mathewhe/aqua_rat huggingface dataset:
Question: The parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
(A) 77.14 cm
(B) 47.14 cm
(C) 26.71 cm
(D) 94.94 cm
(E) 23.57 cm
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(20 + 14) = 68 cm Parameter of the square = 68 cm
i.e. 4a = 68
A = 17
Diameter of the semicircle = 17 cm
Circimference of the semicircle
= 1/2(∏)(17)
= 1/2(22/7)(17) = 374/14 = 26.71 cm to two decimal places
ANSWER:C
Answer: (C) 26.71 cm
Question: The length and breadth of a rectangle is increased by 30% and 45% respectively. What is the increase in the area?
(A) 88.25
(B) 87.5
(C) 86.0
(D) 88.0
(E) 88.5
Rationale: 100*100=10000
130*145=18850
-----------
8850
10000----8850
100-----88.50
Answer E
Answer: (E) 88.5
Question: 9 engines consume 24 metric tonnes of coal, when each is working 8 hours day. How much coal is required for 8 engines, each running 13 hours a day, if 3 engines of former type consume as much as 4 engines of latter type?
(A) 20 metric tonnes
(B) 22 metric tonnes
(C) 24 metric tonnes
(D) 26 metric tonnes
(E) None of these
Rationale: Explanation :
Let required amount of coal be x metric tonnes
More engines, more amount of coal (direct proportion)
If 3 engines of first type consume 1 unit, then 1 engine will consume 1/3 unit which is its the rate of consumption.
If 4 engines of second type consume 1 unit, then 1 engine will consume 1/4 unit which is its the rate of consumption
More rate of consumption, more amount of coal (direct proportion)
More hours, more amount of coal(direct proportion)
⇒ 9 × (1/3) × 8 × x = 8 × (1/4) × 13 × 24
⇒ 3 × 8 × x = 8 × 6 × 13
⇒ 3 × x = 6 × 13
⇒ x = 2 × 13 = 26. Answer : Option D
Answer: (D) 26 metric tonnes
Question: Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "HEN"?
(A) 69
(B) 72
(C) 75
(D) 78
(E) 81
Rationale: "HEN" = (8+5+14)*3=81.
The answer is E.
Answer: (E) 81
Question: Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 65
(B) 69
(C) 72
(D) 75
(E) NOne
Rationale: Sol.
Average
= 66 + 65 + 77 + 62 + 75 / 5)
= (345 / 5)
= 69.
Answer B
Answer: (B) 69
Question: Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louis have to pay each month?
(A) 333
(B) 383
(C) 402
(D) 433
(E) 483
Rationale: After 1st month: (1000)(1.1)-X = 1100-X
After 2nd month: (1100-X)(1.1)-X = 1210-2.21X
After 3rd month: (1210-2.21X)(1.1)-X = 1331-3.31X
Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:
1331-3.31X = 0
X = 1331/3.31 = 402.11
The answer is C
Answer: (C) 402
Question: Express 15 mps in kmph?
(A) 22
(B) 88
(C) 90
(D) 21
(E) 54
Rationale: 15 * 18/5 = 54 kmph
Answer: E
Answer: (E) 54
Question: If 2 (A's capital) = 4 (B's capital) = 6 (C's capital). Then the ratio of their capitals is?
(A) 6:3:2
(B) 5:3:2
(C) 6:3:5
(D) 6:4:2
(E) 6:2:2
Rationale: 2A = 4B = 6 C
A:B:C = 1/2:1/4:1/6
= 6:3:2
Answer: A
Answer: (A) 6:3:2
Question: In how many ways can 7 different objects be dived among 3 persons so that either one or two of them do not get any object?
(A) 381
(B) 180
(C) 36
(D) 84
(E) 94
Rationale: case 1: for all obj are given to one person 3
case 2: choose two out of 3 3c2=3
naw no of ways to distribute 7 obj to two person=2^7
sub two way when no obj is given to both
so no of ways=3+3c2(2^7-2)=381
ANSWER:A
Answer: (A) 381
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 12km?
(A) 3
(B) 5
(C) 8
(D) 9
(E) 6
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 12
T = 12/2 = 6
Answer:E
Answer: (E) 6
Question: A train is 360 meter long is running at a speed of 90 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 87
(B) 69
(C) 40
(D) 72
(E) 20
Rationale: Speed = 90 Km/hr = 90*(5/18) m/sec = 25 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/25) = 20 seconds
Answer: E
Answer: (E) 20
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 7 years ago?
