RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Cream costs twice as much as skim milk. A certain brand of milk is 1/3 cream and 2/3 skim milk. What fraction of the cost of this brand is due to the cream?
A.1/3
B.1/2
C.2/5
D.3/5
Answer: B.1/2
Explanation: Let x be the cost of the skim milk in the mixture.
The cost of the cream is (1/2)*x*2 = x.
The total cost is x+x = 2x and the fraction due to the cream is x/2x = 1/2
The answer is B.
Question: The number 110 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
A.18
B.16
C.15
D.14
Answer: A.18
Explanation: 7^2+5^2+6^2=49+25+36 = 110
7+5+6 =18
Hence answer is A
Question: Given two sets A = {1,1,4,4,5,5} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number
A.1/4
B.1/8
C.1/7
D.1/2
Answer: D.1/2
Explanation: One way to look at it:
The number from set A can be ANYTHING.
The number selected from set B will determine whether the sum is odd or even.
For example, if a 4 is selected from set A, we need a 0 from set B to get an even sum.
If a 5 is selected from set A, we need a 1 from set B to get an even sum.
And so on.
So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)
= P(select ANY number from set A)xP(select the number from set B that makes the sum even)
= 1x1/2
= 1/2
= D
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.22000, my total savings for the two-year is
A.s. 8000
B.s. 9000
C.s. 9900
D.s. 9990
Answer: B.s. 9000
Explanation: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (22000 + 35000)
= 66000 - 57000 = Rs. 9000
B
Question: If the SI on a certain sum of money is 4/25 of the sum and the rate per cent equals the number yrs, then the rate of interest/annum is?
A.4%
B.5%
C.6%
D.7%
Answer: A.4%
Explanation: Sol Let the prmcipal be Rs. x
Then the simple interest (1)
Let the me ofinterestp 3 be 1%,
than tune m : ryears
max! max
pm
‘X:5
4%
A
Question: A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 98 are wrong and other digits are correct, then the correct answer would be:
A.553681
B.555181
C.555681
D.556581
Answer: C.555681
Explanation: 987 = 3 x 7 x 47.
So, the required number must be divisible by each one of 3, 7, 47
553681 --> sum of digits = 28, not divisible by 3
555181 sum of digits = 25, not divisible by 3
555681 is divisible by each one of 3, 7, 47.
556581 sum of digits = 30, not divisible by 7
555581 sum of digits = 29, not divisible by 3
so the answer is C.
Question: One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?
A.120 sq. m
B.140 sq. m
C.125 sq. m
D.130 sq. m
Answer: A.120 sq. m
Explanation: Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m
Area = 15 x 8 =120 sq. m
ANSWER:A
Question: Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 60 marks. How many sums did Sandy get correct?
A.18
B.20
C.22
D.24
Answer: D.24
Explanation: Let x be the correct sums and (30-x) be the incorrect sums.
3x - 2(30-x) = 60
5x = 120
x = 24
The answer is D.
Question: The dimensions of an open box are 52, 40 and 29 cms. Its thickness is 2 cms. If 1 cm3 of metal used in the box weighs 0.5 gms, the weight of the box is?
A.6.892 kg
B.9.832 kg
C.6.830 kg
D.6.832 kg
Answer: D.6.832 kg
Explanation: Explanation:
52 * 40 * 29 = 60320
48 * 36 * 27 = 46650
------------
13664
13664 * 1/2 = 6832 => 6.832 kg
Answer: Option D
Question: How many liters of water must be evaporated from 50 liters of a 4 percent sugar solution to get a 5 percent sugar solution?
A.4
B.6
C.8
D.10
Answer: D.10
Explanation: Let x be the amount that needs to be evaporated.
0.04(50) = 0.05(50-x)
0.05x = 2.5 - 2
x = 0.5/0.05 = 10 liters
The answer is D.
Question: An urn contains 4 white 6 black and 8 red balls . If 3 balls are drawn one by one without replacement, find the probability of getting all white balls.
