mathewhe/aqua_rat huggingface dataset:
Question: What is the twenty-fourth decimal to the right in the fraction 35/36?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 35/36= 0.97222222222...
The answer is B.
Answer: (B) 2
Question: If a coin is tossed three times, what is the probability that on the first toss the coin lands on heads and then lands on tails the next two tosses?
(A) 1/8
(B) 1/3
(C) 1/4
(D) 1/2
(E) 1
Rationale: P(HTT) = 1/2*1/2*1/2=1/8
The answer is A.
Answer: (A) 1/8
Question: The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by two-thirds of the males and one-third of the females in the class?
(A) 160
(B) 168
(C) 191
(D) 192
(E) 204
Rationale: 2/3*2/5 + 1/3*3/5 = 4/15 + 3/15 = 7/15
The number of degrees is 7/15 * 360 = 168 degrees
The answer is B.
Answer: (B) 168
Question: A train is 360 meter long is running at a speed of 36 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 50 seconds
(B) 46 seconds
(C) 40 seconds
(D) 97 seconds
(E) 26 seconds
Rationale: Speed = 36 Km/hr = 36*(5/18) m/sec = 10 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/10)
= 50 seconds
Answer:A
Answer: (A) 50 seconds
Question: In a kilometer race, A beats B by 54 meters or 12 seconds. What time does A take to complete the race?
(A) 212
(B) 190
(C) 277
(D) 181
(E) 122
Rationale: Time taken by B run 1000 meters = (1000 * 12)/54 = 222 sec.
Time taken by A = 224 - 12 = 212 sec.Answer:A
Answer: (A) 212
Question: The events A and B are independent. The probability that event A occurs is r and the probability that event B occurs is s. Which of the following is equal to the probability that exactly one of the events A and B occurs?
(A) r − 2rs
(B) s − rs
(C) r + s− 2rs
(D) r + s −rs
(E) r + s
Rationale: Probability of A occuring = p , Probability of A NOT occuring = 1-r
Probability of B occuring = s , Probability of B not occurring = 1-s
Probability of atleast of one of A and B occuring = 1-(1-r)(1-s) =r+s -rs
D
Answer: (D) r + s −rs
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 333 m
(B) 277 m
(C) 245 m
(D) 279 m
(E) 176 m
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer:C
Answer: (C) 245 m
Question: 7 dogs have got 7 puppies each. Each puppy has got 7 kitten as friend. They are all members of a club along with me. What is the strength of club ?
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: total strength = (7+7*7+7*7*7)+1=400
ANSWER:B
Answer: (B) 400
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 4:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
(A) 10.18 p.m
(B) 10.29 p.m
(C) 11.30 p.m
(D) 10.38 p.m
(E) 10.32 p.m
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
4.30 + 7 h = 11.30 p.m.
Answer:C
Answer: (C) 11.30 p.m
Question: The ratio of the ages of Malini and Radha is 2 : 4. The total of their ages is 2.4 decades. The proportion of their ages after 0.8 decades will be
[1 Decade = 10 years]
(A) 6:5
(B) 3:4
(C) 4:5
(D) 2:3
(E) 3:6
Rationale: Let, Malini’s age = 2A and Radha’s age = 4A
Then 2A + 4A = 24
A = 4
Malini’s age = 8 years
and Radha’s age = 16 years
Proportion of their ages after 8 is = (8 + 8) : (16 + 8)
= 16 : 24
= 2 : 3
Answer : D
Answer: (D) 2:3
Question: A group of people were given 2 puzzles. 72% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?
(A)  11%, 0%
(B)  49%, 33%
(C)  68%, 57%
(D)  79%, 68%
(E)  27%, 67%
Rationale: To solve this question, we don't need any formulas. Just read the question carefully. If 72% of the people solved puzzle X and 89% solved puzzle Y, then maximum % that can solve both correctly can only be 72%. From the given options, only D looks good
Answer E
Answer: (E)  27%, 67%
Question: A university needs to select an eight-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 9 members, the student advisory board consists of 8 members, and 6 students hold membership in both organizations, how many different committee are possible?
(A) 165
(B) 194
(C) 212
(D) 236
(E) 300
Rationale: student government + the student advisory board consists of 9 + 8 = 17 members.
6 students hold membership in both, so they were counted twice.
The total number of people to choose from is 17 - 6 = 11
The number of ways to choose 8 members from 11 is 11C8 = 165
The answer is A.
