RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?
A.28
B.29
C.31
D.35
Answer: A.28
Explanation: Explanation:
Clearly, we have :
A = B - 3 ...(i)
D + 5 = E ...(ii)
A+C = 2E ...(iii)
B + D = A+C = 2E ...(iv)
A+B + C + D + E=150 ...(v)
From (iii), (iv) and (v), we get: 5E = 150 or E = 30.
Putting E = 30 in (ii), we get: D = 25.
Putting E = 30 and D = 25 in (iv), we get: B = 35.
Putting B = 35 in (i), we get: A = 32.
Putting A = 32 and E = 30 in (iii), we get: C = 28.
Answer: A
Question: Two employees X and Y are paid a total of Rs. 330 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
A.s.150
B.s.200
C.s.250
D.s.350
Answer: A.s.150
Explanation: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 330
But x = 120% of y = 120y/100 = 12y/10
âˆ´12y/10 + y = 330
â‡’ y[12/10 + 1] = 330
â‡’ 22y/10 = 330
â‡’ 22y = 3300
â‡’ y = 3300/22 = 300/2 = Rs.150
A)
Question: A certain car increased its average speed by 4 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 20 miles per hour, how many miles did the car travel in the third 5-minute interval?
A.1.0
B.1.5
C.2.0
D.2.5
Answer: D.2.5
Explanation: In the third time interval the average speed of the car was 20+4+5=29 miles per hour;
In 5 minutes (1/12 hour) at that speed car would travel 29*1/12=2.5 miles.
Answer: D.
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
A.868
B.869
C.865
D.860
Answer: D.860
Explanation: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Question: Find the lowest common multiple of 24, 36 and 40.
A.360
B.420
C.510
D.320
Answer: A.360
Explanation: LCM=2*2*2*3*3*5=360.
Answer is A
Question: The measurement of a rectangular box with lid is 25cmx4cmx18cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
A.11.12
B.10.11
C.72
D.10.66
Answer: D.10.66
Explanation: d=4, r=2;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*2*2*2= 10.66πcm3 ANSWER:D
Question: Length of a rectangular plot is 10 mtr more than its breadth. If the cost of fencing the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
A.55 m
B.60 m
C.80 m
D.82 m
Answer: A.55 m
Explanation: Let breadth = x metres.
Then, length = (x + 10) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 10) + x] = 200
2x + 10 = 100
2x = 90
x = 45.
Hence, length = x + 10= 55 m
A
Question: The concentration of spirit in three different vessels A, B and C are 30%, 50% and 25% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.
A.32.54%
B.33%
C.34.67%
D.35%
Answer: C.34.67%
Explanation: Quantity of spirit in new solution=(4*30/100)+(5*50/100)+(6*25/100)=1.2+2.5+1.5=5.2 liters
So % concentration of spirit=100*5.2/(4+5+6)=34.67%
ANSWER:C
Question: The side of a rhombus is 24 m and length of one of its diagonals is 18 m. The area of the rhombus is?
A.410.47
B.403.47
C.420.47
D.400.47
Answer: D.400.47
Explanation: area of the rhombus = 1/2 * p * √4(a)2 - (p)2
a= 24 ; p = 18
A=1/2 * 18 *√4(24)2 - (18)2
=1/2 * 18 *√2304 - 324
=1/2 * 18 *√1980
A =400.47
Answer : D
Question: If the C.I. on a sum for 2 years at 12 1/2 % per annum is Rs. 510, the S.I. on the same sum at the same rate for the same period of time is?
A.298
B.278
C.299
D.480
Answer: D.480
Explanation: Let the sum be Rs. P. Then,
[P(1 + 25/(2 * 100))2 - P] = 510
P[(9/8)2 - 1] = 510.
Sum = Rs. 1920
So, S.I. = (1920 * 25 * 2) / (2 * 100) = Rs. 480
Answer: D
Question: If the number a60,858,61b is evenly divisible by 88, what are the values of a and b?
A.b = 6, a = 6
B.b = 2, a = 3
C.b = 2, a = 1
D.b = 4, a = 6
Answer: A.b = 6, a = 6
Explanation: a60,858,61b, divisible by 88.
Factors of 88 = (8)(11)
Divisible by 8: if the last 3 digits of the number are divisible by 8.