A.1/209
B.1/204
C.1/207
D.1/202
Answer: B.1/204
Explanation: Explanation:
Let A, B, C be the events of getting a white ball in first, second and third draw respectively, then
Required probability =
=
Now, P(A) = Probability of drawing a white ball in first draw = 4/18 = 2/9
When a white ball is drawn in the first draw there are 17 balls left in the urn, out of which 3 are white
Since the ball drawn is not replaced, therefore after drawing a white ball in the second draw there are 16 balls left in the urn, out of which 2 are white.
Hence the required probability
Answer: B) 1/204
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.3629
B.3608
C.rs.3600
D.3613
Answer: C.rs.3600
Explanation: P = 144( 100 / 5)2 => P
= 3600
Answer:C
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is?
A.4%
B.4.04%
C.4.14%
D.5%
Answer: B.4.04%
Explanation: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404	x 100	%	= 4.04%
100 x 100
B)
Question: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/3 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
A.0
B.1/15
C.2/15
D.1/6
Answer: D.1/6
Explanation: Suppose the water in each jug is L liters
CX x (1/3) = L
CX = 3L liters
CX is capacity of X
CY x (2/3) = L
CY = 3L/2 liters
CY is capacity of Y
Now, Y is 3L/2 - L empty = L/2 empty
So, we can put only L/2 water in jug Y from Jug X
Jug X's remaining water = L - L/2 = L/2
Fraction of X which contains water = water / CX
= (L/2)/ 3L
= 1/6
Answer will be D
Question: How many integers n greater than and less than 100 are there such that,if the digits of n are reversed, the resulting integer is n+9 ?
A.5
B.6
C.7
D.8
Answer: D.8
Explanation: (10x+y)=(10y+x)+9
=> 9x-9y=9
=> x-y=1
and only 8 numbers satisfy this condition and the numbers are 21,32,43,54,65,76,87,98
ANSWER:D
Question: An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o’clock in the afternoon?
A.120°
B.90°
C.180°
D.320°
Answer: A.120°
Explanation: Sol.
Angle traced by the hour hand in 4 hours = [360/12 * 4]° = 120°
Answer A
Question: How many ways are there to select a subcommittee of 11 members from among a committee of 17?
A.12376
B.19448
C.28791
D.27711
Answer: A.12376
Explanation: Explanation:
Since it does not matter what order the committee members are chosen in, the combination formula is used.
Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.
C(17,11)= 12,376
Answer: A
Question: The sum of three consecutive even numbers is 93. Find the middle number of the three?
A.14
B.35
C.39
D.31
Answer: D.31
Explanation: Middle value =93/3
=31
Ans D
Question: A boy has 9 trousers and 15 shirts. In how many different ways can he select a trouser and a shirt?
A.100
B.140
C.104
D.135
Answer: D.135
Explanation: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 15 = 135 ways.
D
Question: The average age of husband, wife and their child 3 years ago was 25 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
A.22
B.40
C.34
D.21
Answer: C.34
Explanation: Explanation:
Sum of the present ages of husband, wife and child = (25 x 3 + 3 x 3) years = 84 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (84 - 50) years = 34 years.
Answer: C
Question: The effective annual rate of interest corresponding to a nominal rate of 14% per annum payable half-yearly is?
A.16.06%
B.16.07%
C.16.08%
D.14.49%
Answer: D.14.49%
Explanation: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 7/100)2] = Rs. 14.49 Effective rate = (114.49 - 100) = 14.49%
ANSWER:D
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
A.1877 sq m
B.1976 sq m
C.4312 sq m
D.1987 sq m
Answer: C.4312 sq m
Explanation: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer:C
Question: In a certain province in France there are 13 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
A.76
B.78
C.75
D.98
Answer: B.78
Explanation: 1 city needs 12 roads to connect directly to the rest => 13 city needs 13*12 roads.
One road is counted twice => the number of road needed is 13*12/2 = 78
Answer B
Question: At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:40 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?
