divelab/Sys2Bench huggingface dataset:
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits R are in s(99)?
Options:
A)R=350
B)R=353
C)R=354
D)R=356
E)357
Rationale: Focus on the points where the number of digits in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 =R= 353.B
Answer: B
Question: Two equal containers are filled with a mixture of water and petrol. One of them contains three times as much petrol as in the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to petrol is 3: 2: Find the ratio of water to petrol in each of the original containers.
Options:
A)2:1, 3:4
B)1:3, 1:2
C)2: 3, 4: 1
D)2: 5, 4: 1
E)None of the above
Rationale: In the new mixture, water : petrol = 3 : 2 = 12 : 8
=> The capacity of each container =(12 + 8)/2=10 units
= >The ratios of water to petrol of the containers are 4 : 6 and 8 : 2
= 2 : 3 and 4 : 1
ANSWER:C
Answer: C
Question: Some scientists take their boat, the Vollert, out to an artificial reef they are studying. Nice weather on the way out means they can travel at 12 knots, but a storm blows in and they can only travel at 5 knots on the way home. What was their average speed for the whole trip?
Options:
A)6 knots
B)2.5 knots
C)17 knots
D)7 knots
E)8.5 knots
Rationale: (12 knots +5 knots)/2 = 8.5 knots
Correct option is: E
Answer: E
Question: John was thrice as old as Tom 6 years ago. John will be 9/7 times as old as Tom in 6 years. How old is Tom today?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: J-6 = 3(T-6), so J = 3T-12
J+6 = 9/7 * (T+6)
7J + 42 = 9T + 54
7(3T-12) + 42 = 9T + 54
12T = 96
T = 8
The answer is B.
Answer: B
Question: Calculate the time it will take for a full tank to become completely empty due to a leak given that
the tank could be filled in 7 hours, but due to the leak in its bottom it takes 8 hours to be filled ?
Options:
A)59 hours
B)54 hours
C)59 hours
D)56 hours
E)26 hours
Rationale: Part filled without leak in 1 hour = 1/7
Part filled with leak in 1 hour = 1/8
Work done by leak in 1 hour
=1/7âˆ’1/8=56 hours
Answer:D
Answer: D
Question: Which greatest possible length can be used to measure exactly 12 meter 34 cm, 8 meter 98 cm and 6 meter 65 cm
Options:
A)1cm
B)2cm
C)24cm
D)55cm
E)50cm
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1234 cm, 898cm, 665cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 1.
Option A
Answer: A
Question: In a bag contains 8 White balls and 6 black balls from the bag two balls are taken out at random. Find the Probability that they are of the same color ?
Options:
A)43/91
B)45/91
C)52/91
D)61/91
E)47/91
Rationale: Here S be the sample space so,
n(S) = Number of ways of taken out balls of (8+6) = 14C2 = (14X13)/(2X1)
= 182/2 = 91
E = Event of getting both balls of the same color
Then,n (E) = Number of ways of drawing (2 balls out of 8) or (2 balls out of 6)
= (8C2 + 6C2) = 8 x 7/2 x1 + 6x5/2x1 = 56 /2 + 30/2 = 28 +15 = 43
P(E) = n(E) / n(S) = 43/91
Answer is A
Answer: A
Question: If the square of a Positive Number X is equal to five times the same Number then what is the value of X?
Options:
A)1
B)25
C)8
D)5
E)10
Rationale: X * X = 5X
X = 5
so the correct answer is option D
Answer: D
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.24000. A's share is?
Options:
A)s.7500
B)s.8000
C)s.6000
D)s.5750
E)s.6750
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 24000 = 8000
ANSWER:B
Answer: B
Question: If 1535/ 1038 = a+1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e?
Options:
A)165/2
B)175/2
C)178/3
D)187 by 2
E)197/2
Rationale: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)}
=1+(497/1038) now a=1
=1+{1/(1038/497)}
=1+{1/ (2+42/497)}
=1+{1/(2+1/(497/42)} now b= 2 similarly expand
c=11 d= 1 e=34/8
finally a*b*b*c*d*e
1*2*11*1*34/8
187/2
ANSWER:D
Answer: D
Question: A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?
Options:
A)11 days
B)22 days
C)27 days
D)12 days
E)99 days
Rationale: If A takes x days to do a work then B takes 2x days to do the same work.
--> 1/x+1/2x = 1/18
--> 3/2x = 1/18
--> x = 27 days.
Hence, A alone can finish the work in 27 days.
Answer : C
Answer: C
Question: If shares of two persons in profits are Rs.1600 and Rs.1200 then ratio of their capitals is
Options:
A)3:4
B)2:3
C)4:3
D)1:3
E)1:2
Rationale: profit=time*capital
so 1600:1200=4:3
ANSWER:C
Answer: C
Question: The fourth proportional to 9, 14 and 18 is?
