RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
A.240
B.388
C.379
D.277
Answer: A.240
Explanation: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
Answer: A
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
A.2
B.2.2
C.3
D.3.5
Answer: C.3
Explanation: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.
ANSWER:C
Question: At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $2 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day?
A. 7
B. 8
C. 6
D. 10
Answer: C. 6
Explanation: After renting bowling shoes the person is left with $12.80-$0.5=$12.30, which is enough for 12.3/2<7=~6.
Answer: C.
Question: A batsman has scored an average of 46 runs for a certain number of innings played in England. When he came back to India, he played another two test matches of two innings each and scored at an average of 55 runs. For the innings in England and in India taken together, he has improved his average by 2 runs over the matches played in England.Find the number of innings played in England.
A.12
B.13
C.14
D.15
Answer: C.14
Explanation: Let the number of innings played in England be x.
∴ Total runs scored in England = 46x
Total runs scored for innings played in India
= 55 × 4 = 220
(∵ the number of innings played in India = 4)
Also, 46x+220 /x+4 = 48
⇒ 46x + 220 = 48 x + 192
⇒ 2x = 28
⇒ x = 14
Answer C
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
A.228
B.276
C.199
D.150
Answer: D.150
Explanation: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m. Answer:D
Question: What values of x satisfy the equation x2/3 + x1/3 – 2 ≤ 0 ?
A.– 8 ≤ x ≤ 1
B.– 1 ≤ x ≤ 8
C.1 ≤ x ≤ 8
D.– 8 ≤ x ≤ 8
Answer: A.– 8 ≤ x ≤ 1
Explanation: Explanation :
Let, x1/3 = y. The equation becomes y2 + y – 2 ≤ 0, or y2 + y ≤ 2.
Now, look at the upper limit. We know that y2 + y ≤ 2.
Among the positive numbers, 1 is the biggest number that satisfies the equation. No number greater than 1 can have y2 + y ≤ 2. So the upper limit is 1.
Maximum value of y is 1, hence maximum value of x1/3 is 1, and hence maximum value of x is 1.
This answer is there only for option 1. Hence that is the answer.
Answer : A
Question: If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 123, what is the least possible value of n?
A.37
B.123
C.41
D.52
Answer: C.41
Explanation: 123 is 3 * 41, so n needs to be at least 41, so the answer is C.
Question: 2 men and 4 boys can complete a work in 4 days. 5 men and 6 boys can complete the same work in 3 days. The work done by 2 boys is equal to the work of how many men?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: (2m + 4b)’s one day’s work = 1/4
(5m + 6b)’s one day’s work = 1/3
=> (8m + 16b)’s one day’s work = (15m + 18b) ’s one day’s work
=> 7 men’s work = 2 boy’s work
So, we should be employ 5 more men to be completed the work.
ANSWER:C
Question: Given that x = 2^b – (8^34 + 16^5), which of the following values for b yields the lowest value for |x|?
A.101
B.102
C.103
D.104
Answer: B.102
Explanation: 8^34 + 16^5 = 2^102 + 2^20
Compared to 2^102, the value of 2^20 is negligible.
2^102 - (2^102 +2^20) will minimize the value of |x|.
The answer is B.
Question: If the length of the sides of two cubes are in the ratio 6:1, what is the ratio of their total surface area?
A.6:1
B.12:1
C.24:1
D.36:1
Answer: D.36:1
Explanation: Let x be the length of the small cube's side.
The total surface area of the small cube is 6x^2.
The total surface area of the large cube is 6(6x)^2=216x^2.
The ratio of surface areas is 36:1.
The answer is D.
Question: A number exceeds by 25 from its 3/8 part. Then the number is?
A.32
B.35
C.39
D.40
Answer: D.40
Explanation: Explanation:
x – 3/8 x = 25
x = 40
ANSWER IS D
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
A.14
B.16
C.18
D.22
Answer: A.14
Explanation: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
Option A
Question: CONVERT 1.6 hectares in ares
A.130 ares.
B.160 ares.
C.180 ares.
D.230 ares.
Answer: B.160 ares.
Explanation: 1.6 hectares in ares
1 hectare = 100 ares
Therefore, 1.6 hectares = 1.6 × 100 ares
= 160 ares.
ANSWER- B
Question: 20 beavers, working together in a constant pace, can build a dam in 6 hours. How many hours will it take 12 beavers that work at the same pace, to build the same dam?
A.10.
B.4.
C.5.
