divelab/Sys2Bench huggingface dataset:
Question: Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7200 km and comes back to the starting point. The total time taken by him is:
Options:
A)914.2 hours
B)900 hours
C)915 hours
D)905 hours
E)915 hours
Rationale: Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 7200/18 + 7200/14 = 400 + 514.2 = 914.2 hours
Answer: Option A
Answer: A
Question: The number of arrangements that can be made with the letters of the word MEADOWSS so that the vowels occupy the even places?
Options:
A)14
B)144
C)720
D)992
E)221
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 5 places in 5! i.e., 120 ways.
Hence the total ways are 120 * 6 = 720.
Answer:C
Answer: C
Question: What should come in place of the question mark (?) in the following equation?
45789+ 34567 = 610+ ?
Options:
A)96543
B)13678
C)23456
D)56789
E)79746
Rationale: 45789+ 34567 = 610+ ?
45789+ 34567 – 610 = 79746
Answer E
Answer: E
Question: Today is Monday.After 61 days,it will be
Options:
A)Wednesday
B)Saturday
C)Tuesday
D)Thursday
E)None of these
Rationale: Solution
Each day of the week is repeated after 7 days
So,after 63 days,it will be Monday.
∴ After 61 days,it will be Saturday. Answer B
Answer: B
Question: If 2 men or 3 women can reap a field in 8 days how long will 3 men and 4 women take to reap it?
Options:
A)2/16
B)1/16
C)3/24
D)5/16
E)6/26
Rationale: Explanation:
2 men reap 1/8 field in 1 day
1 man reap 1/(2 x 8)
3 women reap 1/8 field in 1 day
1 woman reap 1/(3 x 8)
3 men and 4 women reap (3/(2 x 8)+ 4/(3 x 8)) =5/16 in 1 day
3 men and 4 women will reap the field in 5/16 days
Answer: Option D
Answer: D
Question: If x is an integer, then x(x – 1)(x – k) must be evenly divisible by 4 when k is any of the following values EXCEPT
Options:
A)-4
B)-3
C)-1
D)2
E)5
Rationale: We have the product of 3 integers: (x-1)x(x-k).
Note that the product of 3 integers is divisible by 4 if at least one multiple is divisible by 4. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 4 these numbers must have different remainders upon division by 4, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 2.
Next, if k=-3 then we'll have (x-1)x(x+2)=(x-1)x(x+3) --> which means that (x-1) and (x+3) will have the same remainder upon division by 4. Thus for k=-3 we won't be sure whether (x-1)x(x-k) is divisible by 4.
Answer: B.
Answer: B
Question: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 5m3 , then the rise in the water level in the tank will be:
Options:
A)31.25 cm
B)25 cm
C)35 cm
D)50 cm
E)None of these
Rationale: Explanation:
Total volume of water displaced =(5 x 50) m3 = 250 m3
Rise in water level = 250/40Ã—20= 0.3125m = 31.25cm
Answer: A
Answer: A
Question: In how many ways can the letters of the word 'PRAISE' be arranged. So that vowels do not come together?
Options:
A)720
B)576
C)440
D)144
E)None of these
Rationale: Required number of possible outcomes
= Total number of possible outcomes – Number of possible outcomes in which all vowels are together
= 6! – 4 ! × 3! = 576
Answer B
Answer: B
Question: What is the remainder when 1271 * 1275 * 1277 *1289 is divided by 12?
Options:
A) 0
B) 1
C) 9
D) 11
E) 7
Rationale: 1271*1275*1277*1285 = (1272 - 1)(1272 + 3)(1284 - 7)(1284 + 5) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)
Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-1)(3)(-7)(5) = 105. Thus the question becomes: what is the remainder upon division of 105 by 12? The answer to this question is 9.
Answer: C.
Answer: C
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 70, the dividend is:
Options:
A)A)5322
B)B)5330
C)C)12320
D)D)53400
E)E)53420
Rationale: Divisor = (5 * 70) = 350
= 10 * Quotient = Divisor
=> Quotient = 350/10 = 35
Dividend = (Divisor * Quotient) + Remainder
Dividend = (350 * 35) + 70 = 12320.
C
Answer: C
Question: A class consists of 6 boys and 5 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?
