mathewhe/aqua_rat huggingface dataset:
Question: We have 36kg flour and 60kg sugar in stock and we would like to use the minimum number of packs that would have the same weight for both flour and sugar. How much more sugar is required if we would like to full 10 packs either of flour or sugar?
(A) 12
(B) 18
(C) 20
(D) 24
(E) 30
Rationale: k is the integer that represents kg of pack
ak = 36 --> k = 36/a
bk = 60 --> k = 60/b
36/a = 60/b --> 5a = 3b and then k=12 for min(a+b)
a=36/12=3 , b=60/12=5
Total number of packs = 3+5 = 8
10-8=2 packs more required
2 *12 = 24 kg more sugar required to have 10 packs.
ANSWER: D
Answer: (D) 24
Question: You are visiting your friend. When you walk in her room, you find that there are seven girls. Each of the seven girls have seven bags which consist of 7 adult cats each. Now, each of the adult cat has seven little cats as well along with them.
We know that each cat has four legs, can you find out the total number of legs in the room?
(A) 26197
(B) 23578
(C) 10992
(D) 14728
(E) 11092
Rationale: C
10992
Each girl has seven bags with seven adult cats each.
Also, each adult cat has seven little cats.
Thus each girl has 49 adult cats and 343 little cats.
Hence, seven girls will have
343 adult cats and 2410 little cats.
If we calculate the number of legs now.
Girls = 7 * 2 = 14
Cats + Little cats = 2744 * 4 = 10976
Total legs = 10976 + 14 = 10990
Since I also walked in the room, there will be two more legs.
Now total legs = 10990 + 2 = 10992.
Answer: (C) 10992
Question: A and B together have Sterling 1260. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
(A) Sterling 460
(B) Sterling 484
(C) Sterling 550
(D) Sterling 504
(E) None
Rationale: Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1260 x 2/5) = Sterling 504.
Answer: Option D
Answer: (D) Sterling 504
Question: In a shop 80% of the articles are sold at a profit of 10% and the remaining at a loss of 40%.what is the overall profit/loss?
(A) 10% profit
(B) 10% loss
(C) 15% profit
(D) no profit, no loss
(E) none
Rationale: 80*1.1+20*0.6/100=1
ANSWER:D
Answer: (D) no profit, no loss
Question: Some ladies can do a piece of work in 12 days. Two times the number of such ladies will do half of that work in :
(A) 6 days
(B) 4 days
(C) 12 days
(D) 3 days
(E) 7 days
Rationale: Let x ladies can do the work in 12 days. More ladies, less days (Indirect)
Less work, less days (direct)
Ladies 2x : x Work 1 : ½
2x : x , 1 : ½ : : 12 : y
:. 2x * 1*y = x* ½ *12 or y = 3
Hence the required number of days = 3
ANSWER:D
Answer: (D) 3 days
Question: A bus can hold 108 passengers. If there are 12 rows of seats on the bus, how many seats are in each row?
(A) 1
(B) 2
(C) 9
(D) 25
(E) 26
Rationale: Total number of passengers = 108
There are 12 rows of seats on the bus.
To find how many seats are there in each row, divide the total number of passengers by the number of rows of seats on the bus.
We get, divide 108 by 12
108 ÷ 12 = 9
Therefore, there are 9 seats in each row
ANSWER IS C
Answer: (C) 9
Question: The average age of M boys is ‘b’ years and of ‘n’ girls ‘c’ years. The average age of all together is?
(A) (mb + nc)/ (m + b) years
(B) (mb + bc)/ (m + n) years
(C) (mb + nc)/ (m + n) years
(D) (nb + nc)/ (m + n) years
(E) (mb + nb)/ (m + n) years
Rationale: (mb + nc) / (m+ n).nswer: C
Answer: (C) (mb + nc)/ (m + n) years
Question: An automobile financier claims to be lending money at S.I., but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes?
