A
Answer: (A) 04
Question: What number has a 5:1 ratio to the number 11?
(A) 22
(B) 50
(C) 55
(D) 52
(E) 12
Rationale: 5:1 = x: 10
x = 55
Answer: C
Answer: (C) 55
Question: In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?
(A) 80
(B) 81
(C) 64
(D) 63
(E) 82
Rationale: Stage 1: Select a box for the 1st ball to go into.
There are 3 available boxes, so we can complete stage 1 in 3 ways
Stage 2: Select a box for the 2nd ball to go into.
There are 3 available boxes, so we can complete stage 2 in 3 ways
Stage 3: Select a box for the 3rd ball to go into.
There are 3 available boxes, so we can complete stage 3 in 3 ways
Stage 4: Select a box for the 4th ball to go into.
There are 3 available boxes, so we can complete stage 4 in 3 ways
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus distribute all 4 balls) in (3)(3)(3)(3)(4) ways (= 81 ways)
Answer:B
Answer: (B) 81
Question: There are two numbers. If 50% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) 5/9
(B) 5/7
(C) 5/3
(D) 5/8
(E) 2/1
Rationale: Let the two numbers be x and y.
50/100 * x + y = 5/4y
=> 1/2 x = 1/4 y => x/y
= 2/1
Answer: E
Answer: (E) 2/1
Question: If m > 0 and y is m percent of x, then, in terms of m, x is what percent of y?
(A) a) 100m
(B) b) 1/100m
(C) c) 10,000/m
(D) d) 10/m
(E) e) 1/m
Rationale: y= m/100 * x
So x= 100/m * y
So x= (10000/m)/100 *y
C
Answer: (C) c) 10,000/m
Question: What is the HCF of 2/3, 4/9 and 6/18
(A) 7/45
(B) 2/45
(C) 1/9
(D) 8/45
(E) 9/45
Rationale: Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 9, 18) = 2/18 = 1/9
Answer: Option C
Answer: (C) 1/9
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) 300
(B) 350
(C) 450
(D) 470
(E) 500
Rationale: Explanation:
10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450
C
Answer: (C) 450
Question: If x and y are odd integers, which of the following must always be a non-integer
(A) -x^2y
(B) y/x
(C) xy/4
(D) x/y
(E) x^2y^2
Rationale: as X and Y are odd, multiplication of x and y would result in odd integer
(Odd Integer)/4 will always be non integer.
C
Answer: (C) xy/4
Question: David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
(A) 19
(B) 28
(C) 30
(D) 37
(E) None
Rationale: EXPLANATION
Suppose their paths cross after x minutes.
Then, 11 + 57x = 51 – 63x <=> 120x = 40
x= 1/3
Number of floors covered by david in (1/3) min = (1/3 x 57) = 19
So, their paths cross at (11 +19) i.e., 30th floor.
Answer C
Answer: (C) 30
Question: From below option 48 is divisible by which one?
(A) A)3
(B) B)5
(C) C)9
(D) D)7
(E) E)11
Rationale: 48/3 = 16
A
Answer: (A) A)3
Question: If (5^5)(9^3)=3(15^x), what is the value of x?
(A)  5
(B)  9
(C)  11
(D)  13
(E)  15
Rationale: (5^5)(9^3)=3(15^x)
=> 5^5 * 3^6 = 3 * 3^x * 5^x
=> 5^5 * 3^6 = 3^(x+1) * 5^x
Value of x = 5
Answer A
Answer: (A)  5
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 60 as remainder. Find the no. is?
(A) 145646
(B) 236578
(C) 645353
(D) 456546
(E) 220060
Rationale: (555 + 445) * 2 * 110 + 60 = 220000 + 60 = 220060
E
Answer: (E) 220060
Question: Find the odd man out. 12, 24, 34, 48, 64, 84
(A) 48
(B) 34
(C) 24
(D) 12
(E) 11
Rationale: Explanation :
All numbers except 34 are multiples of 4. Answer : Option B
Answer: (B) 34
Question: The ratio of the two natural numbers is 5 : 6. If a certain number is added to both the numbers, the ratio becomes 7 : 8. If the larger number exceeds the smaller number by 10, find the number added?
