mathewhe/aqua_rat huggingface dataset:
Question: John tossed a fair coin 3 times. What is the probability that the outcome was “tails” exactly twice?
(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 9/10
Rationale: Total number of outcomes = 2*2*2 = 8
Number of favorable outcomes = Number of ways two places (for tails) can be chosen out of 3 slots = 3C2 = 3
So probability = 3/8
Alternative
Probability of getting tail in single toss = 1/2
Probability of getting head in single toss = 1/2
Probability of getting First Tail = 1/2
Probability of getting Second tail (Such that first tail has occurred, this incidentally is also the probability when first was head and second is tail) = 1/2 * 1/2 = 1/4
Probability of getting Third Head ( such that first was tail and second was tail) = 1/2 * 1/2 * 12 = 1/8
As you can notice the probability will be 1/8 whatever the sequence of Heads and tails.
We can arrange 2 Tails and one head in 3 ways (3C2 ways OR (3P3)/2! OR enumeration, whichever method you prefer to get here)
Since the favorable even can happen in either of these 3 ways, so Probability = 3 * 1/8 = 3/8
Answer:C
Answer: (C) 3/8
Question: A machine can filled a tank in 25 minutes and another machine can empty it in 50 minutes. If the tank is already half full and both the taps are opened together, then the tank is filled in how many minutes?
(A) 25min
(B) 20min
(C) 10min
(D) 15min
(E) 30min
Rationale: T = 1/2 (25*50 / 50-25) = 25 minutes
Tank is filled in 25 minutes
Answer is A
Answer: (A) 25min
Question: A train running at the speed of 60 km/hr crosses a pole in 15 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 324 metres
(D) 250 metres
(E) 180 metres
Rationale: Speed=(60 x 5/18)/m/sec	=	50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50 x 15/3 m = 250 m.
ANSWER : OPTION D
Answer: (D) 250 metres
Question: A committee of 5 is to be selected from among 5 boys and 4 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?
what is the answer choice and how?
(A) 105
(B) 225
(C) 209
(D) 350
(E) 455
Rationale: I'm sure there is some problem with the question.
R U sure its atleast one boy and not atleast 1 boy and 1 girl?
if its 1 boy and 1 girl
6C1*4C1 + 6C2*4C2 + 6C3*4C3 + 6C4*4C4
6*4 + 15*6 + 20*4 + 15*1
24 + 90 + 80 + 15
209
C
Answer: (C) 209
Question: In a class of 39 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: 26 + 20 - 17 = 29
39 - 29 = 10 play neither
Answer is C
Answer: (C) 10
Question: The average of first 12 even numbers is?
(A) 19
(B) 18
(C) 16
(D) 13
(E) 17
Rationale: Sum of 12 even numbers = 12 * 13 = 156
Average = 156/12 = 13
Answer:D
Answer: (D) 13
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 28%
(B) 25%
(C) 23%
(D) 45%
(E) 15%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: B
Answer: (B) 25%
Question: A certain telescope increases the visual range at a particular location from 50 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ?
(A)  30%
(B)  33 1/2%
(C)  40%
(D)  60%
(E)  200%
Rationale: Original visual range = 50 km
New visual range = 150 km
Percent increase in the visual range by using the telescope
= (150-50)/50 * 100%
= 2 * 100%
= 200 %
Answer E
Answer: (E)  200%
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 60,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
(A) 70,000
(B) 60,000
(C) 128,000
(D) 90,000
(E) 10,000
Rationale: The distance traveled by each tyre:
4/5 * 1, 60, 000km = 128,000 km. C
Answer: (C) 128,000
Question: A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much
(A) 0.60 loss
(B) 0.70 loss
(C) 0.80 loss
(D) 0.50 loss
(E) 0.40 loss
Rationale: CP when profit of 25% = 12.8
CP when loss of 20% = 20
Total CP = 32.8
Total SP = 32.00
Total loss = 0.80
ANSWER:C
Answer: (C) 0.80 loss
Question: If PINTU is coded as 79523 in a certain code language, how would you code MINTU in the same language?
(A) 13426
(B) 14236
(C) 49523
(D) 14263
(E) 15263
Rationale: 1 2 3 4 5 6 7 8 9
a b c d e f g h i
j k l m n o p q r
s t u v w x y z
sooo...MINTU is 49523...
