mathewhe/aqua_rat huggingface dataset:
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
(A) 338
(B) 2677
(C) 288
(D) 285
(E) 261
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = Rs. 285.
Answer: D
Answer: (D) 285
Question: A man purchases 2 watches for $ 900. He sells one at 10% loss and the other at a profit of 20%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
(A) $ 900 and $ 300
(B) $600 and $ 900
(C) $900 and $450
(D) $600 and $300
(E) $550 and $ 350
Rationale: x + y = 900 --- (1)
0.90x + 0.80y = 900--- (2)
(2) - (1) --> -.10x +.20y = 0
10x = 20y
x/y = 2/1 = (2*300)/(1*300) = 600/300
Answer: D
Answer: (D) $600 and $300
Question: If a man reduces the selling price of a fan from 400 to 380 his loss increases by 20% .What is the cost price of fan
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: increase in loss=20%
consider loss is x initially, so final loss will increase by .2x which is equal to 20.
.2x=20
x=100,
so total cost =selling price +loss=400+100=500.
so ans is 500.
ANSWER:C
Answer: (C) 500
Question: John and Steve are speed walkers in a race. John is 10 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?
(A) 13 seconds
(B) 17 seconds
(C) 24 seconds
(D) 34 seconds
(E) 51 seconds
Rationale: Let t be the time that John spent for his final push.
Thus, per the question,
4.2t = 3.7t+10+2 ---> 0.5t = 12 ---> t = 24 seconds.
C is the correct answer.
Answer: (C) 24 seconds
Question: The length of rectangle is thrice its breadth and its perimeter is 56 m, find the area of the rectangle?
(A) 432
(B) 252
(C) 299
(D) 276
(E) 111
Rationale: 2(3x + x) = 96
l = 36 b = 7
lb = 36 * 7
= 252
B
Answer: (B) 252
Question: There are different 5 circles. What is the number of the greatest possible points with which the circles intersect?
(A) 20
(B) 10
(C) 15
(D) 22
(E) 21
Rationale: Maximum points of intersection between n different circles = n*(n - 1) = 5*4 = 20
Answer: A
Answer: (A) 20
Question: The speed of a boat in still water is 10 km/hr. If it can travel 78 km downstream and 42 km upstream in the same time, the speed of the stream is
(A) 3 km/hr
(B) 12 km/hr
(C) 1.5 km/hr
(D) 4.4 km/hr
(E) None of these
Rationale: Explanation :
Let the speed of the stream be x km/hr. Then
Speed upstream = (10-x) km/hr
Speed downstream = (10+x) km/hr
Time taken to travel 78 km downstream = Time taken to travel 42 km upstream
=> 78/(10+x) = 42/(10−x)
=> 26/(10+x) = 14/(10−x)
=>13/(10+x) = 7/(10−x)
=>130 − 13x = 70 + 7x
=>20x = 60
=> x = 3 km/hr
Answer : Option A
Answer: (A) 3 km/hr
Question: Two cylindrical candles of the same height but different diameters are lit at the same time. The
first is consumed in 4 hours and the second in 3 hours. Assuming that they burn at a constant
rate, how long after being lit was the first candle twice the height of the second candle?
(A) 1 hr
(B) 1 hr 12 min
(C) 2 hr
(D) 2 hr 12 min
(E) 2 hr 24 min
Rationale: Assume each candle is 1 unit high. Since the burn rates are 1/3 and 1/4 units
per hour, after t hours they have been consumed by an amount of t/3 and t/4. We want
1- t=4 = 2(1 - t=3). This occurs when t = 2.4 = 2*24/60 hrs.
correct answer E
Answer: (E) 2 hr 24 min
Question: If m and n are positive integers and m^2 + n^2 = 20, what is the value of m^3 + n^3?
(A) 72
(B) 224
(C) 320
(D) 512
(E) 1,600
Rationale: You need to integers which squared are equal 20.
Which could it be ? Let's start with the first integer:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
Stop. The integers can't be greater than 4 or we will score above 20.