(A) 17
(B) 14
(C) 10
(D) 16
(E) 20
Rationale: Let the two numbers be 5x and 6x.
Let the numbers added to both so that their ratio becomes 7 : 8 be k.
(5x + k) / (6x + k) = 7/8
=> 40x + 8k = 42x + 7k => k = 2x.
6x - 5x = 10 => x = 10
k = 2x = 20.
Answer:C
Answer: (C) 10
Question: If N = 1/5 + 1/5^2 +1/5^3 , then N is multiplied by 100 , will the product be greater than 100?
(A) Less than 100
(B) Greater than 100
(C) Indeterminate
(D) Equal to 100
(E) Cannot be determined
Rationale: We need to check if (1/5 + 1/5^2 +1/5^3) > 1
If it is greater than 1 then the product 100 * N will be greater than 1 else not
N = 1/5 + 1/5^2 +1/5^3
5^3 * N = 5^3 * 1/5 + 5^3 * 1/5^2 + 5^3 * 1/5 ^3
125 * N = 25 + 5 + 1
125 * N = 31
N = 31/125
N is less than 1 since numerator is less than denominator .
Therefore 100 N would be less than 100
Ans: A
Answer: (A) Less than 100
Question: If x/4 + 24/x = 5, what are the values of 4x - 7?
(A) 8 and 9
(B) 8 and 24
(C) 25 and 41
(D) 12 and 29
(E) 17 and 29
Rationale: I got the same thing C is the answer 25 or 41
Answer: (C) 25 and 41
Question: A thief goes away with a SANTRO car at a speed of 22 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 72 kmph when will the owner over take the thief from the start?
(A) 5/3 hours
(B) 11/25 hours
(C) 2/3 hours
(D) 1/3 hours
(E) 2/5 hours
Rationale: -----------22--------------------|
72 22
D = 22
RS = 72 â€“ 22 = 50
T = 22/50 = 11/25 hours
ANSWER:B
Answer: (B) 11/25 hours
Question: A 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?
(A) 1/4
(B) 2/5
(C) 1/2
(D) 3/5
(E) 2/3
Rationale: you can simply use this formula to avoid confusion:
w1/w2 = (A2 - Aavg)/(Avg - A1)
Here is how you will find the values of A1 an A2.
We have an overall loss (average loss). The average loss is 3 kg when 30 kg alloy is immersed.
This is a loss of (3/30)*100 = 10%.
This is Aavg
The loss of tin is 1.375 kg for every 10 kg.
This means it loses (1.375/10)*100 = 13.75% of its weight in water.
This is A1.
The loss of silver is .375 kg for every 5 kg.
This means it loses (.375/5)* 100 = 7.5% of its weight in water.
This is A2.
Weight of Tin/Weight of Silver = (Silver's loss - Avg loss)/(Avg loss - Tin's loss)
X/Y = (7.5 - 10)/(10 - 13.75) = 2/3
E
Answer: (E) 2/3
Question: A tour group of 25 people paid a total of $1050 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
(A) $22
(B) $23.94
(C) $40
(D) $25.20
(E) $30
Rationale: Soln:-
1050/25=x+0.05x
1050/25=1.05x
x=40
ANSWER:C
Answer: (C) $40
Question: A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train ?
(A) 220 metre
(B) 230 metre
(C) 250 metre
(D) 260 metre
(E) 270 metre
Rationale: Distance covered in 26 seconds = 26Ã—72Ã—5/18=520 meter
Length of the train = 520-250=270 meter
ANSWER: E
Answer: (E) 270 metre
Question: John borrowed 3 soccer boots from Jake, and forgot them on the field, if peter came across a total of 15 boots on the field Jake's boots inclusive, and he took 4 boots at random, what is the probability that Jake's boots were not amongst the 4 taken?.