ANSWER:C
Answer: (C) 49523
Question: 14 men make 1400 toy in 5 days 1 day after work 14 more worker join now how may days work can finish
(A) 1 day
(B) 2 days
(C) 3 days
(D) 4 days
(E) 5 days
Rationale: 14 men make toy in 5 days
after 1 day 14 more worker join
m1/m2=d2/d1
14/28=d2/4
=2 day
ANSWER:B
Answer: (B) 2 days
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 61 unique alphanumeric case sensitive characters.
(A) 63^4
(B) 62^5
(C) 62(61^4)
(D) 63(62^4)
(E) 63(62^6)
Rationale: Total number of passwords = number of 4 character password +number of 5 character password
= 61^4 + 61^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )
=61^4(1+ 61)
=61^4 * 62
Answer C
Answer: (C) 62(61^4)
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 18.23%
(D) 19%
(E) 19.12%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: (B) 16.66%
Question: John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $50. What is the percent decrease?
(A) 20%
(B) 30%
(C) 50%
(D) 70%
(E) 80%
Rationale: The is always the difference between our starting and ending points. In this case, it’s 100 – 50 = 50. The “original” is our starting point; in this case, it’s 100. (50/100)*100 = (0.5)*100 = 50%.
C
Answer: (C) 50%
Question: Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.4500. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?
(A) Rs.750, Rs.2250
(B) Rs.2000, Rs.750
(C) Rs.750, Rs.2000
(D) Rs.800, Rs.1250
(E) Rs.900, Rs.1250
Rationale: Minu’s one day’s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18
Anu’s wages: Binu’s wages: Minu’s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2
Minu’s share = Rs.4500* 2/12 = Rs.750
Anu’s share = Rs.4500* 6 /12 = Rs.2250
ANSWER:A
Answer: (A) Rs.750, Rs.2250
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 55 kmph when will the owner over take the thief from the start?
(A) A)1.33
(B) B)5
(C) C)7
(D) D)5
(E) E)8
Rationale: Explanation:
|-----------20--------------------|
55 40
D = 20
RS = 55 – 40 = 15
T = 20/15 = 1.33 hours
Answer: Option A
Answer: (A) A)1.33
Question: Ed and Flora drive at constant speeds toward each other on a highway. Ed drives at a constant speed of 31 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Ed is 120 km away from Flora at 6 am, and also 120 km away from Flora at 11 am, then how fast is Flora driving (in kilometers per hour)?
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: Ed and Flora complete 240 km / 5 hours = 48 km/hour
Flora's speed is 48-31=17 km/hour
The answer is C.
Answer: (C) 17
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
(A) 4 hrs 29 min
(B) 4 hrs 24 min
(C) 8 hrs 24 min
(D) 4 hrs 44 min
(E) 5 hrs 24 min
Rationale: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
Answer:B
Answer: (B) 4 hrs 24 min
Question: The area of the largest circle that can be drawn inside a square of side 98 Cm in length is:
(A) 8600
(B) 3646
(C) 7546
(D) 7636
(E) 1606
Rationale: Radius of required circle = 49 Cm
its area = 22/7 × 49 × 49
154 × 49 = 7546 Cm(power)2
Answer is C.
Answer: (C) 7546
Question: SI on a sum of money for 2yrs at 5% per annum is Rs.50, what is the CI on the same at the same rate & for the same time?
(A) Rs. 34.24
(B) Rs. 41.25
(C) Rs. 51.25
(D) Rs. 59
(E) Rs. 65
Rationale: Sum = Rs. 50 x 100 = Rs. 500.
2 x 5
Amount
= Rs. 500 x 1 +	5 2
100
= Rs. 500 x	21	x	21
20	20
= Rs. 551.25
C.I. = Rs. (551.25 - 500) = Rs. 51.25
C
Answer: (C) Rs. 51.25
Question: A bowl contains many kinds of fruit. In the bowl there are twice as many pears then there are oranges, and twice times as many plums as oranges. If the total number of pieces of fruit is X, then how many oranges are in the bowl as a fraction of X
(A) X/2
(B) X/3
(C) X/4
(D) X/5
(E) X/6
Rationale: Since X equals the number of fruit, X = pears + oranges + plums.
Since there are twice as many pears as oranges, then pears = 2*oranges.
Since there are twice as many plums as oranges, then plums = 2*oranges
Hence X = 2*oranges + oranges + 2*oranges, which simplifies to X = 5*oranges
Thus Oranges = X/5
Answer: D
Answer: (D) X/5
Question: man walks at speed of 8 km/h 300 mtrs length train crosses man in 30 sec from back, find speed of train?