Answer: (A) 165
Question: The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 2 per metre approximately
(A) 2972
(B) 4567
(C) 4235
(D) 4547
(E) 4675
Rationale: Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 2) = Rs. 2972.
Answer: Option A
Answer: (A) 2972
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 242 runs?
(A) 6.25
(B) 5.25
(C) 6.29
(D) 6.39
(E) 6.13
Rationale: Required run rate
= [242 - (3.2 * 10)]/40
= 210/40
= 5.25
Answer: B
Answer: (B) 5.25
Question: What is the sum of the multiples of 4 from 40 to 80, inclusive?
(A) 560
(B) 660
(C) 800
(D) 760
(E) 480
Rationale: The formula we want to use in this type of problem is this:
Average*Total Numbers=Sum
First, find the average by taking the sum of the F + L number and divide it by 2:
A = (F + L)/2
Second, find the total numbers in our range by dividing our F and L numbers by 4 and add 1.
(80/4) - (40/4) + 1
Multiply these together so what we show Average*Total Numbers=Sum
(80 + 40)/2 * (80/4) - (40/4) + 1 = Sum
60 *11 = 660
B
Answer: (B) 660
Question: Mrs. Rodger got a weekly raise of $115. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $ 145.
(B) $ 146
(C) $ 115
(D) $ 148
(E) None
Rationale: Solution:
Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 115.
So after completing the 1st week she will get $ (x+115).
Similarly after completing the 2nd week she will get $ (x + 115) + $ 115.
= $ (x + 115 + 115)
= $ (x + 230)
So in this way end of every week her salary will increase by $ 115.
Answer C
Answer: (C) $ 115
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 6 days?
(A) 2/5
(B) 1/6
(C) 1/3
(D) 1/9
(E) 2/6
Rationale: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 6 days = 6 (1/18) = 1/3.
ANSWER C
Answer: (C) 1/3
Question: In 130 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
(A) 20 m
(B) 25 m
(C) 22.5 m
(D) 26 m
(E) 12 m
Rationale: Distance covered by B in 9 sec. =	130/45 x 9	m = 26 m.
A beats B by 26 metres.
Answer: Option D
Answer: (D) 26 m
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $700 per sq. metre.
(A) $12537.50
(B) $13537.50
(C) $14437.50
(D) $16437.50
(E) $18537.50
Rationale: C
Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = $700
Hence, total cost
=5.5×3.75×700= $14437.50
Answer: (C) $14437.50
Question: If it is true that x > -3 and x < 7, which of the following must be true?
(A) x > 3
(B) x < -7
(C) x < 3
(D) -7 < x < 3
(E) none of the above.
Rationale: the range is -3 < x < 7
A. x > 3 - no because x can be between -3 < x < 3
B. x < -7 - no because the values of x are always >-7
C. x < 3 - no because x can be between 3 < x < 7
D. -7 < x < 3 - no because x can be between 3 < x < 7
E. none of the above.
Answer: E
Answer: (E) none of the above.
Question: A bucket contains 2 mixtures A and B in the ratio 3:2. If 5 liters of the mixture is replaced by 5 liters of liquid B, then the ratio of the two liquids becomes 3:5. How much of the liquid A was there in the bucket?
(A) 8liters
(B) 10liters
(C) 12liters
(D) 15liters
(E) 18liters
Rationale: 1st ratio = 3:2
2nd ratio = 3:5
Difference of cross products ratio = 3*5-3*2 = 9
common factor of the 1st ratio
= (quantity replaced/sum of terms in 1st ratio) + (Quantity replaced*term A in 2nd ratio/Difference)
= (5/5) + (5*3/9) = 1+5/3 = 2.67
Quantity of A = 3*2.67 = 8liters approximately
Answer is A
Answer: (A) 8liters
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent?
(A) 11
(B) 25
(C) 77
(D) 88
(E) 15
Rationale: 900 --- 100
100 --- ? => 11%
Answer:A
Answer: (A) 11
Question: 3, 4.5, 6.75, 10.13, 15.18, (...)
(A) 60
(B) 60.75
(C) 22.78
(D) 32.52
(E) 88
Rationale: 3
(3Ã—3)Ã· 2 = 4.5
(4.5Ã—3)Ã· 2 = 6.75
(6.75Ã—3)Ã· 2 = 10.13
(10.18Ã—3)Ã· 2 = 15.18
(15.18Ã—3)Ã· 2 = 60.75
Answer is C
Answer: (C) 22.78
Question: The Income of an woman increase consistently by 25% per year. If his present salary is Rs. 30000 then what will his salary be after 3 years ?