D.6
Answer: A.10.
Explanation: Total Work = 20*6= 120 Beaver hours
12 Beaver * x =120 Beaver hours
x=120/12=10
ANSWER:A
Question: If both 2^2 and 3^4 are factors of the number a*4^3*6^2*13^11, then what is the smallest possible value of a?
A.6
B.9
C.12
D.15
Answer: B.9
Explanation: The number a must include at least 3^2 = 9
The answer is B.
Question: Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly?
A.1 litre
B.7 litre
C.31 litre
D.41 litre
Answer: C.31 litre
Explanation: Solution
Required measurement	= H.C.F of (496, 403, 713) litres
‹=›31 litres.
Answer C
Question: If both a and b belongs to the set {1,2,3,4 }, then the number of equations of the form ax2 + bx + 1 = 0 having real roots is
A.10
B.7
C.6
D.12
Answer: B.7
Explanation: Explanation :
ax2 + bx + 1 = 0 .
For real roots
=> b2 -4ac ≥ 0 .
i.e b2 - 4a(1) ≥ 0 .
i.e b2 ≥ 4a.
For a = 1, 4a = 4, ∴ b = 2, 3, 4
a = 2, 4a = 8, ∴ b = 3, 4
a = 3, 4a = 12, ∴ b = 4
a = 4, 4a = 16, ∴ b = 4
∴ Number of equations possible = 7.
Harsh Mishra a year ago
0 upvotes
Answer : B
Question: For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3).
If 3y = –30, then y =
A. –15
B. –6
C. -3
D. 6
Answer: C. -3
Explanation: (3+2)(y-3)=-30..
x-3=-6..
x=-3
C
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
A.Rs.3000
B.Rs.3300
C.Rs.3600
D.Rs.3900
Answer: C.Rs.3600
Explanation: P = 144(100/5)2 => P = 3600
ANSWER:C
Question: The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is?
A.0.7%
B.8.3%
C.0.3%
D.0.39%
Answer: C.0.3%
Explanation: (1500 * R1 * 3)/100 - (1500 * R2 * 3)/100
= 13.50 4500(R1 - R2)
= 1350
R1 - R2 = 0.3%
Answer: C
Question: In a colony of 70 residents, the ratio of the number of men and women is 4 : 3. Among the women, the ratio of the educated to the uneducated is 2 : 3. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
A.A)1:6
B.B)1:1
C.C)1:8
D.D)1:3
Answer: D.D)1:3
Explanation: Number of men in the colony = 4/7 * 70 = 40.
Number of women in the colony = 3/7 * 70 = 40.
Number educated women in the colony = 2/5 * 30 = 12.
Number of uneducated women in the colony = 3/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30.
Number of educated men and uneducated men are in the ratio 10 : 30 i.e., 1:3.
Answer:D
Question: How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?
A.3251
B.2160
C.1203
D.2564
Answer: B.2160
Explanation: In the given word, we treat the vowels IEO as one letter.
Thus, we have DRCTR (IEO).
This group has 6 letters of which R occurs 2 times and others are different.
Number of ways of arranging these letters = 6!/2! = 360.
Now 3 vowels can be arranged among themselves in 3! = 6 ways.
Required number of ways = (360x6) = 2160.
Ans: B
Question: In a garden, 26 trees are planted at equal distances along a yard 600 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?
A.10
B.8
C.12
D.24
Answer: D.24
Explanation: 26 trees have 25 gaps between them.
Length of each gap = 600/25 = 24
i.e., distance between two consecutive trees = 24
Answer is D.
Question: A sum of money becomes 7/6 of itself in 2 years at a certain rate of simple interest. The rate per annum is?
A.50/9
B.50/7
C.50/6
D.50/8
Answer: C.50/6
Explanation: Let sum = x. Then, amount = 7x/6
S.I. = 7x/6 - x = x/6; Time = 2 years.
Rate = (100 * x) / (x * 6 * 2) = 50/6 %.
Answer:C
Question: Gill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity W for the round trip?
A.24 miles per hour
B.48 miles per hour
C.50 miles per hour
D.53 1/3 miles per hour
Answer: B.48 miles per hour
Explanation: Here's an Average Speed question in which the prompt gives you almost all of the immediate numbers needed to work with.
Driving from LA to SD, we have a distance of 120 miles and a speed of 40 miles/hour.
D = (R)(T)
120 = (40)(T)
120/40 = 3 = T
3 hours to drive to SD
On the way back, she drives 50% FASTER. Gill's return speed is (1.5)(40) = 60 miles/hour.