(A) 12/91
(B) 3/15
(C) 12/15
(D) 33/91
(E) 3/91
Rationale: Since Jake owns 3 of the boots, the subset from which the 4 boots should be chosen are the 12 boots not owned by Jake from the universe of 15.
The first boot can be one of the 12 from the 15 with probability 12/15.
The second boot can be one of the 11 from the 14 remaining with probability 11/14.
The third boot can be one of the 10 from the 13 remaining with probability 10/13.
The fourth boot can be one of the 9 from the 12 remaining with probability 9/12.
The total probability will be 12/15 × 11/14 × 10/13 × 9/12 . On cancellation, this comes to 33/91.
Thus, the answer is D - 33/91
Answer: (D) 33/91
Question: Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7:9, how old is Sachin?
(A) 24.8 years
(B) 28.5 years
(C) 84.5 years
(D) 34.5 years
(E) 24.5 years
Rationale: Let Rahul's age be x years.
Then, Sachin's age = (x - 7) years.
(x - 7)/x = 7/9
2x = 63 => x = 31.5
Hence, Sachin's age = (x - 7) = 24.5 years.
Answer:E
Answer: (E) 24.5 years
Question: What will be the difference between simple and compound interest at 16% per annum on a sum of Rs. 1000 after 4 years?
(A) 164.19
(B) 164.12
(C) 170.6
(D) 167.1
(E) 165.11
Rationale: S.I. = (1000 * 16 * 4)/100 = Rs. 640
C.I. = [1000 * (1 + 16/100)4 - 1000] = Rs. 810.6 Difference = (810.6-640) = Rs. 170.6
Answer: C
Answer: (C) 170.6
Question: If paint costs $3.20 per quart, and a quart covers 1200 square feet, how much will it cost to paint the outside of a cube 10 feet on each edge?
(A) $ 1.60
(B) $ 16.00
(C) $ 96.00
(D) $108.00
(E) $196.00
Rationale: total surface area = 6a^2 = 6*10*10 = 600
each quart covers 20 sqr ft
thus total number of quarts = 600/1200 = 0.5
cost will be 0.5*3.2 = $1.6
Ans: A
Answer: (A) $ 1.60
Question: An empty bottle weighs 1/6th of the full bottle. When a certain percent of water was removed and the bottle was weighed, the weight of the bottle turned out to be 1/3rd of the bottle when it was full. What is the percent of water removed?
(A) 89%
(B) 82%
(C) 81%
(D) 50%
(E) 80%
Rationale: Explanation:
Let the weight of full bottle be 6kg.
Therefore, weight of empty bottle is 1kg and that of water is 5kg.
If x% of water is removed, the weight of the bottle becomes 2kg.
Therefore, the amount of water removed is 4kg.
% of water removed = 4/5 *100 = 80%
ANSWER: E
Answer: (E) 80%
Question: A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 20 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s)
(A) 4200
(B) 5400
(C) 6600
(D) 7800
(E) 8900
Rationale: The distance the sound traveled to the man is 20*330 = 6600 meters
The answer is C.
Answer: (C) 6600
Question: a school has 6 maths 5 physics and 5 chemistry teachers each teacher can teach 4 subjects max what is he minimum number of teachers required
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Total subjects = 6+5+5=16
Max subjects by 1 teacher = 4
So, min of teachers required = 16/4 = 4
ANSWER:B
Answer: (B) 4
Question: A person, who decided to go to weakened trip should not exceed 8 hours driving in a day. Average speed of forward journey is 40 m/h. Due to traffic in Sundays, the return journey average speed is 30 m/h. How far he can select a picnic spot?
(A) 120 miles
(B) between 120 and 140 miles
(C) 160 miles
(D) 180 miles
(E) 260 miles
Rationale: let dist travelled be 2x. hence destination is at dist x
x/40+x/30=8
x=137.14
ANSWER:B
Answer: (B) between 120 and 140 miles
Question: Taequan is playing a dice game where he rolls two, fair, six-sided dice twice. If he gets the same roll on his second try as his first, he wins. If he rolled an 8 on his first try, what is the probability that he will win with his second roll?