(A) 50840
(B) 52840
(C) 51740
(D) 51830
(E) 51840
Rationale: Explanation :
Income = 30000 x 1.2 x 1.2 x 1.2 = 51840
Answer : Option E
Answer: (E) 51840
Question: Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace?
(A) 1/2324
(B) 2/13235
(C) 2/5525
(D) 5525/2
(E) None
Rationale: Let Q denote the event that the card drawn is queen and A be the event that
the card drawn is an ace. Clearly, we have to find P (QQA)
Now P(Q) = 4/52
Also, P (Q|Q) is the probability of second queen with the condition that one queen has
already been drawn. Now there are three queen in (52 - 1) = 51 cards.
Therefore P(Q|Q) = 3/51
P(A|QQ) is the probability of third drawn card to be an ace, with the condition
that two queens have already been drawn. Now there are four aces in left 50 cards.
Therefore P(A|QQ) = 4/50
By multiplication law of probability, we have
P(QQA) = P(Q) P(Q|Q) P(A|QQ)
= 4/52 × 3/51 × 4/50
= 2/5525.
C
Answer: (C) 2/5525
Question: To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process?
(A) 800
(B) 840
(C) 864
(D) 900
(E) 1,080
Rationale: We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B.
Answer: (B) 840
Question: A man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 5
(B) 4
(C) 7
(D) 3
(E) 5.1
Rationale: M = 5.5
S = 1.5
DS = 7
US = 4
AS = (2 * 7 * 4) /11 = 5.1
Answer: E
Answer: (E) 5.1
Question: A 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?
(A) 150 metre
(B) 380 metre
(C) 350 metre
(D) 200 metre
(E) 250 metre
Rationale: Speed of the train =300/18 m/s=50/3 m/s
Distance covered in 39 seconds=39 Ã— 50/3 =650 metre
Length of the train =650-300=350 metre
ANSWER: C
Answer: (C) 350 metre
Question: The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.30 in 1970 was 150 percent of its price in 1960, what was its price in 1980?
(A) a) $ 1.80
(B) b) $ 1.95
(C) c) $ 2.40
(D) d) $ 2.70
(E) e) $ 3.00
Rationale: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).
Therefore the price in 1980 = $1.3*1.5 = $1.95.
Answer: B.
Answer: (B) b) $ 1.95
Question: Find the area, diameter = 10m.
(A) 78.24 square meter
(B) 78.57 square meter
(C) 78.26 square meter
(D) 24.24 square meter
(E) 24.43 square meter
Rationale: Diameter = 10 meter.
Radius = diameter/2.
= 10/2.
= 5 meter.
Area of a circle = Ï€r2.
Here, pi (Ï€) = 3.14 meter, radius (r) = 5.
Area of a circle = 3.14 Ã— 5 Ã— 5..
= 3.14 Ã— 25.
= 78.57 square meter ANSWER : B
Answer: (B) 78.57 square meter
Question: The sides of a rectangular region measured to the nearest centimeter are 10 cm and 6 cm. Out of the following which is the largest possible value of actual area of rectangle ?
(A) 48
(B) 65.25
(C) 52.29
(D) 44
(E) 41.25
Rationale: acan be anywhere between 9.5 and 10.4 andbcan be anywhere between 5.5 and 6.4.
Hence max area can be 10.4*6.4 eq 66.56.
largest value which is near to 66.56 is 65.25.
Hence B.
Answer: (B) 65.25
Question: How many different three-digit multiples of 5 can be composed of digits 2, 3, 6, and 5 if none of the digits is repeated?
(A) 3
(B) 6
(C) 10
(D) 12
(E) 18
Rationale: = 3c2 x 2 = 6
can you explain your method. i solved it differently
XYZ, where Z must be 5. therefore 1 variation of digit in Z.
Y can be any of the 3 possible choices.
X can be any of the 2 possible choices.
2+3+1= 6
B
Answer: (B) 6
Question: A block of wood has dimensions 10cm x 10cm x 40cm. The block is painted red and then cut evenly at the 20 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red?
(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%
Rationale: The area of each half is 100+4(200)+100 = 1000
The area that is not painted is 100.
The fraction that is not painted is 100/1000 = 1/10 = 10%
The answer is B.