D = (R)(T)
120 = (60)(T)
120/60 = 2 = T
2 hours to drive to SD
Total Distance = 240 miles
Total Time = 3+2 = 5 hours
Average Speed = 240/5 = 48 miles/hour
Final Answer:
B
Question: Andrew went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.18
B.19
C.19.7
D.21
Answer: C.19.7
Explanation: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
C
Question: B invested $4000 in a business and C invested $3000 in a business. At the end of the year they got $14000 as the profit. Find their share?
A.$8000,$6000
B.$7000,$5000
C.$6000,$4000
D.$6000,$8000
Answer: A.$8000,$6000
Explanation: B:C = 4000:3000
A:B = 4:3
A's share = 14000*4/7 = $8000
B's share = 14000*3/7 = $6000
Answer is A
Question: 40% of a number is more than 20% of 650 by 190. Find the number?
A.997
B.127
C.800
D.128
Answer: C.800
Explanation: (40/100) * X – (20/100) * 650 = 190
2/5 X = 320
X = 800
Answer: C
Question: In expressing a length 81.475 km as nearly as possible with three significant digits, find the percentage error?
A.0.075%
B.0.156%
C.0.031%
D.0.048%
Answer: C.0.031%
Explanation: Error = 81.5-81.475 = 0.028
Required percentage = (0.028/81.475)*100 = 0.031%
Answer is C
Question: A person can row at 9 kmph and still water. He takes 7 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.33
B.28
C.29
D.54
Answer: A.33
Explanation: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 7.5
=> x/10 + x/8 = 15/2 => (4x + 5x)/40 = 15/2 => x
= 33 km.
Answer:A
Question: Set A contains all the even numbers between 8 and 50 inclusive. Set B contains all the even numbers between 108 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
A.2200
B.2550
C.5050
D.6275
Answer: A.2200
Explanation: Set A contains 8, 10, 12... 50
Set B contains 108 , 110 , 112 ... 150
Number of terms in each set = 22
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*22 = 2200
Answer A
Question: The average of 10 numbers is 23. If each number is increased by 6, what will the new average be?
A.36
B.29
C.72
D.29
Answer: B.29
Explanation: Sum of the 10 numbers = 230
If each number is increased by 6, the total increase =
6 * 10 = 60
The new sum = 230 + 60 = 290 The new average = 290/10
= 29.
Answer:B
Question: Little Praveen had $50.50. He spent $12.25 on sweets and gave same money to his two friends and the amount left with him is $31.25. Find how much he spent to two of his friends?
A.$ 16.65
B.$ 18.65
C.$ 19.25
D.$ 16.55
Answer: B.$ 18.65
Explanation: Praveen spent and gave to his two friends a total of
12.25 + 2x= $4.65, x is the amount spent to one friend.
Money left
50.50 -2x = $31.85. Then 2x=$18.65.
correct answer is B) $ 18.65
Question: There are six leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?
A.7 leopard and 3 sheep
B.4 leopard and 7 sheep
C.6 leopard and 4 sheep
D.5 leopard and 1 sheep
Answer: D.5 leopard and 1 sheep
Explanation: D
5 leopard and 1 sheep
since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Question: At 1:00 pm, there were 10.0 grams of bacteria. The bacteria increased to x grams at 4:00 pm, and 19.6 grams at 7:00 pm. If the amount of bacteria present increased by the same fraction during each of the 3-hour periods, how many grams of bacteria were present at 4:00 pm?
A.13.7
B.14.0
C.14.3
D.14.6
Answer: B.14.0
Explanation: Let x be the factor by which the bacteria increases every three hours.
At 4:00 pm, the amount of bacteria was 10x and at 7:00 pm it was 10x^2.
10x^2 = 19.6
x^2=1.96
x=1.4
At 4:00 pm, the amount of bacteria was 10(1.4)=14 grams.
The answer is B.
Question: Over the course of a year, a certain microbrewery increased its beer output by 70 percent. At the same time, it decreased its total working hours by 20 percent. By what percent did this factory increase its output per hour?
A.50%
B.90%
C.112.5%
D.210%
Answer: C.112.5%
Explanation: Let's take the original output to be 100 and the new output to be 170% or 170.
Let's take the original work hours to be 100 hours and the new work hours to be 80% or 80 hours.
The old output per work hour = 100/100 hours or 1.