61b/8 => 616/8 = 77 => b = 6
Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.
a6085861-6 => a608585-5 => a60858-0 => a6085-8 => a607-7 => a60-0 => a6-0 => a6 => 66/11 = 6.
So a = 6.
Answer: A
Question: From a pack of cards, two cards are drawn one after the other, with replacement. What is the probability that the first card is a club and the second card is a king or queen?
A.2/13
B.3/13
C.1/26
D.1/52
Answer: C.1/26
Explanation: P(club) = 1/4
P(king or queen) = 2/13
P(club then a king/queen) = 1/4 * 2/13 = 1/26
The answer is C.
Question: Select the non termination decimal among the following.
A.22/3
B.3/4
C.4/5
D.7/8
Answer: A.22/3
Explanation: A. Non terminating decimal means that 22/3 = 7.33333 and so on.
Question: Two pipes A and B can fill a cistern in 9 and 18 minutes respectively, and a third pipe C can empty it in 24 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
A.6 min
B.7 min
C.8 min
D.10 min
Answer: C.8 min
Explanation: 1/9 + 1/18 - 1/24
= 1/8
8/1= 8
Answer:C
Question: How many liters of water must be evaporated from 50 liters of a 8-percent sugar solution to get a 10-percent solution?
A.8
B.10
C.12
D.14
Answer: B.10
Explanation: 8% of a 50 liter solution is 4L which is 10% of the solution at the end.
The solution at the end must be 40 L.
We need to evaporate 10 liters.
The answer is B.
Question: The salary of a worker is first increased by 20% and afterwards reduced by 20%. What is the net change in the worker's salary?
A.4% decrease
B.8% decrease
C.4% increase
D.8% increase
Answer: A.4% decrease
Explanation: Let x be the original salary.
The final salary is 0.8(1.2x) = 0.96x
The answer is A.
Question: A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 36 years and that of the grandchildren is 6 years. What is the average age of the family?
A.28 4â„7 years
B.31 5â„7 years
C.32 years
D.27 1â„2 years
Answer: C.32 years
Explanation: Required average = (67Ã—2+36Ã—2+6Ã—3/2+2+3)
=224/7
= 32 years
Answer C
Question: Laura has a deck of standard playing cards with 18 of the 54 cards designated as aheart.If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
A.1/4
B.1/3
C.5/26
D.12/42
Answer: B.1/3
Explanation: No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart.
If there is no replacement then how is the (P) that the 10th card is 18/54 ??
there are many cases here to be considered here if there is no replacement such as:
H- Denotes heart X-may be any diamond, spade or club.
1. HXXXXXXXXH
2. HHXXXXXXXH
3. HHHXXXXXXH
.
.
.
.
.
9. HHHHHHHHHH
10. XXXXXXXXXH
All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them.
For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 18/54 = 1/3 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question ----how do we determine that the cards are replaced or not?? based on the question given ....
B
Question: A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer he has 6 black and 8 blue socks. What is the probability that his first pick was a black sock, but his second pick was a blue sock?
A.24/91
B.24/90
C.24/97
D.24/95
Answer: A.24/91
Explanation: This is a case of without replacement. We have to multiply two probabilities. 1. Probability of picking up a black sock, and probability of picking a blue sock, given that first sock is black.
6C114C1×8C113C1=24/91
Answer:a
Question: If y exceeds x by 20%, then x is less than y by?
A.16 2/8%
B.16 8/3%
C.16 2/3%
D.76 2/3%
Answer: C.16 2/3%
Explanation: X=100	y=120
120------20
100-------? => 16 2/3%
Answer:C
Question: 1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?
A.82 days
B.26 days
C.32 days
D.34 days
Answer: C.32 days
Explanation: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1200*x
x = 32 days
Answer:C
Question: Find the angle between the hour hand and the minute hand of a clock when 3.25.
A.47 1/2°
B.45 1/2°
C.48 1/2°
D.46 1/2°
Answer: A.47 1/2°
Explanation: angle traced by the hour hand in 12 hours = 360°
Angle traced by it in three hours 25 min (ie) 41/12 hrs=(360*41/12*12)° =102 1/2°
angle traced by minute hand in 60 min. = 360°.
Angle traced by it in 25 min. = (360 X 25 )/60= 150°
Required angle = 1500 – 102 1/2°= 47 1/2°
Answer is A.