Answer: (B) 10%
Question: From a circular sheet of paper with a radius of 20cm,four circles of radius 5cm each are cut out.what is the ratio of the uncut to the cut portion?
(A) 1:3
(B) 4:1
(C) 3:1
(D) 4:3
(E) 2:3
Rationale: area of uncut=(400-100)3.14
area of cut=4*25*3.14=(100)3.14
ratio=3:1
ANSWER:C
Answer: (C) 3:1
Question: Fonzie, Aunt Bee and Lapis paid $7,000, $8,000 and $9,000 respectively to buy a map to Capt. Plaidstache's treasure. When they found it, the treasure turned out to be worth a cool $900,000. How much of it should Lapis get?
(A) $300,000
(B) $320,000
(C) $335,000
(D) $336,500
(E) $337,500
Rationale: A = 7000
B = 8000
C = 9000
A share 7 parts, B share 8 parts & C share 9 parts
Total 24 parts -----> 900000
----> 1 part -------> 37500
C share = 9 parts -----> 337500
E
Answer: (E) $337,500
Question: If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 46?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: four wheeler=11*4=44(max)
2 wheel=1
so no of 4 wheeler=11
ANSWER:A
Answer: (A) 11
Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 4 flips but not on the last flip?
(A) 1/2
(B) 1/4
(C) 1/8
(D) 1/16
(E) 1/32
Rationale: P(HHHHT) = 1/2*1/2*1/2*1/2*1/2 = 1/32
The answer is E.
Answer: (E) 1/32
Question: The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is
(A) 2.3 m
(B) 4.6 m
(C) 7.8 m
(D) 9.2 m
(E) None
Rationale: Solution
Let AB be the wall and BC be the ladder.
Then, < ABC	= 60°
AC	= 4.6 m.;
AC/BC	= cos 60°
= 1 /2
‹=›BC=2×AC
=(2× 4.6) m
= 9.2 m
Answer D
Answer: (D) 9.2 m
Question: A two digit number is 18 less than the square of the sum of its digits. How many such numbers are there?
(A) 22,33
(B) 22,22
(C) 221,1
(D) 63,82
(E) 23,17
Rationale: Option 2
Take N = 10a+b.
Given that, (10a+b)+18 = K2 = (a+b)2
Given number = K2 - 18 = (10a+b)
That means, when we add 18 to the given number it should be a perfect square. So K2 takes the following values. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ....
1 to 16 are ruled out as if we subtract 18 from them, the resulting number is a single digit number.
Now 25 - 18 = 7
36 - 18 = 18
49 - 18 = 31
64 - 18 = 46
81 - 18 = 63
100 - 18 = 82
121 - 18 = 103
Now 63, 82 satisfies.
Answer:D
Answer: (D) 63,82
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 63 kmph, find the speed of the stream?
(A) 15
(B) 19
(C) 14
(D) 21
(E) 16
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 63/3 = 21 kmph.
Answer:D
Answer: (D) 21
Question: How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits A equal to 28?
(A) 14
(B) 24
(C) 28
(D) 48
(E) 96
Rationale: First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.
Start from the largest number possible 9874.
Then the next largest number possible is 9865.
After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.
So you have two solutions. Each can be rearranged in 4!=24 ways. So A=24+24=48.D
Answer: (D) 48
Question: The average marks obtained by 120 candidates in a certain examinationis 35.if the average marks of passed candidate is 39 and that of the failed candidates is 15,what is the no. of candidates who passed the examination?
(A) 80
(B) 100
(C) 120
(D) 140
(E) 150
Rationale: Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
B
Answer: (B) 100
Question: A speaks truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident?
(A) 35
(B) 30
(C) 25
(D) 20
(E) None of these
Rationale: Let the truth spoken by A and B be pl and p2
respectively, i.e., pl = 3⁄4 and p2 = 4⁄5
They will contradict each other only when one speaks truth and the other is lying.
i.e., 3⁄4 × 1⁄5 + 4⁄5 × 1⁄4 = 3⁄20 + 4⁄20 = 7⁄20 = 35⁄100 i.e, 35%
Answer A
Answer: (A) 35
Question: The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
(A) 1008
(B) 1015
(C) 1022
(D) 1032
(E) 1043
Rationale: Required Number = (L.C.M of 12, 16, 18,21,28)+7
= 1008 + 7
= 1015
Answer: B
Answer: (B) 1015
Question: The distance between West-Town to East-Town is 14 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 5 kilometers per minute and the second bird, leaving from East-Town, at a speed of 2 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
(A) 3.