(A) 40 km/hr
(B) 44 km/hr
(C) 42 km/hr
(D) 43 km/hr
(E) 45 km/hr
Rationale: if speed of train is x kmph, then
relative speed =(x-8 ) km/hr = (x-8)*5/18 m/sec
(x-8)*(5/18)*30=300
x-8=36
x= 44 km/hr
ANSWER:B
Answer: (B) 44 km/hr
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high ?
(A) 13m
(B) 14m
(C) 15m
(D) 16m
(E) NONE OF THESE
Rationale: Explanation:
the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high is
=> mts.
ANSWER IS A
Answer: (A) 13m
Question: Beginning in Town A, Biker Bob rides his bike 20 miles west, 6 miles north, 10 miles east, and then 18 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)
(A) 28 miles
(B) 30 miles
(C) 26 miles
(D) 18 miles
(E) 22 miles
Rationale: Using Pythagoras we have one side i,e total distance traveled in north direction = 18+6=24m
other being the base ie distance traveled west- distance traveled eat=20-10=10 m
now this third side or the distance between town A and Town B=24^2+ 10^2=sq root 676=26m
Answer : C
Answer: (C) 26 miles
Question: A sum of money lent out at S.I. amounts to Rs. 710 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
(A) s.440
(B) s. 586
(C) s. 540
(D) s. 740
(E) s. 840
Rationale: S.I for 5 years = (1020 - 710) = Rs. 310.
S.I. for 2 years = 310/5 * 2 = Rs. 124.
Principal = (710 - 124) = Rs. 586.
ANSWER:B
Answer: (B) s. 586
Question: Which of the following fractions is greater than 2/3?
(A) 1. 12/50
(B) 2. 3/11
(C) 3. 2/9
(D) 4. 4/17
(E) 5. 6/24
Rationale: 1. 12/50
12.5/50 = 1/4 thus 12/50 < 1/4
2. 3/11
3/12 = 1/4 thus 3/11 > 1/4
3. 2/9
2/8 = 1/4 thus 2/9 < 1/4
4. 4/17
4/16 = 1/4 thus 4/17 < 1/4
5. 6/24
6/24 = 1/4
C
Answer: (C) 3. 2/9
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
A. 20 B. 54
(A) 20
(B) 27
(C) 28
(D) 22
(E) 27
Rationale: There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee
= ⁶C₃ = (6 * 5 * 4)/6
= 20.
Answer:A
Answer: (A) 20
Question: Two numbers are respectively 40% and 60% more than a third number. What percentage is the first of the second?
(A) 72%
(B) 87.5%
(C) 63.7%
(D) 56.9%
(E) 90%
Rationale: Required answer = (100+x)/(100+y)*100 = 140*100/160 = 87.5%
Answer is B
Answer: (B) 87.5%
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
(A) 12
(B) 24
(C) C is elder than A
(D) Data inadequate
(E) None
Rationale: Solution
[(A+B) - (B+C)]	= 12
‹=›A - C
= 12.
Answer A
Answer: (A) 12
Question: Find a sum for first 7 prime numbers?
(A) 22
(B) 58
(C) 29
(D) 32
(E) 34
Rationale: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17) = 58
Note: 1 is not a prime number
Option B
Answer: (B) 58
Question: Set Q consists of the following five numbers: Q = {5, 8, 11, 21, 34}. Which of the following sets has the same standard deviation as Set Q?
I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75}
(A)  I only
(B)  III
(C)  IIII
(D)  IIIII
(E)  I, II,III
Rationale: (1)	Multiplying all the numbers change Standard Deviation
(2)	Adding and subtracting all the numbers with the same number keeps the standard deviation same.
If you observe Set I and III are added versions of Set Q .
Set I: 5 has been added to the Set Q
Set III: Subtract each element from 80 and you would find a number there in the Set Q.
Set II: elements are multiplied by 2 and standard deviation changes.
Hence the answer is D.
Answer: (D)  IIIII
Question: A number when divided by a divisor leaves a remainder of 25. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 12
(B) 13
(C) 35
(D) 38
(E) 59
Rationale: Let the number is N, the divisor = D,
I will make the two equations-
N = xD+25
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 38
as D is also integer and 38 is a prime number, the D should be 38 to satisfy the above equation.