A.0.5 + (p - 0.5s)/(r + s)
B.(p - 0.5s)/(r + s)
C.0.5 + (p - 0.5r)/r
D.(p - 0.5r)/(r + s)
Answer: D.(p - 0.5r)/(r + s)
Explanation: The distance A is going to cover between 1:00 and 1:30
= .5r
now the distance between the two trains = (p-.5r)
the relative velocity = (r-(-s)) = r+s
From 1:30, time is going to take when they meet = (p-.5r)/(r+s)
so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]
ans is D
Question: The cost price of 30 articles is the same as the selling price of x articles. If the profit is 20%, what is x?
A.20
B.21
C.23
D.25
Answer: D.25
Explanation: Let the cost price = y
The cost price of 30 articles = 30y
The selling price of x articles = 1.20y*x
1.20y*x = 30y
x = 30 / 1.2 = 25
The answer is D.
Question: A man can row 5 kmph in still water. When the river is running at 2.3 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.2.91
B.3.48
C.2.98
D.3.78
Answer: D.3.78
Explanation: M = 5
S = 2.3
DS = 6.3
US = 2.7
x/6.3 + x/2.7 = 1
x = 1.89
D = 1.89* 2 = 3.78
Answer: D
Question: D is the set of all the multiples of 3 between 30 and 100. E is the set of all the factors of 400. Set D and Set E have how many numbers in common?
A.1
B.0
C.3
D.5
Answer: B.0
Explanation: D is a set of multiples of 3.
400 is NOT a multiple of 3, hence none of its factors is a multiple of 3.
Therefore, those two sets won't have any overlap.
Answer: B
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
A.267 m
B.420 m
C.167 m
D.287 m
Answer: B.420 m
Explanation: Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer:B
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
A.4 1/8 km
B.5 4/8 km
C.6 1/8 km
D.4 3/8 km
Answer: D.4 3/8 km
Explanation: D
4 3/8 km
RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8 = 4 3/8 km
Question: Rasik walked 20 m towards north. Then he turned right and walks 30 m. Then he turns right and walks 35 m. Then he turns left and walks 15 m. Finally he turns left and walks 15 m. In which direction and how many metres is he from the starting position?
A.23
B.38
C.37
D.45
Answer: D.45
Explanation: 45 m East
Answer: D
Question: If 10^(b-1)< 0.000125 <10^b, what is the value of an integer b?
A.-4
B.-3
C.-2
D.3
Answer: B.-3
Explanation: -> Multiply 10^6- > (10^6){10^(b-1)}<125<(10^6)(10^b) -> 125 is bigger than 100
-> (10^6)(10^(b-1))=100 -> 10^(6+b-1)=10^2, b+5=2 -> b=-3
Thus, the answer is B
Question: A chair is bought for Rs.900/- and sold at Rs.810/- find the loss percentage?
A.10% Loss
B.20% Loss
C.30% Loss
D.40% Loss
Answer: A.10% Loss
Explanation: Formula = (Selling price ~ Cost price)/Cost price * 100
= (810 ~ 900)/900 = 10% Loss
A)
Question: At 1:00, Annie starts to bicycle along a 84 mile road at a constant speed of 14 miles per hour. Thirty minutes earlier, Scott started bicycling towards Annie on the same road at a constant speed of 12 miles per hour. At what time will they meet?
A.2:30
B.3:00
C.4:00
D.5:00
Answer: C.4:00
Explanation: In the first 30 minutes, Scott can travel 6 miles, so there are 78 miles left.
Together Annie and Scott can complete 26 miles.
78/26 = 3, so they will meet 3 hours after 1:00.
The answer is C.
Question: How many integers from 20 to 150, inclusive, are divisible by 3 but not divisible by 7?
A.37
B.40
C.42
D.45
Answer: A.37
Explanation: We should find # of integers divisible by 3 but not by 3*7=21.
# of multiples of 21 in the range from 20 to 150, inclusive is (147-21)/21+1=7;
44-7=37.
Answer: A.
Question: The product of all the prime numbers less than 12 is closest to which of the following powers of 10 ?
A.10^7
B.10^4
C.10^8
D.10^5
Answer: B.10^4
Explanation: Product of Prime numbers less than 12 is 2*3*5*7*11
2*5=10 .
10*11*3*7 = 10*10*3*10 (approximately) ~ Product will be >10^3 <10^5 i.e. 10^4
B is the answer
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is?