(A)  8
(B)  10
(C)  12
(D)  14
(E)  7
Rationale: Let's say
Age of Richard isR
Age of David isD
Age of Scott isS
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 7 years ago?
i.e. D-7 = 14-7 = 7 years
Answer: Option
E
Answer: (E)  7
Question: A bowl was filled with 10 ounces of water, and 0.014 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
(A) 0.004%
(B) 0.04%
(C) 0.40%
(D) 7%
(E) 40%
Rationale: Total amount of water evaporated each day during a 50-day period = .014 * 50
=.014 * 100/2
= 1.4/2
= .7
percent of the original amount of water evaporated during this period = (.7/10) * 100%
= 7 %
Answer D
Answer: (D) 7%
Question: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2, such that a, b, c are the lengths of sides of the triangle. If the triangle has 360, 360, and 300 as the side’s lengths, what is the triangle’s area?
(A) 34,200
(B) 36,200
(C) 38,200
(D) 42,200
(E) 49,089
Rationale: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2,
-> P=(360+360+300)/2=510, area=√(510(510-360)(510-360)(510-300))=49,089. Therefore, the answer is E.
Answer: (E) 49,089
Question: Oranges are bought at 7 for Rs.4.50. At what rate per hundred must they be sold to gain 33%?
(A) 57.5
(B) 85.5
(C) 89.5
(D) 94.5
(E) 95.0
Rationale: 7 oranges bought for rs 4.5
1 orange cost =4.5/7
therefore for 100 oranges =100*(4.5/7)
gain =33%
450/7+(33/100)*450/7=rate per hundred he want to sell
ans :85.50
ANSWER:B
Answer: (B) 85.5
Question: If 4 persons can do 4 times of a particular work in 4 days, then, 7 persons can do 7 times of that work in?
(A) 3 days
(B) 4 days
(C) 6 days
(D) 7 days
(E) 8 days
Rationale: That is, 1 person can do one time of the work in 4 days.
Therefore, 7 persons can do 7 times work in the same 4 days itself
B)
Answer: (B) 4 days
Question: An alloy of copper and zinc contains copper and zinc in the ratio 9 : 6. Another alloy of copper and zinc contains copper and zinc in the ratio 6 : 9. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?
(A) 1 : 5
(B) 1 : 4
(C) 1 : 3
(D) 1 : 1
(E) 1 : 2
Rationale: Let Alloy_1 be x units, and let Alloy_2 be y units.
So, fraction of copper in Alloy_1 = 9x/15, and fraction of zinc in Alloy_1 = 6x/15
Similarly, fraction of copper in Alloy_2 = 6y/15, and fraction of zinc in Alloy_2 = 9y/15.
Mixing them, we get
copper = 9x/15 +6y/15; zinc = 6x/15 + 9y/15
So, 9x+6y = 6x+9y
-> 3x = 3y
-> x/y =3/3 = 1/1
So, they must be mixed in the ratio 1 : 1
Answer : D
Answer: (D) 1 : 1
Question: In how many ways can the letters D, I, G, I, K be arranged so that the two I's are not next to each other?
(A) 36
(B) 48
(C) 72
(D) 96
(E) 128
Rationale: 1 D
2 I
1 G
1 K
Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60
Consider 2 Is as 1 entity and thus the number of arrangements for (II)DGK = 4! = 24
Total allowed cases = 60-24 =36
A is the correct answer.
Answer: (A) 36
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B =6:3 and B:C = 6:5. If the total runs scored by all of them are 118, the runs scored by B are?
(A) 24
(B) 20.13
(C) 30.93
(D) 20.93
(E) 10.93
Rationale: A:B = 6:3
B:C = 6:5
A:B:C = 36:18:15
12/59 * 118 = 24
ANSWER:A
Answer: (A) 24
Question: Assume all pieces of rope are equal.
If 44 pieces of rope measure A feet, how long would B pieces of rope be in inches?
(A) 44/AB
(B) 11/3AB
(C) 6/11AB
(D) AB/44
(E) 3AB/11
Rationale: 44 ropes measure A feet or 12*A inches
1 rope will measure = 12*A/44 = 6*A/22 = 3*A/11
B piece of rope measure = B*3*A/11 = 3AB/11
Hence, the answer is E.