Question: A rectangular rug with side lengths of 2 feet and 6 feet is placed on a square floor that has an area of 65 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?
A.A.3/16
B.1/4
C.C.1/2
D.53/65
Answer: D.53/65
Explanation: Area of the rectangular rug = 2*6 = 12
Fraction not covered by the rug = (Total Area - Rug area) / Total Area
= (65 - 12)/65
= 53/65=D
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
A.34
B.97
C.37
D.80
Answer: D.80
Explanation: 1/2 * d (10 + 6) = 640
d = 80
Answer: D
Question: 2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 16 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?
A.12 km/hr
B.16.5 km/hr
C.17 km/hr
D.18 km/hr
Answer: A.12 km/hr
Explanation: Explanation :
Total distance covered by B=16*6=96kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=96/8=12 km/hr
Answer : A
Question: A trader sells 85 meters of cloth for Rs. 8500 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
A.Rs. 80
B.Rs. 85
C.Rs. 90
D.Rs. 95
Answer: B.Rs. 85
Explanation: SP of 1m of cloth = 8500/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 100 - Rs. 15 = Rs. 85.
ANSWER:B
Question: How much more would Rs.15000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
A.A)Rs.3,961.50
B.B)Rs.3,962.50
C.C)Rs.3,963.50
D.D)Rs.3,964.50
Answer: A.A)Rs.3,961.50
Explanation: 15000(11/10)4 - 15000(6/5)2 = 3,961.50
ANSWER:A
Question: Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 7 weeks have been $406, $413, $420, $436, $395, $410, $360. What must his average (arithmetic mean) income over the next two weeks be to increase his average weekly income to $500 over the 9-week period?
A.$570
B.$790
C.$630
D.$830
Answer: D.$830
Explanation: OFFICIAL SOLUTION:
(D) First, we need to add up the wages over the past 7 weeks: $406 + $413 + $420 + $436 + $395 + $410 + $360 = $2840.
To average $500 over 9 weeks, the salesman would need to earn: $500 × 9 = $4500.
Subtract $2840 from $4500 to determine how much he would need to earn, in total, over the next 2 weeks to average $500 for the 9 weeks: $4500 – $2840 = $1660.
Dividing $1660 by 2 will give us the amount he needs to earn on average over the next 2 weeks: $1660/2 = $830.
The correct answer is choice (D).
Question: A student was asked to find the arithmetic mean of the numbers 13,31,78,92,115,103,68,10,57,21,34 and a. He found the mean to be 60. What should be the remainder in the place of a?
A.98
B.105
C.120
D.165
Answer: A.98
Explanation: We have (13+31+78+92+115+103+68+10+57+21+34+a) / 12 = 60
622+a= 720
a = 98
Answer is A
Question: How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a vowel, and each letter can be used only once?
A.21
B.42
C.120
D.600
Answer: C.120
Explanation: Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)
Fifth letter can be filled in 1 Ways ( As the question states that the last letter has to be a vowel)
Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and Fifth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
Fourth letter can be filled in 3 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 3 ways x 1 ways = 120
Answer C
Question: Average of 80 numbers are 42. When 5 more numbers are included, the average of 85 numbers become 45. Find the average of 5 numbers.
A.82
B.89
C.93
D.98
Answer: C.93
Explanation: Solution: Total of 80 numbers = 80*42 = 3360;
Now, total of 85 numbers = 85*45 = 3825;
Hence, sum of 5 numbers = 3825-3360 = 465;
Average of five numbers = 465/5 = 93.
Solve while reading Method:
Average of 80 number was 42, when 5 more numbers are added average become 45, that means 3 is given to each number to make their average 45 and 5 numbers also keep 45 as to maintain the entire average.
So, the sum of five numbers = 240+225 = 465,
Hence, average of five numbers = 93.
Answer: Option C
Question: A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.10.50 less, he would have gained 30%. Find the cost of the article.
A.30
B.40
C.50
D.60
Answer: C.50
Explanation: Let C.P=100
Gain=25%
S.P=125
Supposed C.P=80
Gain=30%
S.P=(130*80)/100=104
Diff=(125-104)=21
Diff 21 when C.P=100
then Diff 10.50 when C.P=(100*10.50)/21=50
ANSWER:C
Question: if abcd is four digit highest number that is divisible by 10.9.22 give remainder 4,9,10. find bc
A.75
B.89
C.95
D.98
Answer: C.95
Explanation: 9954.............>95
ANSWER:C
Question: Which of the following numbers completes
the sequence 3, 8, 14, 21, 29, 38, 48, 59, 71, 84, ___?