The second integer need to be picked up the same way.
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
The only pair that matches is 4^2 + 2^2 = 20.
So 4^3 + 2^3 = 72.
Answer A.)
Answer: (A) 72
Question: If 144/x is an integer and 72/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer.
(A) I, II, and III
(B) I and II only
(C) III only
(D) II and III only
(E) I only
Rationale: The largest possible value of x is 36 (the greatest common factor of 144 and 72), and if x=36 then
C
Answer: (C) III only
Question: There are 5 people and 5 chairs. In how many different ways people can occupy the chairs?
(A) 12
(B) 15
(C) 24
(D) 36
(E) 120
Rationale: number of ways =5! = 120
Answer is E
Answer: (E) 120
Question: Q. How many 4-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3?
(A) 180
(B) 240
(C) 210
(D) 270
(E) 300
Rationale: the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2
i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _
case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6
when the units digit is 2 i.e 1 _ _ _ _ _ 2
number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60
when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30
case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6)
number of ways this can be done would be 5! / (2!) for 2 =60
and 5! / 2! for 6 ... = 60
adding all of these ... gives the answer 300 ...
the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat
E
Answer: (E) 300
Question: There are 16 cans in the refrigerator. 9 of them are red and 7 of them are blue. In how many ways we can remove 10 cans so that at least one red and at least one blue cans to remain the refrigerator.
(A) 460
(B) 490
(C) 833
(D) 455
(E) 445
Rationale: Ways to pick 6 cans so that at least one red and at least one blue cans to remain the refrigerator =
total ways to pick 6 can out of 12 - ways to pick 6 red out of 7 red - ways to pick 6 blue out of 5 blue
12C6âˆ’9C6âˆ’7C6=924âˆ’84âˆ’7=833
ANSWER:C
Answer: (C) 833
Question: This is a famous probability puzzle in which you have to choose the correct answer at random from the four options below.
Can you tell us whats the probability of choosing correct answer in this random manner.
(A) 0%
(B) 2%
(C) 3%
(D) 6%
(E) 1%
Rationale: A
0%
Explanation:
1) why cant be 1/4 : If the answer is 1/4, then as we know two out of four answer choices is '1/4', the answer has be 1/2.
This is a contradiction, so the answer cannot be 1/4.
2) why cant be 1/2 : If the answer is 1/2 then because answer:"1/2" is 1 out of 4 answer choices, the answer must be 1/4. This is also a contradiction. So the answer cannot be 1/2.
3) why cant be 1 : If the answer is 1 then because answer:"1" is 1 out of 4 answer choices, the answer must be 1/4. Again the same contradiction and therefore answer cannot be 1.
Answer: (A) 0%
Question: If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a club or a red jack?
(A) 7/13
(B) 4/7
(C) 15/52
(D) 9/13
(E) 19/26
Rationale: There are 13 clubs and 2 red jacks.
P(club or red jack) = 15/52 = 15/52
The answer is C.
Answer: (C) 15/52
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
(A) Rs.429
(B) Rs.480
(C) Rs.429
(D) Rs.128
(E) Rs.419
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160
= Rs.480
Answer:B
Answer: (B) Rs.480
Question: The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was $11,500?
(A) $15,594
(B) $15,322.
(C) $14,786
(D) $14,543
(E) $12,988
Rationale: price of the car in 1990 = $11500
from 1990 to 1996
increase = 13%
which is (13*115)
price of the car in 1996= $12995
from 1996 to 2001
increase = 20 %
which is (12995)/5 =2599
price of the car in 2001 = 15594
ANSWER:A
Answer: (A) $15,594
Question: If a dealer wants to earn 20% profit on an article after offering 30% discount to the customer, by what percentage should he increase his marked price to arrive at the label price?