Answer: (E) 3AB/11
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 4.25 sec
(C) 5 sec
(D) 12.5 sec
(E) 12 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
ANSWER:A
Answer: (A) 2.5 sec
Question: In one hour, a boat goes 15 km along the stream and 5 km against the stream. the sped of the boat in still water (in km/hr) is :
(A) 3
(B) 5
(C) 8
(D) 9
(E) 10
Rationale: Solution
Speed in still water= 1/2(15+5) km/hr= 10kmph. Answer E
Answer: (E) 10
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
(A) 3.34 sq m
(B) 3.97 sq m
(C) 1.17 sq m
(D) 2.98 sq m
(E) 2.67 sq m
Rationale: Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4)
= 53.38/16 = 3.34 sq m
Answer: A
Answer: (A) 3.34 sq m
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
(A) 704 m
(B) 300 m
(C) 350 m
(D) 450 m
(E) 500 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m
ANSWER A
Answer: (A) 704 m
Question: If a and b are positive numbers, and a^3 + b^3 = 30, then the greatest possible value of a is between:
(A) 0 and 3
(B) 3 and 4
(C) 4 and 5
(D) 5 and 7
(E) 7 and 9
Rationale: If a = 3.1 and b is very small, then a^3 + b^3 can equal 30.
If a > 4, then a^3 + b^3 > 30.
The answer is B.
Answer: (B) 3 and 4
Question: A shop owners pays an average salary of $400 to his 10 employees and $100 to the 2 accountants. What is the average salary for the shop owner?
(A) $350
(B) $500
(C) $460
(D) $120
(E) $800
Rationale: Number of employees in the shop is 10
Their average salary is $400
Number of accountants in the shop is 2
Their average salary is $100
Total salary of the employees is 10*400=$4,000
Total salary of the accountants is 2*100=$200
Total salary for the shop owner is $4,200
Average salary for the shop owner is 4,200/12=$350
Answer is A
Answer: (A) $350
Question: What is the difference between the local value of 6 and 9 in the number 2694?
(A) 510
(B) 377
(C) 288
(D) 277
(E) 112
Rationale: Explanation:
600 â€“ 90 = 510
Answer: A
Answer: (A) 510
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 12-meter platform and caught it after it had traveled 35.65 meters. How many times did the ball bounce?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Ans: 6
Division of total diatance travelled will be 12+12+6+3+1.5+.75+0.4 ANS B
Answer: (B) 6
Question: An woman sitting in a train which is travelling at 20 kmph observes that a goods train travelling in a opposite direction, takes 15 seconds to pass him. If the goods train is 300 m long, find its speed.
(A) 52
(B) 54
(C) 56
(D) 58
(E) 60
Rationale: Relative speed = (300/15)m/s = (300/15)*(18/5) = 72 kmph
speed of goods train = 72-20 = 52 kmph
Answer is A
Answer: (A) 52
Question: A train 600 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 277 m
(B) 700m
(C) 500 m
(D) 187 m
(E) 1678 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (600 + x)/60 = 65/3
x = 700 m.
Answer:B
Answer: (B) 700m
Question: By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
(A) 25
(B) 96
(C) 22
(D) 76
(E) 11
Rationale: Explanation:
To earn Rs. 135, investment = Rs. 1620.
To earn Rs. 8, investment == Rs. 96.
Market value of Rs. 100 stock = Rs. 96.
Answer: B) 96
Answer: (B) 96
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 349
(B) 349
(C) 342
(D) 346
(E) 344
Rationale: 400*(90/100)*(95/100) = 342
Answer:C
Answer: (C) 342
Question: If the selling price of 7 articles is same as the cost price of 10 articles. Find the gain or loss percentage?
(A) 93%
(B) 23%
(C) 33%
(D) 43%
(E) 53%
Rationale: Let the C.P of each article be Re 1. Then,
S.P of 7 articles = C.P of 10 articles = Rs. 10
Now, C.P of 7 articles = Rs. 7, S.p of 7 articles = Rs 10
Gain = Rs ( 10 - 7 ) = Rs 3.
Gain% = ( 3/7 × 100 ) % = 43%
Answer : D
Answer: (D) 43%
Question: How many 4 letter words can we make from the letters in an alphabet?
(A) 358800
(B) 358802
(C) 358801
(D) 358809
(E) 358810
Rationale: There are 26 letters in an alphabet
to choose 4 from these 26 would mean
26P4 = 26!/(26-4)!
We take Permutation and not Combination since the arrangement of letters matter in forming a word. Like MAPS and PAMS both are different words.
Therefore the answer is 26!/ 22! = 26*25*24*23 = 358800
Answer:A
Answer: (A) 358800
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation f of the mean, what percent of the distribution is less than m+f?
(A)  16%
(B)  32%
(C)  48%
(D)  84%
(E)  92%
Rationale: 16%
________________________________________________ m+f
34%
________________________________________________ m
34%
________________________________________________ m-f
16%
since 68% lies one standard deviation from mean m, => 50% of 68% lies on either side as it is symmetric about m.
thus 16% lie below m-f and 16% lie above m+f
now below m+f = 16+34+34 = 84%
hence D
Answer: (D)  84%
Question: one pipe can fill a tank in 15 hour.but because of hole in a tank,this tank fill in 20 hour.so in how much time this hole will empty the full tank?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: in 1 hour hole empty=[1/15-1/20]=1/60
so total time taken to empty the full tank through hole=60 hour.
answer D
Answer: (D) 60
Question: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 115 mangoes.