(A) 10.28%
(B) 10.25%
(C) 10.85%
(D) 30.25%
(E) 10.15%
Rationale: Let the sum be Rs. 100. Then,
S.I. for first 6 months = (100 * 10 *1) / (100 * 2) = Rs. 5
S.I. for last 6 months = (105 * 10 * 1) / (100 * 2) = Rs. 5.25
So, amount at the end of 1 year = (100 + 5 + 5.25) = Rs. 110.25
Effective rate = (110.25 - 100) = 10.25%.
Answer: B
Answer: (B) 10.25%
Question: Two numbers are less than third number by 32% and 37% respectively. How much percent is the second number less than by the first
(A) 8%
(B) 10%
(C) 9%
(D) 11%
(E) 14%
Rationale: Let the third number is x.
then first number = (100-32)% of x
= 68% of x
Second number is (63x/100)
Difference = 68x/100 - 63x/100 = x/20
So required percentage is, difference is what percent of first number
(x/20 * 100/68x * 100 )% = 14% ANSWER :E
Answer: (E) 14%
Question: A train 3000 m long can cross an electric pole in 120 sec and then find the speed of the train?
(A) 90
(B) 95
(C) 100
(D) 105
(E) 110
Rationale: Length = Speed * time
Speed = L/T
S = 3000/120
S = 25 M/Sec
Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 90 Kmph
Answer:A
Answer: (A) 90
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 876 cm
(B) 800 cm
(C) 167 cm
(D) 765 cm
(E) 167 cm
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200
= 800 cm.
Answer:B
Answer: (B) 800 cm
Question: x and y are positive integers. If xy + 4x is odd, then which of the following must be even?
(A) x
(B) y
(C) x + y
(D) xy − x
(E) y+4
Rationale: Given that xy + 4x is odd, which means x(y+4) is odd.
Product of two nos. will be odd only if both the nos. are odd.
Hence x is odd, y+4 is also odd.
y+4 is odd means y is even. Answer will be E.
Answer: (E) y+4
Question: By selling 200 apples, a fruit-seller gains the selling price of 50 apples. Find the gain percent?
(A) 33.33%
(B) 35%
(C) 27.75%
(D) 35.75%
(E) 32.25%
Rationale: SP = CP + g
200 SP = 200 CP + 50 SP
150 SP = 200 CP
150 --- 50 CP
100 --- ? => 33.33%
Answer: A
Answer: (A) 33.33%
Question: If C is the temperature in degrees Celsins and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C=5(F-32). In a weekly range of temperature recorded at a certain weather station differed by 25 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?
(A) a) 65/9
(B) b) 13
(C) c) 25
(D) d) 45
(E) e) 81
Rationale: The relationship is 9/5 - 32, so approximately half of difference in Celsius (the -32 part won't be used in this case). Just looking at the answer choices you can pick B which is the only number near half of 25. The other answer choices are too far apart so no need to calculate.
Answer: (B) b) 13
Question: Pipe A can fill a tank in 10 hours, pipe B in 20 hours, and pipe C in 60 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: The part filled by A + B + C in 1 hour is 1/10 + 1/20 + 1/60 = 1/6
All the three pipes together will fill the tank in 6 hours.
The answer is A.
Answer: (A) 6
Question: A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 35%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?
(A) 20%
(B) 25%
(C) 33.33%
(D) 40%
(E) 30%
Rationale: Say 100g pure butter costs $100
But; $100 is his 35% profit because he just used 80gram pure butter.
80g would have costed him $80 and he sold it for $100 by adding 20g of freely available fat. $100 is 1.35(70)
so;
total weight=100g
fat=30g
30%
E
Answer: (E) 30%
Question: Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 67
(B) 55
(C) 77
(D) 83
(E) 75
Rationale: Average
= (76 + 65 + 82 + 67 + 85)/5
= 375/5 = 75.
Answer:E
Answer: (E) 75
Question: If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability Q that their product will be of the form of x^2-(by)^2, where b is an integer?