(A) 71 3/7%
(B) 50%
(C) 75%
(D) 60 2/3%
(E) 90%
Rationale: Profit = 20%
discount = 30%
Required answer = (20+30 / 100-30)*100 = 71 3/7 %
Answer is A
Answer: (A) 71 3/7%
Question: The area of a square is equal to five times the area of a rectangle of dimensions 36 cm * 20 cm. What is the perimeter of the square?
(A) 289 cm
(B) 800 cm
(C) 829 cm
(D) 240 cm
(E) 289 cm
Rationale: Area of the square = s * s
= 5(36 * 20)
=> s = 60
= 60 cm
Perimeter of the square
= 4 * 60
= 240 cm.
Answer: D
Answer: (D) 240 cm
Question: Three dwarves and three elves sit down in in the row of six chairs. If no dwarf will sit next to another dwarf and no elf will sit next to another elf, in how many different ways can the elves and dwarves sit.
(A) 72
(B) 74
(C) 76
(D) 78
(E) 80
Rationale: The elves and dwarves must alternate:
e d e d e d or d e d e d e
Considering the first case, the total number ways is to rotate the elves 3! times while keeping the dwarves to one combination. Then rotate the dwarves 3! times while keeping the elves to one combination.
However, that is only for the first case. We must multiply by 2 as we need to account for the second case.
Total = 3! * 3! * 2 = 72
ANS:A
Answer: (A) 72
Question: Find the value of x from the below equation? : 3x^2+6x+3 = 0
(A) -5/6
(B) 5/6
(C) 5
(D) 6
(E) 25
Rationale: a = 3, b = 6, c = 3
x1,2 = (-5 Â± âˆš(6^2 - 4Ã—3Ã—3)) / (2Ã—3) = (-5 Â± âˆš(36-36)) / 6 = (-5 Â± 0) / 6
x1 = X2 = -5/6
A
Answer: (A) -5/6
Question: You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Solution
Start with 11 coins.
Sharon takes 3 coins from you: 11 - 3 = 8 coins.
Steven takes 4 coins from you: 8 - 4 = 4 coins.
So you have 4 at the end.
Correct answer : C
Answer: (C) 4
Question: At night a man who is 6 feet tall stands 5 feet away from a lamppost. The lamppost’s lightbulb
is 16 feet above the ground. How long is the man’s shadow?
(A) 15/8 feet
(B) 3 feet
(C) 10/3 feet
(D) 4 feet
(E) 5 feet
Rationale: Let x be the length of the man’s shadow. Considering similar triangles we get
x/x + 5
=
6/16
correct answer C
Answer: (C) 10/3 feet
Question: At what price must an Book costing $47.50 be marked in order that after deducting 8% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 72.5
(B) 64.5
(C) 62.5
(D) 82.5
(E) 60.5
Rationale: C
$62.50
CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(92/100) = 59.375
MP = 64.5
B
Answer: (B) 64.5
Question: In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.55 sec
(B) 2.9 sec
(C) 1.3 sec
(D) 3.75 sec
(E) 1.8 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 100/40
= 3.75 sec.
Answer:D
Answer: (D) 3.75 sec
Question: A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 90 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally.
(A) 180
(B) 130
(C) 140
(D) 160
(E) 288
Rationale: White:Yellow = x:(x+90) = 8:13 --> 13x = 8x + 720 --> x = 144.
The total # of balls originally x + x = 144 + 144 = 288.
Answer: E.
Answer: (E) 288
Question: Find the value of sin 75° + sin 15° = ?
(A) 0
(B) 1/2
(C) 1
(D) 3/2
(E) 2
Rationale: sin A + sin B = 2 sin [ (A + B) / 2 ] cos [ (A - B) / 2 ]
=2 sin [ (75 +15) / 2 ] cos [ (75 - 15) / 2 ]
=2 sin90cos60=2*1*(1/2)=1
ANSWER:C
Answer: (C) 1
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share?