A.Rs. 112.75
B.Rs. 121.75
C.Rs. 124.75
D.Rs. 118.75
Answer: C.Rs. 124.75
Explanation: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
A.$20000
B.$15000
C.$12000
D.$10000
Answer: A.$20000
Explanation: Since investment doubles in 70/r years, then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).
Answer: A.
Question: In an intercollegiate competition that lasted for 3 days, 115 students took part on day 1, 80 on day 2 and 100 on day 3. If 50 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 40 took part on all three days, how many students took part only on day 3?
A.20
B.35
C.40
D.55
Answer: A.20
Explanation: Day 1&2 = 50; Only Day 1&2 (50-40) = 10,
Day 2&3 = 70; Only Day 2&3 (70-40) = 30,
Only Day 3 = 100 - (10+30+40) = 20
Answer:A
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.227
B.177
C.120
D.288
Answer: C.120
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.Answer:C
Question: If d is a positive integer, and if the units' digit of d^2 is 4 and the units' digit of (d + 1)^2 is 1, what is the units' digit of (d + 2)^2 ?
A.	0
B.	2
C.	4
D.	6
Answer: A.	0
Explanation: A for me.
_1² = _1
_2² = _4
_3² = _9
_4² = _6
_5² = _5
_6² = _6
_7² = _9
_8² = _4
_9² = _1
_0² = _0
On the list, the only number that squared has the units digit = 4 preceding a number that squared has the units digit = 1 is the _8.
So, d = _8, that has square 4. The next square is 1 andnext nextsquare is 0.
Question: Find the number of square tiles to cover the floor of a room measuring 10.5 m * 9.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
A.422
B.476
C.1440
D.428
Answer: C.1440
Explanation: Floor area to be covered by tiles = 10 * 9 = 90
tiles area = 0.25 * 0.25 =0.0625
No. of tiles = 90/0.0625 = 1440
Answer : C
Question: If p=25*343*9/1575, how many digits are in p?
A.7
B.2
C.1
D.4
Answer: B.2
Explanation: p = 25 * 343 * 9 / 1575
p = 5^2 * 7^3 * 3^2 / (5^2 * 3^2 * 7)
p = 7 ^ 2
p = 49
Ans: B
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
A.8
B.7
C.6
D.5
Answer: C.6
Explanation: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) = 42 years.
Required difference = (42 - 36) = 6 years.
Answer: C
Question: How many four digit even numbers do not use any digit more than once
A.1720
B.2160
C.None of these
D.2460
Answer: C.None of these
Explanation: The Way i solved it is
A B C D ( thousand , hundreds, tens, units)
D can be 0 2 4 6 8 ( any of the 5 digits )
A can be anything except (D or 0) so 8 possibilities
C can be anything execpt A and B so 8 possibilities
B can be anything execpt ( A D C ) so 7 possibilities
total ways are 8 * 7 * 8 * 5 = 2240
Ans : C
Question: Given that 0 < a < b < c < d, which of the following the largest ?
A.(c+d) / (a+b)
B.(a+d) / (b+c)
C.(b+c) / (a+d)
D.(b+d) / (a+c)
Answer: A.(c+d) / (a+b)
Explanation: Explanation :
For the fraction to be largest, denominator should be minimum and numerator should be maximium.
Here a and b is minimum which is in denominator of option 1. and c and d is maximum which is also in the numerator of option 1.
Hence 1.) (c+d) / (a+b
Answer : A
Question: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
A.1979
B.1456
C.1699
D.1485
Answer: D.1485
Explanation: 22/7 * 14 * 3/2 * 3/2 = 99 m2
99 * 15
=1485
Answer:D
Question: If a new town has 350 residents, and the population doubles every 10 years, what will be its population after 75 years?
A.63357 residents
B.9051 residents
C.12068 residents
D.15075 residents
Answer: A.63357 residents
Explanation: 350*2^(75/10)=350*2^7.5=100*181.02=63357
The answer is A.
Question: If 4f^4 − 41f^2 + 100 = 0, then what is the sum of the two greatest possible values of f ?