The new output per work hour = 170/80 or 2.125. So the resulting increase is actually new minus old or 1.125 or 112.5%.
Choice C
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.T
B.E
C.R
D.HG
Answer: B.E
Explanation: The first, fourth, seventh and eleventh letters of the word 'SPHERVLVODS'
The word formed is LESS
The second letter is E.
Answer: Option 'B'
Question: In a camp, there is a meal for 100 men or 200 children. If 130 children have taken the meal, how many men will be catered to with remaining meal?
A.20
B.30
C.35
D.10
Answer: C.35
Explanation: There is a meal for 200 children. 130 children have taken the meal.
Remaining meal is to be catered to 70 children.
Now, 200 children 100 men.
70 children (100/200)	* 70 = 35 men
Answer is C.
Question: 15 men can complete a work in 10 days while 20 boys can complete the same work in 15 days .How many days will 10 men and 10 boys together take to complete the same work
A.10 days
B.11 days
C.12 days
D.13 days
Answer: A.10 days
Explanation: Solution:
Work done by one man in one day=1/(15*10)
Work done by one boy in one day=1/(20*15)
Work done by 10 men and 10 boys in one day=10[ 1/(15*10) + 1/(20*15)]
Days taken=1/Work done by 10 men and 10 boys in one day
=10 days
Answer A
Question: If pq represents a positive two digit number, where p and q are single digit integers, which of the following cannot be true?
A.p+q =9
B.(p)(q)=9
C.p-q = 9
D.q-p= 9
Answer: D.q-p= 9
Explanation: (A) pq = 45 or 63 or 27
(B) pq = 33 or 19
(C) 90
(D) impossible
(E) pq = 91
(D) is impossible because 09 is not a valid two digit number --- if there's a zero in the ten's place, that's just 9, a single digit number. Therefore, no valid two digit number would satisfy (D).
ans D
Question: Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes.
How much time will it take Roy to consume all the five tablets?
A.60 minutes
B.65 minutes
C.50 minutes
D.45 minutes
Answer: A.60 minutes
Explanation: A
60 minutes
Roy will be able to consume all the five tablets in an hour.
Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min.
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
A.31.9
B.31.1
C.31.6
D.31.2
Answer: C.31.6
Explanation: :
100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer: C
Question: Eight mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?
A.20160
B.2400
C.12000
D.36002
Answer: A.20160
Explanation: Arrangement of 8=8!. In half of the cases Frankie will be behind Joey and in half of the cases Joey will be behind Frankie (as probability doesn't favor any of them). So, the needed arrangement is 8!/2=20160.
Answer: A
Question: Line Q has the equation 5y – 3x = 90. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.)
A.58
B.61
C.64
D.67
Answer: D.67
Explanation: 5y - 3x = 90 and so y = 3x/5 + 18
When x = 0, then y = 18.
When y = 0, then x = -30
The slope is 3/5, so the slope of line S is -5/3.
Through the point (-30, 0), 0 = -5(-30)/3 + c
The y-intercept is c = -50.
Thus the perpendicular line S can have y-intercepts from -49 up to 17.
The number of possible lines is 49 + 17 + 1 = 67
The answer is D.
Question: If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 5 children have two children of the same sex and one of the opposite sex?
A.1/3
B.2/3
C.1/4
D.5/16
Answer: D.5/16
Explanation: No of ways of selecting a gender - 2C1
No of ways of selecting any 2 children out of 5 = 5C2
Total possible outcomes - 2^5 (each child can be either a girl or a boy)
Probability=2C1*5C2/2^5= 2*5/2*2*2*2*2=10/32=5/16
Ans=D
Question: The total circumference of two circles is 25. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?
A.5.7
B.6.0
C.4.0
D.9.7
Answer: C.4.0
Explanation: Let r= Radius of smaller circle. Let R = Radius of larger circle
Therefore:
2πr + 2πR = 25
where 2r = R
Thus:
2πr + 4πr = 25
6πr = 25
r = approx 1.33
πR + 2Rπ = 25
3πR = 25
R = approx 2.65
r + R = approx 3.98 = 4.0
Answer : C
Question: The salary of a person was reduced by 14%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
A.10%
B.16.3%
C.13.7%
D.15.1%
Answer: B.16.3%
Explanation: Let the original salary be $100
New salary = $86
Increase on 86=14
Increase on 100 = 14/86* 100 = 16.3%
Answer is B
Question: A and B can complete a work in 30days and 15day. They started doing the work together but after 5days B had to leave and A alone completed the remaining work. The whole work was completed in?