(A) Q=1/2
(B) Q=1/3
(C) Q=1/4
(D) Q=1/5
(E) Q=1/6
Rationale: Only (X+y)(x-y) pair will give the form x^2-(by)^2
The probability of selecting these two pairs are 1/4 * 1/3 = 1/12, assuming x+y is picked first, then x-y, but x-y can be picked first followed by x+y. So the probability Q= 1/12 * 2 = 1/6
Ans E
Answer: (E) Q=1/6
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
(A) 33
(B) 40
(C) 38
(D) 27
(E) 211
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years.
Answer: B) 40
Answer: (B) 40
Question: A boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 1
Rationale: Explanation:
Rate downstream = (20/2) kmph = 10 kmph;
Rate upstream = (20/5) kmph = 4 kmph
Speed in still water = 1/2 (10 + 4) kmph = 7 kmph
ANSWER: B
Answer: (B) 7
Question: A man sells a car to his friend at 12% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :
(A) Rs.21136.36
(B) Rs.31136.36
(C) Rs.51136.36
(D) Rs.61136.36
(E) None of these
Rationale: Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.[100/120Ã—54000]
=Rs. 45000
This is the price the first person sold to the second at at loss of 12%.
Now S.P = Rs.45000 and loss = 12%
C.P. Rs.[100/88Ã—45000]= Rs.51136.36
Correct Option : C
Answer: (C) Rs.51136.36
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 5500, the number of valid votes that the other candidate got, was:
(A) 2800
(B) 1980
(C) 2900
(D) 2200
(E) 2300
Rationale: B
Number of valid votes = 80% of 5500 = 4400.
Valid votes polled by other candidate = 45% of 4400
= (45/100 x 4400) = 1980.
Answer: (B) 1980
Question: How many meters are there in 330 centimeters?
(A) 550 meters
(B) 3.3 meters
(C) 100 meters
(D) 3.5 meters
(E) 3 meter
Rationale: Solution:
1 meter = 100 centimeters
Just divide 330 by 100
330 Ã· 100 = 3.3, so there are 3.3 meters in 330 centimeters
Option B
Answer: (B) 3.3 meters
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 40
(B) 44
(C) 47
(D) 83
(E) 84
Rationale: Explanation:
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: Option B
Answer: (B) 44
Question: The sum of the mean, the median, and the range of the set {1,2,3} equals which one of the following values?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Here Mean => 1+2+3/3 => 2
median => 2
and range => 3-1 => 2
hence sum => 2+2+2 => 6
Answer: D
Answer: (D) 6
Question: The speed of light is approximately 1,86 * 10^4 miles per second. This approximate speed is how many miles per hour?
(A)  1,11 * 10^7
(B)  6,70 * 10^7
(C)  1,11 * 10^8
(D)  1,86 * 10^8
(E)  6,70 * 10^8
Rationale: The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be.
(1.86*10^4)*3600 = (1.86*10^4)*(3.6*10^3) = some number*10^7...
The key is realizing that thesome numberhas to be bigger thatn 1.86 (because 1.86*3.6), and the only answer that fits that is B
Answer: (B)  6,70 * 10^7
Question: A train 280 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 200 m long?
(A) 32 sec
(B) 42 sec
(C) 45 sec
(D) 18 sec
(E) 49 sec
Rationale: total length= 280+200=480
speed=54km/h=(54*5)/18= 15/1m/s
time=(480*1)/15=32 sec.
ANSWER:A
Answer: (A) 32 sec
Question: If 4/(a - 5) = 5/(a + 5), then a = ?
(A) 40
(B) 45
(C) 35
(D) 55
(E) 50
Rationale: Multiply all terms of the given equation by (a - 5)(a + 5), simplify and solve
(a - 5)(a + 5)[ 4/(a - 5) ] = (a - 5)(a + 5) [5/(a + 5) ]
4 (a + 5) = 5 (a - 5)
a =45
correct answer B
Answer: (B) 45
Question: In August,a cricket team that played 120 matches won 26% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?