(A) 360
(B) 383
(C) 400
(D) 406
(E) 412
Rationale: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.
Method 1:
Let price per mango = x. Let number of mangoes be n. Then, nx = 360.
Now price = 0.9x; number of mangoes = n + 12. Total amount = 0.9x*(n+12) = 360.
nx = 0.9nx + 10.8x => 0.1nx = 10.8x => n = 108 => x = 360/108 = 3.33
Original price of 115 mangoes = 115*3.33 = 383.
Answer B
Answer: (B) 383
Question: A meal cost $ 33.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
(A) 40-42
(B) 39-41
(C) 38-40
(D) 37-39
(E) 36-37
Rationale: 10%(33.5) = 3.35
15%(33.5) = 5.025
total amount could have been 33.5+3.35 and 33.5+5.025
=> could have been between 36.85 and 38.525
=> approximately between 37 and 39
Answer is D.
Answer: (D) 37-39
Question: A line with slope 2 intersects a line with slope 6 at the point (40, 30).
What is the distance between the x-intercepts of these lines?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: The line with slope 2 passing through (40, 30) has x-intercept 40−(30/2). The line with slope
6 passing through (40, 30) has x-intercept 40 − (30/6). So the difference in the x-intercepts is
(30/2) − (30/6) = 10.
correct answer D
Answer: (D) 10
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 20 kmph
(B) 40 kmph
(C) 30 kmph
(D) 55 kmph
(E) 68 kmph
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
Answer: (C) 30 kmph
Question: Four balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?
(A) 60
(B) 90
(C) 120
(D) 150
(E) 180
Rationale: Since the balls are all of different colors, let's permute them and then decide how many balls we put in each box.
For example, arrange in a row the balls, then decide: two balls go into the first box, next two in the second box, and the last ball goes to the third box.
Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.
For the 2,2,1 type arrangements, we have [6!/(2!2!1!)]*3 = 100 possibilities. Inside a box, it doesn't matter the order of the balls.
For the 3,1,1 type arrangements, we have [6!/(3!1!1!)]*3 = 80 possibilities.
Total of 100 + 80 = 180 possibilities.
Answer E.
Answer: (E) 180
Question: In what ratio must rice at Rs.9.30 per Kg be mixed with rice at Rs.10.80 per Kg so that the mixture be worth Rs.10 per Kg?
(A) 8 : 7
(B) 7 : 8
(C) 8 : 9
(D) 9 : 8
(E) None
Rationale: Solution
Required ratio = 80 : 70 = 8 : 7.
Answer A
Answer: (A) 8 : 7
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in:
(A) 14 hrs
(B) 15 hrs
(C) 10 hrs
(D) 8 hrs
(E) 9 hrs
Rationale: work done by leak in 1 hr = (1/2-3/7)=1/4
=>14 hrs
ANSWER A
Answer: (A) 14 hrs
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
(A) Rs.167
(B) Rs.144
(C) Rs.148
(D) Rs.179
(E) Rs.121
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6
= Rs. 120.
To get 20% profit, New SP
= [(100 + p%)CP]/100
= (120 * 120)/100 = Rs.144
Answer: B
Answer: (B) Rs.144
Question: S1 = 5 S2 = 8 ... Sn = 3n + 4 For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50?
(A) 15
(B) 14
(C) 13
(D) 12
(E) 16
Rationale: term 16 = 3*16+4 = 52
Answer : E
Answer: (E) 16
Question: Two numbers are in the ratio 1:2, if 7 is added to both, their ratio changes to 3:5. The greatest number is
(A) 24
(B) 26
(C) 28
(D) 32
(E) 44
Rationale: Let the numbers be x and 2x
Then, (x+7)/(2x+7)=3/5
X=14
There fore answer is 28
ANSWER C 28
Answer: (C) 28
Question: one disk of 20cm radius, out of that 4 disk of 5cm are cut , find diffrence of leftout and cut out area?