A.35
B.36
C.37
D.98
Answer: D.98
Explanation: The numbers increase at a somewhat steady rate, so you have to figure out how much
you have to add to each number to produce the next in the sequence: 3 + 5 = 8; 8 + 6 = 14;
14 + 7 = 21; 21 + 8 = 29, and so on. The rule for the sequence is to add successively larger
numbers to each number; therefore, the next number is 84 + 14 = 98.
correct answer D)98
Question: Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points?
A.25 Fruits
B.20 Fruits
C.23 Fruits
D.21 Fruits
Answer: A.25 Fruits
Explanation: A
25 Fruits
Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.
For the first sack:
He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,
(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M
M = 10
Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.
Now he must get rid of the second sack.
For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.
(Space in First Sack) N = (Remaining fruits in second sack) 30 – N
N = 15
Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,876,397 minutes earlier? (Assume standard time in one location.)
A.6:30
B.6:25
C.6:17
D.6:12
Answer: A.6:30
Explanation: 6:27 minus 2,876,397 in any way must end with 0.
The only answer choice which ends with 0 is A.
The answer is A.
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
A.50 km
B.16 km
C.18 km
D.29 km
Answer: A.50 km
Explanation: Let the actual distance traveled be x km. Then,
x/10 = (x + 20)/14
4x - 200 =>x = 50 km.
Answer:a
Question: Which of the following is not a leap year?
A.700
B.800
C.900
D.1000
Answer: A.700
Explanation: The century divisible by 400 is a leap year.
The year 700 is not a leap year.
Answer: Option A
Question: Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 144 seconds. The length of each train is:
A.82m
B.150m
C.172m
D.200m
Answer: D.200m
Explanation: Explanation:
The relative speed of train is 46-36 = 10 Km/hr = (10 X 5) / 18 = 25/9 m/s10×518=259m/s
In 144 secs the total distance traveled is 144x25/9 = 400 m.
Therefore the length of each train is = 400/2 = 200 m.
Answer D
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
A.8/41
B.9/31
C.9/42
D.7/31
Answer: C.9/42
Explanation: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
A.33 1/8%
B.33 1/2%
C.33 1/3%
D.33 6/3%
Answer: C.33 1/3%
Explanation: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Question: Simplify: 5793405 x 9999
A.57925286595
B.57928256595
C.57989252865
D.57568226348
Answer: B.57928256595
Explanation: 5793405 x 9999=5793405(10000-1)
=57934050000-5793405
=57928256595.
Answer is B
Question: A man buys a cycle for Rs. 1600 and sells it at a loss of 12%. What is the selling price of the cycle?
A.1410
B.1420
C.1430
D.1408
Answer: D.1408
Explanation: S.P. = 88% of Rs. 1600 = 88/100 x1600= Rs. 1408
answer : D
Question: Angela, Bernie, and Colleen can complete a job, all working together, in 3 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 4 hours. How long would it take Colleen, working alone, to complete the entire job?
A.8 hours
B.10 hours
C.12 hours
D.16 hours
Answer: C.12 hours
Explanation: A+B+C complete the job in 3 hours.
A+B complete the job in 4 hours.
A+B and C complete the job in 3 hours -->1/(A+B) + 1/C = 1/3-->1/4+1/C=1/3 ----> C=12 hours. ANS C
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
A.24.5
B.28.5
C.30
D.Data inadequate
Answer: C.30
Explanation: Explanation:
Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
ANSWER IS C
Question: The average number of shirts with Salman, Ambani and Dalmiya is 40, if all of them reached a shopping mall in Delhi and purchased 8 shirts each of them then average number of shirt each of them now has
A.66
B.63
C.48
D.can't be determined
Answer: C.48
Explanation: Answer
Required average
= Old average + New average
= 40 + 8 = 48
Correct Option: C
Question: A positive whole number has factors of 2 and 4. The number MUST be divisible by: I. 16 II. 8 III. 4
A.I & II
B.II & III
C.III
D.I
Answer: D.I
Explanation: 4 , 8 is not divisible by 16.But 16 is divisible by 2,4,8
So answer is I
Answer : D
Question: What is the probability of a/b will be an integer when a=2x3y and b=2l3m and all of x, y, I, m are positive integers?