A.10days
B.12days
C.20days
D.18days
Answer: C.20days
Explanation: A+B 1day work = 1/30 + 1/15 = 1/10
Work done by A and B in 10days = 1/10 * 5 = 1/2
Remaining work = 1-1/2 = 1/2
Now 1/30 work is done by A in 1day
1/2 work will be done by A in 30*1/2 = 15days
Total time taken = 15+5 = 20days
Answer is C
Question: Let a1, a2, . . . , ar be r not necessarily distinct positive integers such that
(x + a1)(x + a2) · · · (x + ar) = xr + 230xr−1 + · · · + 2007,
where each missing term on the right has degree between 1 and r − 2
inclusive. What is the value of r ?
A.4
B.12
C.63
D.669
Answer: A.4
Explanation: The conditions imply a1 + a2 + · · · + ar = 230 and a1a2 · · · ar = 2007. One checks that
2007 = 32 · 223, where 223 is prime. We deduce that some aj is 223, two aj’s are 3, and the
remaining aj’s are 1. Since their sum is 230 = 223 + 3 + 3 + 1, we obtain r = 4.
correct answer A
Question: In a school with 652 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of girls in the school is
A.150
B.200
C.250
D.163
Answer: D.163
Explanation: Sol.
Let the number of grils be x.
Then, number of boys = (652 - x).
Then, (11 3/4 × 652)
⇔ 11x + 12(652 - x) ⇔ x = 7824 - 7661 ⇔ 163.
Answer D
Question: Find the annual income derived by investing $ 6800 in 30% stock at 136.
A.550
B.1500
C.250
D.1300
Answer: B.1500
Explanation: By investing $ 136, income obtained = $ 30.
By investing $ 6800, income obtained = $ [(30/136)*6800] = $ 1500.
Answer B.
Question: A sum of money at simple interest amounts to $ 680 in 3 years and to $710 in 4 years. The sum is:
A.$153
B.$698
C.$590
D.$549
Answer: C.$590
Explanation: C
$590
S.I. for 1 year = $(710- 680) = $30.
S.I. for 3 years = $(30 x 3) = $90.
Principal = $(680 - 90) = $590.
Question: A car covers a distance of 984 km in 6 ½ hours. Find its speed?
A.104 kmph
B.187 kmph
C.164 kmph
D.175 kmph
Answer: C.164 kmph
Explanation: 984/6
= 164 kmph
Answer: C
Question: A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 9. What are the coordinates of P?
A.(57/10, 57/10)
B.(3/10, 3/10)
C.(63/10, 63/10)
D.(27/10, 27/10)
Answer: A.(57/10, 57/10)
Explanation: The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.
x = 3 + (6-3)*(9/10) = 3 + 27/10 = 57/10 = y
The answer is A.
Question: At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 48 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 45 cents?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: Let number of Apples = A
number of oranges = B
A+B=10 --- 1
.48 =(.4A + .6 B)/10
=> 48 = 4A + 6B ----2
Solving 1 and 2, we get
A= 6
B= 4
Let the number of oranges put back = C
45*(10-c) = 40*6 + 60(4-C)
=> C= 2
Answer B
Question: If the average (arithmetic mean) of five consecutive negative integers is 10k – 1, what is the difference between the greatest and least of the five integers?
A.4K
B.4k^2 -4k
C.4-4k
D.4
Answer: D.4
Explanation: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 10k - 1
=> n = 50k - 5
Greatest = n + 2 = 50k - 5 + 2 = 50k - 3
Least = n - 2 = 50k - 5 - 2
=> Difference = 50k - 3 - (50k - 7)
= 4
Answer - D
Question: In some code, letters, a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. However, we don’t know which letter represent which number.
Consider the following relationships:
i. a + c = e
ii. b – d = d
iii. e + a = b
A.b = 4, d = 2
B.a = 4, e = 6
C.b = 6, e = 2
D.a = 4, c = 6
Answer: B.a = 4, e = 6
Explanation: Explanation :
From the given equations, we see that , b=10 and d=5.
Now 'a' and 'c' must be 4 and 2 respectively.
So, e = 6.
Answer : B
Question: The cost price of a radio is Rs.2400 and it was sold for Rs.2100, find the loss %?
A.12.5%
B.11%
C.13%
D.15%
Answer: A.12.5%
Explanation: 2400 ---- 300
100 ---- ? => 12.5%
Answer:A