A.4
B.9/2
C.7
D.41/4
Answer: B.9/2
Explanation: just forget about the value of f^4 for the moment and let f^2= X. (its better to work with power of 2 than 4)
now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.
so f^2 = 4 and 25/4
so f= +2 and minus 2 and +5/2 and minus 5/2
The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
A.45%
B.54%
C.57%
D.60%
Answer: C.57%
Explanation: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Question: If X and Y are consecutive integers (Y>X), which of the following statements could be false?
1. The multiplication XY is an even number.
2. (Y/X) > 1.
3. (X + Y) is always an odd number.
A.1 only
B.2 only.
C.1 and 2 only.
D.1 and 3 only.
Answer: B.2 only.
Explanation: Consecutive numbers means that one will be even and one will be odd.
1. The multiplication XY is an even number. Odd*even= even. True
2. (Y/X) > 1.
If Y= 1 and X=0
Y/X= Undefined
Or if Y =-1 and X=-2
Y/X= 1/2 <1
Could be False
3. (X + Y) is always an odd number.
Even+ Odd= Odd. True
B is the answer
Question: Of the 100 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
A.20
B.30
C.50
D.80
Answer: A.20
Explanation: Full time employee who have NOT worked for at least one year = a
Full time employee who have worked for at least one year = b
NON Full time employee who have worked for at least one year = c
NON Full time employee who have NOT worked for at least one year = d
a+b+c+d = 150
a+b = 80
i.e. c+d = 70
b+c = 100
i.e. a+d = 50
d = 20
i.e. c = 70-20 = 50
i.e. b = 100-50 = 50
i.e. a = 80-50 = 30
b = 20
Answer: Option A
Question: An alloy weighing 26 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?
A.6
B.9
C.12
D.34
Answer: D.34
Explanation: In 24 ounces, gold is 26 * (70/100) = 18.2 ounces. Now we add x ounces of pure gold to make it 90% gold.
So 18.2 + x = (24 + x)* 90/100 => x =34.
Answer is D.
Question: By approximately what percent is x greater than 1/3 if (2/3)(x) = 1?
A.173%
B.516%
C.461%
D.350%
Answer: D.350%
Explanation: what percent is x greater than 1/3 if (2/3)(x) = 1?
=> x = 3/2
% change =[(3/2 -1/3) /(1/3) ] * 100
= 350
Ans D, 350%
Question: By travelling at 50 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
A.23 kmph
B.24 kmph
C.25 kmph
D.26 kmph
Answer: C.25 kmph
Explanation: Let the time taken to reach the destination be 3x hours. Total distance = 50 * 3x = 150x km
He covered 2/3 * 150x = 100x km in 1/3 * 3x = x hours So, the remaining 50x km, he has to cover in 2x hours. Required speed = 50x/2x
=25 kmph.
Answer: C
Question: If e = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =
A.-2
B.-1
C.0
D.2
Answer: D.2
Explanation: Let us transform the formula:
e = (x – 5)² + (x +1)² – 6 =
x² – 10x + 25 + x² + 2x + 1 – 6 =
2x² – 8x + 20 = 2 × (x² – 4x + 10) =
2 × ((x² – 4x + 4) + 6) =
2 × ((x – 2)² + 6)
Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.
x – 2 = 0
x = 2
The correct answer is choice (D).
Question: Three times the first of three consecutive odd integers is 4 more than twice the third. The third integer is:
A.9
B.11
C.13
D.16
Answer: D.16
Explanation: Let the three integers be x, x + 2 and x+ 4.
Then,
3x = 2(x + 4) + 4
x = 12
Third integer = x + 4 = 16.
ANSWER:D
Question: A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
A.5.15 kmph
B.4.14 kmph
C.4.25 kmph
D.4.4 kmph
Answer: B.4.14 kmph
Explanation: in 100 m race
A's speed is 5kmph so in m/s it is 5*5/18
time taken by A=D/S=100*18/25=72 sec
Now
B would take 72+8=80 seconds
Speed of B is=(100-8)=(92/80)*18/5= 4.14kmph
ANSWER:B