(A) 1/18
(B) 1/12
(C) 1/9
(D) 1/6
(E) 5/36
Rationale: There are 5 ways to roll an 8: 2 and 6, 6 and 2, 3 and 5, 5 and 3, 4 and 4 (4 and 4 is counted just once).
There are 6*6=36 ways to roll two six-sided dice.
The dice are fair, so the probability of rolling an 8 is 5/36.
E
Answer: (E) 5/36
Question: A thief is spotted by a policeman from a distance of 100 metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?
(A) 100 m
(B) 200 m
(C) 400 m
(D) 500 m
(E) 300 m
Rationale: Relative speed of the policeman = (10-8) km/hr =2 km/hr.
Time taken by police man to cover 100m
100/1000 x 1/2 hr = 1/20 hr.
In 1/20 hrs, the thief covers a distance of 8x 1/20km =2/5km = 400 m
ANSWER C
Answer: (C) 400 m
Question: Mangala completes a piece of work in 18 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is
(A) 6 days
(B) 7 days
(C) 15 days
(D) 9 days
(E) 11 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 18 Ã— 40/48 = 15 days.
C
Answer: (C) 15 days
Question: The average weight of 8 person's increases by 5 kg when a new person comes in place of one of them weighing 35 kg. What might be the weight of the new person?
(A) 80 kg
(B) 85 kg
(C) 75 kg
(D) 100 kg
(E) 110 kg
Rationale: Total weight increased = (8 x 5) kg = 40 kg.
Weight of new person = (35 + 40) kg = 75 kg.
Answer : C
Answer: (C) 75 kg
Question: What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
? ? ? ?
(A) 20 18 48 61
(B) 50 18 48 62
(C) 10 18 48 68
(D) 30 18 48 66
(E) 40 18 48 69
Rationale: D
30 18 48 66.
Starting at the top, add pairs of numbers in each column to arrive at the next number.
Answer: (D) 30 18 48 66
Question: A tradesman sold an article at a loss of 20%. If the selling price had been increased by $100, there would have been a gain of 5%. What was the cost price of the article ?
(A) $400
(B) $150
(C) $300
(D) $550
(E) $610
Rationale: Let C.P. be $x
Then 105% of x - 80% of x = 100
25% of x = 100
x/4 = 100
x = 400
Answer is A
Answer: (A) $400
Question: On January 1, 2011, James invests 80% of his retirement savings in Antarctic largecap stocks, 10% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2011, largecaps rise 10%, midcaps rise 10%, and smallcaps rise 20% in the Antarctic stock market; however, in 2012, largecaps fall 5% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2013,James has the same total amount of retirement savings as he did two years before, then x is between
(A) 10 and 20
(B) 20 and 30
(C) 30 and 40
(D) 40 and 50
(E) 50 and 60
Rationale: Pick a smart number for the total retirement savings James starts with—say, $1,000. (If you pick $100, you’ll wind up needing to track decimals, so give yourself more zeros to start with.)
Here are the starting values:
L = $800
M = $100
S = $100
Apply the first year’s changes, so that you have these numbers on 1/1/2012:
Newer L = $800 + 10% = $880
Newer M = $100 + 10% = $110
Newer S = $100 + 20% = $120
Now apply the second year’s changes to L and M:
Newest L = $880 – 5% = $880 – $44 = $836
Newest M = $110 – 10% = $110 – $11 = $99
Add these to get $935. So the newest S must be $1,000 (the target final total of James’s retirement savings) minus $935, $65
The dollar change in S from 1/1/12 to 1/1/13 is $120 – $55 = $65. So the question is this: what percent change does $65 represent, from a starting point of $120? Since $120 is a nasty divisor, switch to benchmarks:
20% of $120 = $24.
So 40% is just double that, or $48.
And 50% is equal to or $60.
From this $55 lies between $48 and $60
The correct answer is D.