Options:
A)28
B)66
C)88
D)99
E)26
Rationale: (14*18)/9 = 28
Answer: A
Answer: A
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
Options:
A)176
B)190
C)150
D)278
E)292
Rationale: 1/2 * 15 * 20
= 150
Answer:C
Answer: C
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
Options:
A)13
B)28
C)12
D)45
E)21
Rationale: Answer: Option B
any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
Answer: B
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
Options:
A)16 2/3% loss
B)16 7/3% loss
C)16 2/8% loss
D)17 2/3% loss
E)13 2/3% loss
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Answer: A
Question: 1,3,5,7,9,....50 find term of sequnce
Options:
A)1000
B)1200
C)1300
D)1800
E)2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500 .
E
Answer: E
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
Options:
A)3^5
B)2^3
C)5^3
D)2
E)4
Rationale: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 3^5.
Ans: A
Answer: A
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 40.
Options:
A)3
B)4
C)7
D)32
E)35
Rationale: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.
Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form
n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc
and
n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc
So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)
Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form
n = 5a + 1
and
n = 7b + 3
Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.
Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)
Now this question is exactly like the question above. So when you divide n by 40, remainder will be -4 i.e. n will be 4 less than a multiple of 40. So you must add 7 to n to make it a multiple of 40
C
Answer: C
Question: A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed T of the train.
Options:
A)a) 45
B)b) 33
C)c) 48
D)d) 55
E)e) 61
Rationale: Let y be the balance distance to be covered and x be the former speed.
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late
so, y/(3x/4) - y/x = 35/60
4y/3x - y/x = 7/12
y/x(4/3-1)=7/12
y/x*1/3=7/12
y/x=7/4
4y-7x=0 ........ 1
Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late
so, (y-24)/(3x/4) - (y-24)/x = 25/60
4(y-24)/3x - (y-24)/x = 5/12
(y-24)/x (4/3-1) = 5/12
(y-24)/x *1/3 = 5/12
(y-24)*12 = 3x*5
(y-24)*4 = 5x
4y-5x = 96 ....... 2
eq2 - eq1
2x=96
x=48=T
Ans = C
Answer: C
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 90, what is the value of c âˆ’ a?
Options:
A)25
B)90
C)100
D)140
E)It cannot be determined from the information given
Rationale: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=180 --2
subtracting 1 from 2 we have
c-a=90;
ANSWER:B
Answer: B
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
Options:
A)5/21
B)5/28
C)5/27
D)5/29
E)5/25
Rationale: Number of ways of (selecting at least two couples among five people selected) =
As remaining person can be any one among three couples left.
Required probability
= (10 * 6)/252 = 5/21
Answer:A
Answer: A
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
Options:
A)270
B)280
C)290
D)300
E)310
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
A)
Answer: A
Question: The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 7 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
Options:
A)30
B)20
C)18
D)12
E)6
Rationale: Given: mean=21 and SD=7
The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=14 and 2 SD below the mean ismean-2*SD=7 ,so the number of hours that Pat watched television was between 7 and 14 hours.
Answer: D.
Answer: D
Question: Statement: Unemployment allowance should be given to all unemployed Indian youth above 18 yrs of age.
Assumptions:
1) There are unemployed youth in India who needs monetary support.
2) The government has sufficient funds to provide allowance to all unemployed youth.
Options:
A)Only assumption I is implicit
B)Only assumption II is implicit
C)Either I or II is implicit
D)Neither I nor II is implicit
E)Both I and II are implicit
Rationale: I directly follows from the statement and so is implicit. Also, the statement is a suggestion and does not tell about a government policy or its position of funds. So, II is not implicit.
A
Answer: A
Question: In a nationwide poll, N people were interviewed. If 1/6 of them answered yes to question 1, and of those, 1/3 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?
Options:
A)N/9
B)8N/9
C)11N/18
D)17N/18
E)31N/36
Rationale: The number of people who answered yes to both questions is (1/3)(1/6)N = N/18
The number of people who did not answer yes to both is 1 - N/18 = 17N/18
The answer is D.
Answer: D
Question: Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 40 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
Options:
A) 60
B) 80
C) 100
D) 120
E) 140
Rationale: 30% of the members have passed the test, thus 70% have not passed the test.
We also know that 30+40=70 members have not passed the test, thus 0.7*Total=70 --> Total=100.
Answer: C.
Answer: C
Question: Two persons starting from the same place walk at a rate of 10kmph and 12.5kmph respectively. What time will they take to be 10km apart, if they walk in the same direction?