(A) 40
(B) 52
(C) 65
(D) 80
(E) 98
Rationale: let the no of matches played more=x
so,
(120+x)*52/100=31.2+x
by solving we get x=65
ANSWER:C
Answer: (C) 65
Question: A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 72 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?
(A) 20
(B) 30
(C) 48
(D) 56
(E) 72
Rationale: Total distance = 72
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 16
Time traveled in bike = t2
d1 + d2 = 72
s1t1 + s2t2 = 72
8*t1 + 16*t2 = 72
t1 + 2*t2 = 9 ----- (1)
Given: t1 + t2 = 8 ----- (2)
(1) - (2) --> t2 = 1 and t1 = 8 - 1 = 7
Walking distance = s1*t1 = 8*7 = 56
Answer: D
Answer: (D) 56
Question: If it is possible to from a word with the first, fourth, seventh and eleventh letters in the word 'SPHERVLVODS' write the second letter of thet word. Otherwise, X is the answer.?
(A) D
(B) E
(C) S
(D) P
(E) Q
Rationale: The first, fourth, seventh and eleventh letters of the word 'SPHERVLVODS'
The word formed is LESS
The second letter is E.
ANSWER B
Answer: (B) E
Question: What is the units' digit of the following expression (11)^5*(1)^3*(21)^5?
(A) 0
(B) 1
(C) 3
(D) 5
(E) 9
Rationale: We do not have to do any calculations or find units digit of remaining numbers...
all three terms - 11,1,21 - are ODD and since the PRODUCT contains 1, the units digit of the product will remain 1
B
Answer: (B) 1
Question: By selling 28 metres of clothes, a shopkeeper gains the price of 3 metres of clothes. His gain per cent is
(A) 16%
(B) 15%
(C) 14%
(D) 13%
(E) 12%
Rationale: Suppose S.P of 28 meters of cloth = Rs 28
Therefore, Gain = Rs 3 => C.P = Rs 25
Gain % = 3/25 x 100 = 12%
Gain = 12%
ANSWER:E
Answer: (E) 12%
Question: The sum of three consecutive odd natural numbers, each divisible by 3 is 87. What is the largest among them?
(A) 21
(B) 24
(C) 27
(D) 32
(E) 45
Rationale: Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6
Given, X + X+3 + X+6 =87
3X = 78
X = 26
The numbers are 26, 29, 32
Therefore the largest number is 32
Answer D.
Answer: (D) 32
Question: The current ofa stream runs at the rate of 2 km/hour. A motor boat goes 10 km upstream & back again to the starting point in 55 min. Find the speed of the motor boat in still water?
(A) 20 km/hr
(B) 22 km/hr
(C) 28 km/hr
(D) 30 km/hr
(E) 34 km/hr
Rationale: Let the speed of the boat in still water =x km/hr
Speed of the current = 2 km/hr
Then, speed downstream =(x+2) km/hr
speed upstream =(x−2) km/hr
Total time taken to travel 10 km upstream and back = 55 minutes =5560 hour = 1112 hour
⇒10x−2+10x+2=1112 120(x+2)+120(x−2)=11(x2−4) 240x=11x2−44 11x2−240x−44=0 11x2−242x+2x−44=0 11x(x−22)+2(x−22)=0 (x−22)(11x+2)=0 x=22 or −211
Since x cannot be negative, x = 22
i.e., speed of the boat in still water = 22 km/hr
B
Answer: (B) 22 km/hr
Question: Which of the following is the median number of goals scored per student?
(A) 0
(B) 1
(C) 2
(D) 3
(E) None of the above
Rationale: Total number of students = 8+2+5= 15
so median must be the middle term out of the 15 terms i.e., 8th term when arranged in ascending order
arranging in ascending order we have {1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3}
median number of goals scored per student = 1
ANSWER:B
Answer: (B) 1
Question: A bag contains 25p coins, 50p coins and 1 rupee coins whose values are in the ratio of 8:4:2. The total values of coins are 840. Then find the total number of coins
(A) 220
(B) 240
(C) 260
(D) 280
(E) 340
Rationale: Value is given in the ratio 8:4:2.