(B) 7.
(C) 10.
(D) 12.
(E) 15.
Rationale: Time taken by the birds to meet = 14/(5+ 2) = 2 mins
Distance traveled by the bird traveling from West-Town = 5 * 2 = 10
Answer: C
Answer: (C) 10.
Question: If a boat is rowed downstream for 96 km in 3 hours and upstream for 88 km in 11 hours, what is the speed of the boat and the river?
(A) 12 , 20
(B) 20 , 20
(C) 20 , 11
(D) 20 , 12
(E) 12 , 12
Rationale: Explanation:
If x: speed of boats man in still water
y: speed of the river
Downstream speed (Ds) = x + y
Upstream speed (Us) = x â€“ y
x = (Ds + Us) / 2
y = (Ds â€“ Us) / 2
In the above problem Ds = 32 ; Us = 8
x = (32 + 8) / 2 = 40/2 = 20 km/hr
y = (32 - 8)/2 = 24/2 = 12 km/hr
ANSWER: D
Answer: (D) 20 , 12
Question: A bag marked at $250 is sold for $120. The rate of discount is?
(A) 10%
(B) 25%
(C) 20%
(D) 52%
(E) 45%
Rationale: Rate of discount = 130/250 * 100 = 52%
Answer is D
Answer: (D) 52%
Question: Rs 3500 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part.
(A) s 4000
(B) s 2800
(C) s 1800
(D) s 1500
(E) s 1550
Rationale: Explanation :
Average rate = (144/3500)*100 = 4.11
Ratio = 8.85:11.14
So, first part = (8.85/20)*3500 = Rs 1550.
Answer : E
Answer: (E) s 1550
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
(A) 1276
(B) 1200
(C) 2832
(D) 1299
(E) 1236
Rationale: Explanation:
l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 10 = 1200
Answer: Option B
Answer: (B) 1200
Question: The radius of a semi circle is 2.1 cm then its perimeter is?
(A) 32.5
(B) 11.12
(C) 32.1
(D) 10.8
(E) 32.3
Rationale: 36/7 r = 2.1 = 10.80
Answer:D
Answer: (D) 10.8
Question: Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose?
(A) 2%
(B) 2.15%
(C) 2.25%
(D) 2.50%
(E) 3.34%
Rationale: Generally in such cases, there is always loss.
So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss.
Loss% = Common loss and gain% 2 = x 2
10 10
Therefore, here common loss and gain % = 15%
Hence,
Loss% = 15 2 = 2.25%
C
Answer: (C) 2.25%
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
(A) 1:2
(B) 3:4
(C) 4:5
(D) 5:7
(E) 5:9
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4
B
Answer: (B) 3:4
Question: To furnish a room in a model home an interior decorator is to select 2 chairs and 3 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 6 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse?
(A) A)5
(B) B)8
(C) C)10
(D) D)15
(E) E)30
Rationale: Total number of ways to choose 6 chairs from 5= 6C2=15
Total number of combination=150
That means we need get 10 combinations from the selection of tables....
Screening through the answers.... 5C3=10..... 10*15=150
Answer is 5... A
Answer: (A) A)5
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is
(A) 20 years
(B) 21 years
(C) 22 years
(D) 24 years
(E) 23 years
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years
=> (x + 24) + 2 = 2(x + 2)
=> x + 26 = 2x + 4
So, x = 22
Answer: Option C
Answer: (C) 22 years
Question: The difference between two angles of a triangle is 24o. The average of the same two angles is 54o. Which one of the following is the value of the greatest angle of the triangle
(A) 45o
(B) 45o
(C) 66o
(D) 72 degree
(E) None of these
Rationale: Solution:
Let a and b be the two angles in the question, with a > b. We are given that the difference between the angles is 24o.
=> a – b = 24.
Since the average of the two angles is 54o, we have (a+b)/2 =54.
Solving for b in the first equation yields b=a–24, and substituting this into the second equation yields,
[{a+(a−24)}/2] =54
2a−24 = 54*2
2a−24 = 108
2a = 108 +24
2a =132
a =66
Also,
b=a−24=66−24=42.
Now, let c be the third angle of the triangle. Since the sum of the angles in the triangle is
180o, a+b+c =180.
Putting the previous results into the equation yields 66+42+c =180.
Solving for c yields c =72
Hence, the greatest of the three angles a, b and c is c, which equ
Answer: Option D
Answer: (D) 72 degree