Options:
A)17 hrs
B)4 hrs
C)6 hrs
D)12 hrs
E)16 hrs
Rationale: The relative speed of the boys = 12.5kmph – 10kmph
= 2.5 kmph
Distance between them is 10 km
Time= 10km / 2.5 kmph = 4 hrs
Answer : B
Answer: B
Question: A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,020 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
Options:
A)25
B)30
C)35
D)40
E)45
Rationale: Day 1
2t+3=21
t=9
Day 2
t+3
9+3=12
9r+12(r+15)=1020
r=40
Answer:D
Answer: D
Question: The number of positive integer solutions for the equation x +y +z + t = 18 is
Options:
A)640
B)780
C)380
D)540
E)680
Rationale: The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k
(k-1)C(n-1)- where k is the number and n is number of variable in the equation.
18-1 C 4-1 = 17C3 = 680
Answer : E
Answer: E
Question: A man rows his boat 90 km downstream and 72 km upstream, taking 3 hours each time. Find the speed of the stream?
Options:
A)6
B)5
C)7
D)3
E)2
Rationale: Speed downstream = d/t = 90/3 = 30 kmph
Speed upstream = d/t = 72/(3) = 24 kmph
The speed of the stream = (30 - 24)/2 = 3 kmph
Answer:D
Answer: D
Question: If two sides of a triangle have lengths 3 and 6, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19
Options:
A)None
B)I only
C)II only
D)II and III only
E)I, II, and III
Rationale: Let x be the length of the third side.
6-3 < x < 6+3
3 < x < 9
12 < perimeter < 18
The answer is C.
Answer: C
Question: Pipe A can fill a tank in 20 hrs and pipe B can fill it in 60 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill quarter of that tank?
Options:
A)3 hr 15 mins
B)3 hr 25 mins
C)3 hr 35 mins
D)3 hr 45 mins
E)3 hr 55 mins
Rationale: Part filled A in 1 hr= (1/20)
Part filled B in 1 hr= (1/60)
Part filled by (A+B) together in 1 hr=(1/20)+(1/60)=1/15
So, The tank will be full in 15 hrs
Time taken to fill Exact quarter tank = (15) * (1/4) = 3.45 hr= 3 hr 45 mins
Answer : D
Answer: D
Question: A shopkeeper loses 15%,if an article is sold for $102. What should be the selling price of the article to gain 20%?
Options:
A)$165
B)$174
C)$144
D)$164
E)$183
Rationale: C
$144
Given that SP = $102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = $120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = $144
Answer: C
Question: If a coin is tossed 5 times what is the probability that it will land either heads 5 times or tails 5 times?
Options:
A)1/4
B)1/8
C)1/16
D)1/32
E)1/64
Rationale: The probability of 5 heads is (1/2)^5 = 1/32
The probability of 5 tails is (1/2)^5 = 1/32
The probability of 5 heads or 5 tails is 1/32 + 1/32 = 1/16
The answer is C.
Answer: C
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Options:
A)5/5
B)5/3
C)5/2
D)5/6
E)5/9
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - 6C1/10C3 = 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer:D
Answer: D
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
Options:
A)57/7 sec
B)80/7 sec
C)20/7 sec
D)60/7 sec
E)65/7 sec
Rationale: Explanation:
Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
ANSWER IS B
Answer: B
Question: At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 9'o clock.
Options:
A)60sec
B)62sec
C)66sec
D)48sec
E)76sec
Rationale: At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
8'o clock 7 *6=42sec
9'o clock 8 *6=48sec
So, 48sec at 9'o clock.
ANSWER:D
Answer: D
Question: The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 12 minutes is:
Options:
A)9
B)5
C)7
D)6
E)51
Rationale: Explanation:
Speed downstream = (20+5) kmph = 25 kmph
Distance travelled = (25*(12/60)) km = 5 km.
ANSWER:B
Answer: B
Question: Two kinds of Vodka are mixed in the ratio 2:6 and 6:3 and they are sold fetching the profit 10% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
Options:
A)20%
B)40%
C)18%
D)23%
E)Cannot be determined
Rationale: The profit on the first kind of vodka = x%;
The profit on the second kind of vodka = y%.
When they are mixed in the ratio 1:2 (total of 3 parts) the average profit is 10%: (x + 2y)/3 = 10.
When they are mixed in the ratio 2:1 (total of 3 parts) the average profit is 20%: (2x + y)/3 = 20.
Solving gives: x = 30% and y = 0%.
After the individual profit percent on them areincreased by 4/3 and 5/3 times respectively the profit becomes 40% and 0%,on the first and te second kinds of vodka, respectively.