(8x/0.25) + (4x/0.5) + (2x/1) = 840.
X = 20. Total amount = 14*20 = 280
Answer:D
Answer: (D) 280
Question: In his pocket, a boy has 3 red marbles, 4 blue marbles, and 5 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: The worst case scenario would be that he has taken 4 blue and 5 green, a total of 9 marbles, and still doesn't have 3 distinct colors. But the next draw will surely be red as only the red marbles are left in his pocket.
The answer is D.
Answer: (D) 10
Question: A man invests a certain sum of money at 6% per annum simple interest and another sum at 7% per annum simple interest. His income from interest after 2 years was Rs. 354. One-forth of the first sum is equal to one-fifth of the second sum. The total sum invested was :
(A) Rs.3100
(B) Rs.2700
(C) Rs.2200
(D) Rs.1800
(E) Rs.2100
Rationale: Explanation :
Let the man invests Rs.x at 6% and Rs.y at 7%
Simple Interest on Rs.x at 6% for 2 years + Simple Interest on Rs.y at 7% for 2 years = Rs.354
x × 6 ×2 /100+y×7×2/100=354
x × 6 × 2+y×7×2=354×100
x × 6+y × 7=177×100
6x+7y=17700⋯(1)
One-forth of the first sum is equal to one-fifth of the second sum
=>x/4=y/5
=>x=4y/5⋯(2)
Solving (1) and (2),
6x+7y=17700
6(4y/5)+7y=17700
24y+35y=17700×5
59y=17700×
y=300×5=1500
x=4y/5
=4×1500/5
=4×300
=1200
total sum invested = x + y = 1500 + 1200 = 2700
Answer : Option B
Answer: (B) Rs.2700
Question: If 1/(x+2)+1/(x-2)=1/(x+2), what is the value of x?
(A) -1
(B) 2
(C) 1
(D) -2
(E) 0
Rationale: If we solve the question, we get x=-2.
Option: D
Answer: (D) -2
Question: A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed Q of the train.
(A) a) 45
(B) b) 33
(C) c) 48
(D) d) 55
(E) e) 61
Rationale: Let y be the balance distance to be covered and x be the former speed.
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late
so, y/(3x/4) - y/x = 35/60
4y/3x - y/x = 7/12
y/x(4/3-1)=7/12
y/x*1/3=7/12
y/x=7/4
4y-7x=0 ........ 1
Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late
so, (y-24)/(3x/4) - (y-24)/x = 25/60
4(y-24)/3x - (y-24)/x = 5/12
(y-24)/x (4/3-1) = 5/12
(y-24)/x *1/3 = 5/12
(y-24)*12 = 3x*5
(y-24)*4 = 5x
4y-5x = 96 ....... 2
eq2 - eq1
2x=96
x=48=Q
Ans = C
Answer: (C) c) 48
Question: If a survey shows that 40 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
(A) 56%
(B) 64%
(C) 80%
(D) 82%
(E) 86%
Rationale: Those who support = 40.
% of those who don't support it is (200-40)/ 200 = 80%
Answer C
Answer: (C) 80%
Question: Evaluate: 2344 - 12*3*2 =?
(A) 2337
(B) 1227
(C) 3327
(D) 5457
(E) 7677
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
2344 - 12*3*2 = 2344 - 8 = 2337
correct answer A
Answer: (A) 2337
Question: Total of the ages of A, B ahd C at present is 90 years. Ten years ago, the ratio of their ages was 1: 2: 3. What is the age of B at present
(A) 25
(B) 30
(C) 45
(D) 60
(E) 65
Rationale: Explanation:
Let their ages 10 years ago is x, 2x and 3x years.
10 + 2x + 10 + 3x + 10 = 90 hence x= 10
B’s present age = (2x + 10) =30 years
Option B
Answer: (B) 30
Question: A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time W it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?