(A) 15
(B) 18
(C) 12
(D) 17
(E) 20
Rationale: Face value of each share = Rs.20
Dividend per share = 9% of 20 = 9×20/100=9/5
He needs to have an interest of 12% on his money
ie, Money Paid for a share×12/100=9/5
Money Paid for a share=9/5×100/12=15
ie, Market Value of the share = Rs.15
Answer is A.
Answer: (A) 15
Question: Which of the following cannot be the sum of 4 different prime numbers?
(A) 21
(B) 17
(C) 29
(D) 32
(E) 30
Rationale: Option A: 21 = 2+3+5+11. Sum of 4 different prime numbers
Option B: 17 = 2+3+5+7. Sum of 4 different prime numbers
Option C: 29 = 2+3+7+17. sum of 4 different prime numbers
Option D: 32 = 5+3+11+13. Sum of 4 different prime numbers
Option E: 30 = This is not a Sum of 4 different prime numbers
Correct Option:E
Answer: (E) 30
Question: What is the distance from (–7, 2) to (5, –3)?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: solutions
Suppose we made a right triangle, as in the example above. The difference in the x-coordinates is (–7) – 5 = –12, so the horizontal leg would have a length of 12 (length has to be positive). The difference in the y-coordinates is 2 – (–3) = 5, so this is the length of the vertical leg. We recognize that we have a common Pythagorean triplet, so we don’t even need to perform a calculation: we know the length of the hypotenuse, and hence, the distance between the two points, is 13. Answer = D
Answer: (D) 13
Question: A large box contains 20 small boxes and each small box contains 32 chocolate bars. How many chocolate bars are in the large box?
(A) A)220
(B) B)490
(C) C)380
(D) D)450
(E) E)640
Rationale: the only thing you have to do is a simple multiply
we have:
20*32
=640
correct answer is:
E) 640
Answer: (E) E)640
Question: In an athletic event with N participants, if 1/5 could not complete 100 meter race within cut off time of 10 seconds. And of those who didnt clear 100 meter race within cut off time, 1/3 also did not qualify in long jump. How many athletes cleared both events ?
(A) N/15
(B) 4N/15
(C) 14N/15
(D) N/5
(E) 4N/5
Rationale: 1/5 did not clear running event, thus N/5 did not clear.
Of those who didnt clear running event, 1/3 also did not clear long jump event, thus 1/3*N/5 = N/15 had both not cleared both events.
Therefore, N - N/15 = 14N/15 cleared both events.
Answer: C.
Answer: (C) 14N/15
Question: Simple question but big one on average age.sth like a, b, c weighted separately 1st a, b, c ,then a& b, then b &c then c & a at last abc, the last weight was 167,then what will be the average weight of the 7 reading?
(A) 32
(B) 92
(C) 94
(D) 95
(E) 100
Rationale: avg=A+B+C+(A+B)+(B+C)+(C+A)+(A+B+C)/7
Now,4A+4B+4C/7
=4(167)/7 (GIVEN ABC=167)
=95.43
ANSWER:D
Answer: (D) 95
Question: How many prime numbers n exist such that 90 < n < 106 and n is a factor of 99999919?
(A) Zero
(B) One
(C) Two
(D) Three
(E) More than three
Rationale: There are 3 primes in the range: 97, 101 and 103.
99,999,919=10^8−81=(10^4+9)(10^4−9)
=(10^4+9)(10^2+3)(10^2−3)
=10,009∗10^3∗97
97 and 103 are factors of 99,999,919 but 101 is not a factor of 10,009. Thus 2 primes from the range are factors of 99,999,919.
Answer: C.
Answer: (C) Two
Question: In an election between the two candidates ,The candidates who gets 60% of votes polled is winned by 280 votes majority. What is the total number of votes polled?
(A) 1400
(B) 1600
(C) 1800
(D) 2000
(E) 2100
Rationale: Note : majority (20 %) = difference in votes polled to win (60 %) & defeated candidates (40 %)
20 % = 60 % - 40 %
20% -----> 280 (20×14 = 280 )
100% -----> 1400 (100×14 = 1400)
A)
Answer: (A) 1400
Question: A can complete a work in 15days and B can do the same work in 7days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work?