(A) 200pi
(B) 300pi
(C) 100pi
(D) 400pi
(E) 500pi
Rationale: Radius r=20cm
Total areal of big disc = pi* r^2 = pi * 20 * 20 = 400 pi
Total cut out area = 4 * pi * 5 * 5 = 100 pi
Difference between them = 400 - 100 = 300pi
ANSWER:B
Answer: (B) 300pi
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
(A) 8%
(B) 5%
(C) 6%
(D) 4%
(E) 2%
Rationale: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%
Answer:B
Answer: (B) 5%
Question: If the Average (mean ) of 11 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) 9x
(C) 5x/3
(D) 3x/2
(E) 3x/5
Rationale: Let the 5 numbers be 1,2,3,4,5,...,11 (since no restrictions are given). There mean is 6 (x).
Now the sum of greatest three would be 9+10+11= 30
so the answer has to be 9x....that is option B
Answer: (B) 9x
Question: The average expenditure of a labourer for 6 months was 75 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i
(A) 70
(B) 72
(C) 75
(D) 78
(E) 80
Rationale: Income of 6 months = (6 × 75) – debt
= 450 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 720
Average monthly income = 720 ÷ 10 = 72
Answer B
Answer: (B) 72
Question: Sum of the squares of 3 no. is 156 and the sum of their products taken two at a time is 50. Find the sum?
(A) 18
(B) 16
(C) 19
(D) 21
(E) 15
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 156 + 2* 50
a + b + c = âˆš256 = 16
Answer B
Answer: (B) 16
Question: log xy3 = a; log x2y = b then then value of log y /log x
(A) 23
(B) 277
(C) 997
(D) 1781
(E) 123
Rationale: log xy3 = logx + 3logy = a - - - (1)
log x2y = 2logx + logy = b - - - (2)
Multiplying (1) by 2 and subtracting (2) from it
5logy = 2a-b
logy = 2a−b52a−b5
Put the value of log y in equation (2),
2logx + 2a−b52a−b5 = b
logx = 3b−a53b−a5
logylogx=2a−b53b−a5log⁡ylog⁡x=2a−b53b−a5 = 2a−b3b−a
Answer:B
Answer: (B) 277
Question: The slant height of a cone is 20 cm and radius of the base is 10 cm, find the curved surface of the cone.
(A) 330
(B) 159
(C) 150
(D) 200
(E) 628
Rationale: π * 10 * 20 =628
Answer:E
Answer: (E) 628
Question: A bag of potatoes weighs 16 kg divided by a quarter of its weight. How much does the bag weigh?
(A) 4 kg
(B) 8 kg
(C) 7 kg
(D) 3 kg
(E) 9 kg
Rationale: B
8 kg
8 kg : 16/2
Answer: (B) 8 kg
Question: Two boats are heading towards each other at constant speeds of 5 miles/hr and 21 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
(A) 1/12
(B) 5/12
(C) 1/6
(D) 13/30
(E) 1/5
Rationale: The question asks: how far apart will they be 1 minute=1/60 hours before they collide?
Since the combined rate of the boats is 5+21=26 mph then 1/60 hours before they collide they'll be rate*time=distance --> 26*1/60=13/30 miles apart.
Answer: D.
Answer: (D) 13/30
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
(A) 7
(B) 8!
(C) 9
(D) 3
(E) 1
Rationale: Total number of letters = 8
Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.
Answer:B
Answer: (B) 8!
Question: The distance between Delhi and Mathura is 130 kms. A starts from Delhi with a speed of 25 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 30 kmph at 9 p.m. from Delhi. When will they meet?
(A) 11
(B) 77
(C) 16
(D) 10
(E) 98
Rationale: D = 130 – 25 = 105
RS = 30 + 25 = 55
T = 105/55 = 2 hours
8 a.m. + 2 = 11 a.m..Answer: A
Answer: (A) 11
Question: In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x+y?
(A) -5
(B) -1
(C) 1
(D) 5
(E) 6
Rationale: lets start from z, as per the question stem
z + 5 + 7 = 16
-->> z= 4
similarly, y + 4 + 5 = 7
--> y = -2
similarly,, x + -2 + 4 = 5
--> x = 3
hence , x+y = 3-2 = 1
ANSWER:C
Answer: (C) 1
Question: If x and y are positive integers, then xy + x is
(A) Always even
(B) Always odd
(C) Even whenever x is even
(D) Even whenever x + y is odd
(E) It cannot be determined from the information given
Rationale: xy + x can be factorized as x(y + 1) by taking out x common.
Now, anything multiplied by even is always even.
Answer (C).
Answer: (C) Even whenever x is even
Question: What is the product of all the possible values of x if x^2+4x+7=|x+2|+3
(A) -6
(B) –12
(C) 12
(D) 29
(E) 168
Rationale: x^2+4x+4=|x+2|
(X+2)^2 = |x+2|
Only 3 values possible,
x = -3, x = -2, x =-1
So multiplication = -6
answer option -6
ANSWER:A
Answer: (A) -6