(A)  0.8(80 – y)
(B)  0.8 + 0.0025y
(C)  80/y – 1.25
(D)  80/1.25y
(E)  80 – 0.25y
Rationale: This may be a case of bad numberpicking but it worked for me.
80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 40*1/10 = 4 houses per week will be painted at this rate.
80-y = 80-40 = 40 houses are to be painted at the faster rate. X*1,25=12,5 houses per week <=> 1/12,5 weeks per house * 40 houses = 40/12,5 = 80/25 = 320/100 = 3,2 weeks.
Which means finishing all houses at normal rate W=> 2*4 = 8 weeks. Faster rate = 4+3,2 = 7,2 weeks.
7,2/8 = 9/10 = 0,9. Insert y=40 in equations and it is clear that only (B) gives us 0,9.
Answer: (B)  0.8 + 0.0025y
Question: Set M contains number that satisfy the condition that, if integer x is in the set then x + 2 will also be in the set M. If -4 is one value in the set, which of the following values must also be present in the set M?
I) -6
II) -2
III) 2
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Since -4 is in the set, then the set must also include -2, 0, 2, 4, etc...
Depending on whether -4 is the starting element in the set or not, we can have -6...or not.
The answer is D.
Answer: (D) II and III only
Question: What is the HCF of 2/3, 4/12 and 6/5
(A) 7/45
(B) 2/45
(C) 4/15
(D) 1/30
(E) 9/45
Rationale: Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 12, 5) = 2/60 = 1/30
Answer: Option D
Answer: (D) 1/30
Question: n a Festival season Director informed his 20 staffs with their family to go for a one day tour. Package for one day is 750/- Some staffs are married and some are unmarried and some having their Kids. Director & 8 staffs are married with 2 kid each. What is the total package:
(A) 30000
(B) 38000
(C) 45000
(D) 33000
(E) 36000
Rationale: Total staffs = 20
Married staffs including Director = 9 *4= 36
Unmarried Staff = 20-8 = 12
Total persons = 48
Total package = 48 * 750 = 36000
Answer is E
Answer: (E) 36000
Question: From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 3, what is the probability that the 2 numbers included the number 1?
(A) 1/5
(B) 2/5
(C) 1
(D) 3/5
(E) 1/4
Rationale: We know that the sum of two numbers picked was 3. So, there could be the following cases:
(1, 2);
(2, 1);
Total of 2 cases out of which 2 have 1, thus the probability is 2/2=1.
Ans C
Answer: (C) 1
Question: Each family in a locality has atmost two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls and more girls than families. Then the minimum possible number of families in the locality is
(A) 4
(B) 5
(C) 2
(D) 3
(E) 1
Rationale: Explanation :
As per the question, we need to satisfy three
conditions namely:
1. Adults (A) > Boys (B)
2. Boys (B) > Girls (G)
3. Girls (G) > Families (F)
Clearly, if the number of families is 2, maximum number of adults can only be 4. Now, for the second condition to be satisfied, every family should have atleast two boys and one girl each.
This will result in non-compliance with the first condition because adults will be equal to boys. If we consider the same conditions for 3 families, then all three conditions will be satisfied.
Answer : D
Answer: (D) 3
Question: A runs twice as fast as B and gives B a start of 50m.How long should the racecourse be so that A and B might reach in the same time?
(A) 75 m.
(B) 80 m.
(C) 150 m.
(D) 100 m.
(E) None of the above
Rationale: ratio of speeds of a and b is 2:1
b is 50m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 50m is 50/1=50m
so the total time taken by a and b to reach =2*50=100m
ANSWER:D
Answer: (D) 100 m.
Question: An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres
(A) 1300
(B) 1400
(C) 2400
(D) 2500
(E) 2600
Rationale: It means that 0.08% of x = 2
(8100×100 ×x)=2
x=2×100×1008
x=2500
ANSWER :D
Answer: (D) 2500