If they are mixed in equal ratio (1:1), then the mixture will fetch the profit of (40 + 0)/2 = 20%.
Answer:A
Answer: A
Question: A number x is 18 times another number y. The percentage that y is less than x is
Options:
A)12.5%
B)87.5%
C)80%
D)94.4%
E)1%
Rationale: Say y=1 and x=18.
Then y=1 is less than x=18 by (18-1)/18*100=17/18*100=94.4%.
Answer: D.
Answer: D
Question: A housewife saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction ?
Options:
A)8
B)9
C)7
D)6
E)4
Rationale: Explanation:
Actual price = Rs. (25 + 2.50) = Rs. 27.50.
Saving = 2.50
Percentage Saving =
Answer: B) 9
%
Answer: B
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
Options:
A)7/20
B)1/2
C)16/19
D)3/5
E)4/5
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
A)
Answer: A
Question: On a certain transatlantic crossing, 25 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
Options:
A)33 1/3%
B)40%
C)50%
D)62.5%
E)66 2/3%
Rationale: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Solution: Let total number of passengers be 100
According to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then
40% of X = 25 => X= 62.5.
Answer D
Answer: D
Question: The number of oranges in three basket are in the ratio 3 : 4 : 5. In which ratio the no. of oranges in first two basket must be increased so that the new ratio becomes 5 : 4 : 3 ?
Options:
A)3:4
B)2:3
C)1:3
D)2:1
E)None of these
Rationale: Solution: Let,
B1 : B2 : B3 = 3x : 4x : 5x
Again,
B1 : B2 : B3 = 5y : 4y : 3y
Number of oranges remain constant in third basket as increase in oranges takes place only in first two baskets.
Hence, 5x = 3y
and,
3x : 4x : 5x
→ 9y /5 : 12y /5 : 15y /5 = 9y : 12y : 15y
And,
5y : 4y : 3y → 25y : 20y : 15y
Therefore, Increment in first basket = 16.
Increment in second basket = 8.
Thus, Required ratio = 16 /8 = 2 : 1
Answer: Option D
Answer: D
Question: 225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
Options:
A)10
B)13
C)15
D)16
E)17
Rationale: 26 trees have 25 gaps between them,
Required distance (225/25) = 10
A
Answer: A
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Options:
A)35.55 km/hr
B)36 km/hr
C)71.11 km/hr
D)71 km/hr
E)72 km/hr
Rationale: Total time taken = 160/64 + 160/80 = 9/2 hours
--> Average speed = 320 x 2/9 = 71.11 km/hr.
Answer : C.
Answer: C
Question: What will be 70 percent of a number whose 200 percent is 90 ?
Options:
A)144
B)72
C)31.5
D)None of these
E)Cannot be determined
Rationale: Answer
∵ 200% of N = 90
⇒ N = (90 x 100) / 200 = 45
∴ 70% of N = (70 x 45) / 100 = 31.5
Correct Option: C
Answer: C
Question: If the selling price of 50 articles is equal to the cost price of 20 articles, then the loss or gain percent is:
Options:
A)45%
B)23%
C)20%
D)60%
E)56%
Rationale: C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 20.
Loss % = 30/50 * 100 = 60%
ANSWER D
Answer: D
Question: The average of 10 numbers is 20 and the average of 10 other numbers is 25. What is the average of all 20 numbers?
Options:
A)22.5
B)21.1
C)2.6
D)7.5
E)4.6
Rationale: The average of 10 numbers is 20....
The sum of those numbers is (10)(20) = 200.
The average of 10 other numbers is 25....
The sum of those numbers is (10)(25) = 250
The sum of ALL 20 numbers is 200+250 = 450. The average of those numbers is 450/20 = 22.5
Answer is A
Answer: A
Question: The mean of 50 observations was 36. It was found later that an observation 44 was wrongly taken as 23. The corrected new mean is
Options:
A)35.22
B)36.12
C)36.22
D)36.42
E)None
Rationale: Solution
Correct sum = (36x50+44-23)
= 1821.
âˆ´ Correct mean = 1821 / 50
= 36.42.
Answer D
Answer: D
Question: How many 4 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?
Options:
A)20
B)40
C)120
D)60
E)10
Rationale: 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 fourth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 1 ways = 40
Answer B
Answer: B
Question: Simplify: 81 X 81 + 68 X 68-2 x 81 X 68.
Options:
A)169
B)159
C)189
D)179
E)219
Rationale: = (81)^2 + (68)^2 – 2x 81 x 68 = a^2 + b^2 – 2ab,Where a =81,b=68
= (a-b)^2 = (81 –68)^2 = (13)^2 = 169.
Answer is A.
Answer: A