Hence answer is 'D'
Answer: (D) 38
Question: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 4/7 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
(A) 0
(B) 1/15
(C) 2/15
(D) 1/20
(E) 2/10
Rationale: Suppose the water in each jug is L liters
CX x (1/5) = L
CX = 5L liters
CX is capacity of X
CY x (4/7) = L
CY = 7L/4 liters
CY is capacity of Y
Now, Y is 7L/4 - L empty = 3L/4 empty
So, we can put only 3L/4 water in jug Y from Jug X
Jug X's remaining water = L - 3L/4 = L/4
Fraction of X which contains water = water / CX
= (L/4)/ 5L
= 1/20
Answer will be D
Answer: (D) 1/20
Question: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?
(A) 700
(B) 721
(C) 702
(D) 703
(E) None of the above
Rationale: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.
Answer B
Answer: (B) 721
Question: The area of a triangle is with base 4m and height 5m?
(A) 11
(B) 10
(C) 787
(D) 122
(E) 12
Rationale: 1/2 * 4 * 5 = 10 m2
Answer: B
Answer: (B) 10
Question: If a and b are positive integers such that a/b = 1.92, which of the following must be a divisor of a?
(A) 19
(B) 13
(C) 9
(D) 8
(E) 15
Rationale: 1) A and B are positive INTEGERS
2) A/B = 1.92
A = 192
B = 100
192/100 = 1.92
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 96
B = 50
96/50 = 1.92
Dividing by 2 again:
48/25 = 1.92
There is no other way to reduce this fraction, so A must be a multiple of 48 and B must be an equivalent multiple of 25. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 48, we have to 'factor-down' 48. This gives us (6)(8). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Answer: C
Answer: (C) 9
Question: If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 28, 19, 33 and 35 ?
(A) 33
(B) 25
(C) 27
(D) 24
(E) 23
Rationale: It is given that a quartile is the middle number of all numbers less than median..
so lets arrange the number in ascending order- 42, 24, 30, 22, 28, 19, 33 and 35
19, 22, 24, 28, 30 , 33, 35, 42...
numbers less than median are 19, 22, 24, 28..
the median of these numbers = center of 22 and 24 = 23
E
Answer: (E) 23
Question: A car travels at a speed of 65 miles per hour. How far will it travel in 9 hours?
(A) 125 miles
(B) 225 miles
(C) 585 miles
(D) 425 miles
(E) 525 miles
Rationale: During each hour, the car travels 65 miles. For 9 hours it will travel
65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65= 9 × 65 = 585 miles
correct answer is C) 585 miles
Answer: (C) 585 miles
Question: 100 liter solution of cool-drink is made from 10% jasmine water. If 5 liters of jasmine and 10 liters of water were added to the solution, what percent of the solution is jasmine?
(A) 1/13
(B) 2/23
(C) 3/31
(D) 4/15
(E) 2/3
Rationale: Denominator
100+5+10
115
Numerator
100*0.1=10--->Jasmine water
10+5=15--->New content of Jasmine water in new solution
Ratio
3/23
Answer is B
Answer: (B) 2/23
Question: Which of these expressions has the greatest value?
(A) 1532672/1532676
(B) 1423765/1423769
(C) 1215672/1205679
(D) 1823561/1823566
(E) 1237842/1788545
Rationale: Using elimination method on options
1215672/1205679 = 1.00828827574...
ANSWER:B
Answer: (B) 1423765/1423769
Question: The product of two successive numbers is 7832. Which is the smaller of the two numbers?
(A) 78
(B) 68
(C) 88
(D) 97
(E) 37
Rationale: C
88
From the given alternatives,
88 × 89 = 7832
∴ Smaller number = 88
Answer: (C) 88
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
(A) 233 1/6
(B) 833 1/3
(C) 833 1/9
(D) 833 1/6
(E) 833 1/2
Rationale: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer: B
Answer: (B) 833 1/3
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 27 km
(B) 26 km
(C) 60 km
(D) 28 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1)
= 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40
= 9/2 => x = 20 km.
Answer:E
Answer: (E) 20 km
Question: 0, 2, 4, 8, 12, 18, 24, 32, ?What number should replace the question mark?
(A) 24
(B) 20
(C) 40
(D) 26
(E) 47
Rationale: C 40add 2, 2, 4, 4,6, 6,.....