(A) 2days
(B) 5 1/2 days
(C) 6 1/2 days
(D) 7 1/2days
(E) 10days
Rationale: The required answer = (15-3)*7 / 15 = 84/15 = 5 1/2 days
Answer is B
Answer: (B) 5 1/2 days
Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is
(A) 8
(B) 9
(C) 13
(D) 15
(E) 17
Rationale: Solution
Let the three numbers be x, x+2, x+4
Then 3x = 2(x+4) + 3
‹=›x = 11
Third integer = x + 4 = 15.
Answer D
Answer: (D) 15
Question: A customer went to a shop and paid a total of $40, out of which $1.28 was for sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items?
(A) $19.54
(B) $2076
(C) $21.36
(D) $22.72
(E) $23.58
Rationale: The total cost was $40.
The tax was $1.28
Let the original price of the taxable items = x
Given that tax rate = 8%
0.08x = 1.28
x = $16
The cost of the tax free items was $40 - $16 - $1.28 = $22.72
The answer is D.
Answer: (D) $22.72
Question: If |x^2 − 6| = x, which of the following could be the value of x?
(A) –3
(B) –2
(C) 0
(D) 1
(E) 2
Rationale: The LHS is not negative, so the RHS is also not negative. Thus x >= 0.
First, let's assume that x^2-6 is negative.
-(x^2 - 6) = x
x^2 + x - 6 = 0
(x+3)(x-2) = 0
x = 2 or x = -3 (However, x can not be negative.)
Then x=2 is a possible value for x.
The answer is E.
Answer: (E) 2
Question: The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (g) around the mirror, which of the following could be the value, in inches, of g ?
I. 2
II. 3 1/2
III. 5
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
Rationale: Area of picture = 16x Area of frame = 33x
Area of picture / (Area of picture + area of frame) = 16x / 49x = 4x/7x.
This results in g value to be a multiple of 1.5 = multiple of 3/2 and since g is not constrained to be only integer all the three choices are possible
For i) the multiple of g is 4/3
For ii) the multiple of g is 7/3
For iii) the multiple of g is 10/3
The key is g can be any real positive number... very tricky problem.. took me > 15 minutes.
Answer is E
Answer: (E) I, II, and III
Question: A reduction of 46% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) 2.45
(B) 8.45
(C) 7.45
(D) 3.45
(E) 1.45
Rationale: Explanation:
40*(46/100) = 18.4 --- 64
? --- 12 => Rs.3.45
Answer: D
Answer: (D) 3.45
Question: If the cost price of 58 articles is equal to the selling price of 50 articles, then what is the percent profit?
(A) 12%
(B) 16%
(C) 20%
(D) 24%
(E) 28%
Rationale: Let x be the cost price of one article.
Let y be the selling price of one article.
50y = 58x
y = 1.16x
The answer is B.
Answer: (B) 16%
Question: When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 727 more than 4times the middle integer. Find the numbers?
(A) 650
(B) 678
(C) 727
(D) 710
(E) 729
Rationale: x + 4 (x + 4) = 727 + 4 (x + 2)
Solve for x and find all three numbers
x + 4 x + 16 = 727 + 4 x + 8
x = 719
x + 2 = 721
x + 4 = 723
Check: the smallest is added to four times the largest
719 + 4 * 723 = 3611
four times the middle
4 * 721 = 2884
3611 is more than 2884 by
3611 - 2884 = 727
C
Answer: (C) 727
Question: Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?
(A) 90 sec
(B) 30 sec
(C) 10 sec
(D) 70 sec
(E) 30 sec
Rationale: Let the length of each train be x m.
(x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5) = 90 sec.