A.1/6
B.2/3
C.1/2
D.1/4
Answer: D.1/4
Explanation: There r 4 numbers to be filled i.e, x,y,l,m
out of which only one condition satisfies to get a/b as integer
ANSWER:D
Question: A Fruit Seller buys lemons at 2 for a rupee and sells them at 5 for three rupee. His profit percentage is
A.30%
B.50%
C.60%
D.20%
Answer: D.20%
Explanation: C.P of 2 Lemons= Re 1
So, C.P of 5 Lemons= 5*1/2=5/2
S.P of 5 Lemons= Rs 3
Therefore, Profit Percentage={(3-5/2)5/2}100 =20%
Answer: Option D
Question: 8 3/4 + 7 2/17 - 9 1/15=?
A.7 719/1020
B.9 817/1020
C.9 719/1020
D.6 817/1020
Answer: D.6 817/1020
Explanation: Given sum=8+3/4+7+2/17-(9+1/15)
=(8+7-9)+(3/4+2/17-1/15)
=6+(765+120-68/1020
=6 817/1020
Answer is D
Question: 10^(600) Ã· 10^(580) = ?
A.10^10
B.10^20
C.10^22
D.10^23
Answer: B.10^20
Explanation: 10^(600) Ã· 10^(580) = 10^ (600-580) = 10^20
Answer : B
Question: What decimal fraction is 30 ml of a litre ?
A..3
B..0003
C..003
D.0.03
Answer: D.0.03
Explanation: Answer
Required fraction = 30/1000
= 3/100
= .03
Correct Option: D
Question: Simplify: 896 x 896 - 204 x 204
A.761200
B.761400
C.761800
D.761500
Answer: A.761200
Explanation: (896)^2 - (204)^2 = (896 + 204) (896 - 204) = 1100 x 692 = 761200.
Answer is A.
Question: The sum of digits of a two digit number is 10,The difference between the digits is 6. Find the number
A.85
B.94
C.82
D.72
Answer: C.82
Explanation: Description :
=> x+y=10, x-y=6
Adding these 2x =16
=> x=8, y=2.
Thus the number is 82
Answer C
Question: In a certain supermarket, a triangular display of cans is arranged in 10 rows, numbered 1 through 10 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 150 cans in the entire display, how many cans are in the fifth row?
A.10
B.11
C.13
D.14
Answer: C.13
Explanation: Let x be the number of cans in row 1.
The total number of cans is x + (x+3) + ... + (x+27) =
10x + 3(1+2+...+9) =
10x + 3(9)(10)/2 =
10x + 135
Since the total is less than 150, x must equal 1.
The number of cans in the 5th row is 1 + 3(4) = 13
The answer is C.
Question: Consider a right triangle EBC with length of sides being x,y and z where y represents the hypotenuse , Which of these represent the radius of the circle which is inscribed in triangle EBC
A.[A] x+y+z/3
B.[B] x-y+z/3
C.[C] x-y+z/2
D.[D] (x^2 + y^2 + z^2)/3
Answer: C.[C] x-y+z/2
Explanation: Radius of a circle inscribed in the right triangle EBC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.
Answer: C
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 6m/h. what is the speedof the person while he was going to his office?
A.4km/h
B.9km/h
C.10km/h
D.11km/h
Answer: A.4km/h
Explanation: u = k , v= 3k
{2uv}{u+v}/2uv
\frac{2\times k\times 3k}{(k+3k)}=6
1.5k = 6
k=4km/h
A
Question: Two trains, A and B, started simultaneously from opposite ends of a 75-mile route and traveled toward each other on parallel tracks. Train A, traveling at a constant rate, completed the 75-mile trip in 3 hours; Train B, traveling at a constant rate, completed the 75-mile trip in 2 hours. How many miles had train A traveled when it met train B?
A. 20
B. 22.5
C. 30
D. 37.5
Answer: C. 30
Explanation: As the ratio of the rates of A and B is 2 to 3 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that X would cover 2/(2+3)=2/5 of 75 miles: 75*2/5=30 miles.
Answer: C.