Answer: (C) 40
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
The sum of the first 55 positive even integers is 2550. What is the sum of the even integers from 108 to 200 inclusive?
(A) 5,100
(B) 8,085
(C) 10,100
(D) 15,500
(E) 20,100
Rationale: even numbers from 94 to 200=108/2+1=55
Sum= (200+94)x55/2=8085
So B is the ans
Answer: (B) 8,085
Question: If T= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + ......... 1/[n(n+1)], for some positive integer n, what is the smallest value of n such that T>0,97?
(A) 29
(B) 30
(C) 31
(D) 32
(E) 33
Rationale: we can break the T as : (n + 1 -n)/n(n+1)----for n=1 to n
1/n - 1/ n + 1
plug value ,1,2..n we will get a pattern
1-1/2---for 1
1/2-1/3--for 2
1/3-1/4--for 4
now work with options..
for 31,T =1- 1/32=30/31=0.968
for 32,T=1-1/33=0,9696
for 33,T=1-1/34=33/34-0.97
so E is correct answer
Answer: (E) 33
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car?
(A) 277
(B) 266
(C) 960
(D) 77
(E) 211
Rationale: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km
AnswerC
Answer: (C) 960
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 76 kmph
(C) 12 kmph
(D) 97 kmph
(E) 15 kmph
Rationale: Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer:A
Answer: (A) 10 kmph
Question: In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate?
(A) 358000
(B) 368000
(C) 357000
(D) 358000
(E) 367000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 75 %
Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 357000
Answer:C
Answer: (C) 357000
Question: The product of two numbers a and b equals one-quarter their average. What is a in terms of b?
(A) a= b/(8b-1)
(B) a= b/(7b-1)
(C) a= b/(8b)
(D) a= b/(8b-4)
(E) a= 2b/(8b-1)
Rationale: a*b = ( a+b)/8
8ab =a+b
a= b/(8b-1)
ANSWER:A
Answer: (A) a= b/(8b-1)
Question: How many different positive integers are factors of 40?
(A) 3
(B) 2
(C) 1
(D) 6
(E) 4
Rationale: 2*20
4*10
8*5
Answer : D
Answer: (D) 6
Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 91, the three numbers in order are?
(A) 39, 78, and 156
(B) 39, 156, and 78
(C) 78, 39, and 156
(D) 78, 156, and 39
(E) 156, 39, and 78
Rationale: Let the numbers be 2x, x and 4x
(2x + x + 4x)/3 = 91
7x/3 = 91
x = 39
The numbers in order are 78, 39, and 156
The answer is C.
Answer: (C) 78, 39, and 156
Question: If |x – 9/2| = 5/2, and if y is the median of a set of r consecutive integers, where r is odd, which of the following must be true?
I. xyr is odd
II. xy(r^2 + r) is even
III. x^2y^2r^2 is even
(A) II only is true
(B) III only is true
(C) I and III
(D) II and III
(E) I, II, and III
Rationale: given:
r is Odd
y is the median of odd numbers, hence y is Odd
x = solving the modulus you get 7 and 2. Hence x is Even or Odd
Therefore: r = O, y = O and x = O or E
Statement I = x*y*r = y*r*x = O x O x O/E = O x O/E = Odd or even. So False
Statement II = xy(r^2 + r) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true
Statement III. x^2y^2r^2 is even. E/O x O x O = Odd or even. Hence False.
Answer = A.
Answer: (A) II only is true
Question: How many seconds will a train 200 meters long running at the rate of 36kmph take to pass a certain telegraph post?
(A) 10sec
(B) 20sec
(C) 25sec
(D) 30sec
(E) 35sec
Rationale: Distance = length of train = 200meters
Speed = 36kmph = 36*5/18 = 10m/s
Required time = 200/10 = 20sec
Answer is B
Answer: (B) 20sec
Question: A machine, working at a constant rate, manufactures 18 pens in 30 minutes. How many pens does it make in 1 hr 45 min?
(A) 63
(B) 65
(C) 62
(D) 60
(E) 45
Rationale: Change 1 hr 45 min to 105 min. For this, we need to set up a simple proportion of pens per time
18/30= S/105
The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. Instead, cancel before you multiply. For what we can see this post. We can cancel 18/30 as 6/10
6/10= S/105
we can cross-multiply.
10*S = 6*105 = 630
If we divide both sides by 10,
S = 63
The machine would be 63 pens in 1 hr 45 min.
Answer: A
Answer: (A) 63