Answer:A
Answer: (A) 90 sec
Question: For a certain article, if discount is 25%, the profit is 25%. If the discount is 10%, then the profit is
(A) 10%
(B) 20%
(C) 35%
(D) 50%
(E) None of these
Rationale: For same article, 100−d1/100−d2=100+g1/100+g2
⇒ 100−25/100−10=100+25/100+g2 ⇒75/90=125/100+g2
⇒ 100 + g2 = 90×125/75 =150 ⇒ g2 = 50%
Answer D
Answer: (D) 50%
Question: The sum of first five prime numbers is?
(A) 11
(B) 18
(C) 26
(D) 28
(E) None
Rationale: Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
A)
Answer: (A) 11
Question: If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 2000 papers and 20% discount after first 10000 papers, how much will it cost to buy 45000 sheets of xerox paper?
(A) $1250
(B) $1060
(C) $1350
(D) $900
(E) $2100
Rationale: 30 sec approach - solve it using approximation
45000 sheet at full price, 5 cent = 2250
45000 sheet at max discount price, 4 cent = 2000
Your ans got to be between these two.
Ans E it is.
Answer: (E) $2100
Question: The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?
(A) 248
(B) 240
(C) 228
(D) 236
(E) 246
Rationale: Let the five consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) and 2(x + 2)
Their sum = 10x = 440
x = 44 => 2(x - 2) = 84
Second least number of the other set = 2(84) - 121 = 47
This set has its least number as 46.
Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50
= 48 - 2 + 48 - 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240
ANSWER:B
Answer: (B) 240
Question: A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 6, what is the smallest possible total number of tokens in the jar?
(A)  9
(B)  12
(C)  15
(D)  18
(E)  21
Rationale: (Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)
i.e. Red*White = Blue*Total Coins
Let, Red = 3a
White = 3b
Blue = 3c
Total Coins = 3(a+b+c)
i.e. 3a * 3b = 3c*3(a+b+c)
i.e. a*b = c*(a+b+c)
For smallest values of a, b and c
2*3 = 1*(1+2+3)
i.e. Minimum Total Coins = 3*(1+2+3) = 21
Answer: Option E
Answer: (E)  21
Question: A coin is tossed seven times. What is the probability that there is at the least one tail?
(A) 127/128
(B) 31/138
(C) 31/167
(D) 31/117
(E) 31/128
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed seven times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/128 ; P(T) = 1 - 1/128
= 127/128
Answer: A
Answer: (A) 127/128
Question: A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 10 seconds. Find the length of the train and its speed.
(A) 10 m/sec
(B) 15 m/sec
(C) 18 m/sec
(D) 19 m/sec
(E) 25 m/sec
Rationale: If length of train is l and speed of train is s, then
l/s = 10
(l+180)/s = 20
(l+180)/l = 20/10 =2
l+180 =2l
l= 180
l=180 mtrs
s= l/10 = 180/8 = 10 m/sec
ANSWER:A
Answer: (A) 10 m/sec
Question: If m and n are whole numbers such that
mn=121
, the value of
(m−1)n+1 is
(A) 1
(B) 10
(C) 100
(D) 1000
(E) None of these
Rationale: Explanation:
We know that
(11)2=121
So, putting values in said equation we get,
(11−1)2+1=(10)3=1000
Option D
Answer: (D) 1000
Question: In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what A percentage of those asked favoured more than one of the 3 proposals.
(A)  10
(B)  12
(C)  17
(D)  22
(E)  30
Rationale: Bunuel, my answer for exactly 2 people was 17 and this was my approach:
100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to
A=100%=(50+30+20)-(at least 2 people)-5%+22%.C
Answer: (C)  17
Question: In the first 12 overs of a one day cricket game, the run rate was only 3 What should be the run rate in the remaining 38 overs of a one day match to reach the target of 282 runs?
(A) 4.47
(B) 5.47
(C) 6.14
(D) 6.47
(E) 6.84
Rationale: Runs scored in the first 12 overs = 12 × 3 = 36
Total runs = 282
Remaining runs to be scored = 282 - 36 = 246
Remaining overs = 38
Run rate needed = 246/38
=6.47
ANSWER:D
Answer: (D) 6.47