Answer: (D) 40 and 50
Question: √{(3.5)(10^9)} is closest to which of the following?
(A) 60,000
(B) 75,000
(C) 140,000
(D) 220,000
(E) 250,000
Rationale: √{(3.5)(10^9)} = √{(35)(10^8)} = √(35)√(10^8) = (√35) * 10,000 which is almost 60,000.
The answer is A.
Answer: (A) 60,000
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2:5
(B) 2:7
(C) 4:3
(D) 2:4
(E) 2:9
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5
Answer:A
Answer: (A) 2:5
Question: A tank is filled by 3 pipes A,B,C in 5 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?
(A) 25hr
(B) 35hr
(C) 40hr
(D) 20hr
(E) 50hr
Rationale: Suppose pipe A alone take x hours to fill the tank
Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/5
7/x = 1/5
x = 35 hours
Answer is B
Answer: (B) 35hr
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 200 m
(B) 700 m
(C) 800 m
(D) 100 metre
(E) 1050 m
Rationale: Explanation:
A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: (D) 100 metre
Question: In a certain province in Russia there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
(A) 30
(B) 105
(C) 330
(D) 14!
(E) 15!
Rationale: Method-1:
Russia has Total Cities = 15 and each city should be connected with every other city
So Total Roads required to connect 1st City with other 14 cities = 14
Now 1st City is connected with all other cities so,
So Total Roads required to connect 2nd City with 13 cities (Other than 1st) = 13
Now 1st and 2nd Cities are connected with all other cities so,
So Total Roads required to connect 3rd City with 12 cities (Other than 1st, and 2nd) = 12
......and so on...
Total Roads required = 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105=B
Answer: (B) 105
Question: In an apartment building that has 441 units, 4 out of every 7 units are currently rented, including 1/5 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
(A) 45
(B) 70
(C) 100
(D) 105
(E) 140
Rationale: rented = 4/7*441 = 252.
Rented two-bedroom = 6/7*252 = 216;
Rented one-bedroom = 1/7*252 = 36or 252-216=36).
Rented one-bedroom units are 1/5 of all one-bedroom: 1/5*{All one bedroom} = 36 --> {All one-bedroom} = 180.
{All two-bedroom} = 441 - 180 = 261.
Two-bedroom not rented = 261 - 216 = 45.
Answer: A.
Answer: (A) 45
Question: How many minutes does it take Dhoni to type 64 words if he types at the rate of 16 words per minute?
(A) 10
(B) 15
(C) 12
(D) 16
(E) 14
Rationale: time*rate=job --> time*16=64 --> time=64/4=16.
Answer: D.
Answer: (D) 16
Question: A and B start walking towards each other at 6pm at speed of 6kmph and 4kmph. They were initially 50km apart. At what time do they meet?
(A) 8pm
(B) 6pm
(C) 11pm
(D) 10pm
(E) 5pm
Rationale: Time of meeting = distance / relative speed = 50/4+6 = 50/10 = 5 hrs after 6pm = 11pm
Answer is C
Answer: (C) 11pm
Question: Manoj borrowed Rs.4200 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?
(A) 22877
(B) 5855
(C) 2778
(D) 6787
(E) 1771
Rationale: Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 4200.3.6/100 = Rs.824.85
27P = 75600 = 82485
P = (82485 + 75600)/27 = 3055 + 2800 = Rs.5855
Answer: B
Answer: (B) 5855
Question: Find the remainder of the division (3^50)/7.
(A) 5
(B) 3
(C) 2
(D) 1
(E) 7
Rationale: Find the pattern of the remainders after each power:
(3^1)/7 remainder 3
(3^2)/7 remainder 2
(3^3)/7 remainder 6
(3^4)/7 remainder 4
(3^5)/7 remainder 5
(3^6)/7 remainder 1 -->this is where the cycle ends
(3^7)/7 remainder 3 -->this is where the cycle begins again
(3^8)/7 remainder 2
Continuing the pattern to (3^50)/7 gives us a remainder of 2
Final Answer:
C) 2
Answer: (C) 2