Options:
A)50
B)18
C)32
D)60
E)240
Rationale: Easiest way is to treat it like an arrangements question in the following manner:
From the boys we need to select 2 to be clown and pet: This can be done in 5*6 ways
Similarly for the girls, we have 4*5 ways.
Thus total = 30+20 = 50 ways. Thus A is the correct answer.
Answer: A
Question: The value of land increases by u% during June and decreases by v% during July. If the value of the land is the same at the end of July as at the beginning of June, what is v in terms of u?
Options:
A)200u/(100+2u)
B)100u/(100+u)
C)u(2+u)/(1+u)2
D)u(200+u)/10000
E)2u/u+2u
Rationale: The simplest pairing is a 25% increase will be offset by a 20% decrease.
Here's the proof:
Starting value = 100
25% increase = 100 + (.25)(100) = 125
20% decrease = 125 - (.2)(125) = 100
Ending value = 100
So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...
Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.
Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.
Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.
Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.
Answer E: (50/25) + 50 = 52. ELIMINATE E.
ans B
Answer: B
Question: A cricket bat is sold for $900, making a profit of $100. The profit percentage would be
Options:
A)24%
B)12.5%
C)30%
D)36%
E)40%
Rationale: 100/(900 - 100) = 100/800 = 0.125 = 12.5%.
Answer: B
Answer: B
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)111.12 m
B)888.88 m
C)777.52 m
D)756.34 m
E)766.34 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
ANSWER:A
Answer: A
Question: The average weight of A, B and C is 75 kg. If the average weight of A and B be 88 kg and that of B and C be 72 kg, then the weight of B is:
Options:
A)60 kg
B)59 kg
C)62 kg
D)63 kg
E)61 kg
Rationale: EXPLANATION
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (75 x 3) = 225 â€¦. (i)
A + B = (88 x 2) = 176 â€¦. (ii)
B + C = (72 x 2) = 144 â€¦.(iii)
Adding (ii) and (iii), we get: A + 2B + C = 288 â€¦. (iv)
Subtracting (i) from (iv), we get : B = 63.
Bâ€™s weight = 63 kg.
Answer D
Answer: D
Question: Tough and Tricky questions: Work/Rate Problems.
If it takes 60 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job?
Options:
A)40/3
B)11
C)6
D)7/3
E)9/7
Rationale: 60 Workers = 3 hours then,
1 Worker = 3*60 Hours
30 Workers = (3*60) /(30) = 6 Answer.C
Answer: C
Question: A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work , how much time shall B take to do it ?
Options:
A)30 days
B)35 days
C)40 days
D)None of these
E)Cannot be determined
Rationale: Solution
Suppose B taken x days to do the work.
∴ A takes (2 x 3/4x) =2x/2 days to do it.
(A + B)'s 1 days work = 1/8.</p><p>
therefore 1/x + 2/3x -1/18 or x=30
Answer A
Answer: A
Question: A man has some hens and cows. If the number of heads be 50 and the number of feet equals 140, then the number of hens will be:
Options:
A)22
B)23
C)24
D)30
E)28
Rationale: let hens be x and cows be y
now,
feet: x*2+y*4=140
heads: x*1+y*1=50
implies, 2x+4y=140 and x+y=50
solving these two equations, we get x=30 and y=20
Therefore, hens are 26.
ANSWER:D
Answer: D
Question: There is a five-digit number. The fifth digit is one fourth of the third digit and one half of the fourth digit. Third digit is one half of the first digit. Second digit is 5 more than the fifth digit. What is that 5-digit number?
Options:
A)86421
B)86424
C)89421
D)96421
E)76421
Rationale: we can prove it as follows
suppose number is pqrst, now
t=(1/4)r=(1/2)s......(1),r=(1/2)p.....(2),q=t+5....(3)
now from (1)4t=r=2s=k(suppose)....(4)
from (2) 2r=p...(5)
now(4)*2 then we get 8t=2r=4s=k(again some integer)....(6)
from (5) and (6)
8t=2r=4s=p=k.........(7)
now we have to choose the value of k
1)if choose k=0 then it is worthless number will be 00000(not a answer)
2)for k=1 to 7 and for k=9 digits will be in fractions
3)for k=8 we get p=8,s=2,r=4,t=1 and q=6
and number is pqrst=86421
ANSWER:A
Answer: A
Question: When a is divided by b the remainder is 13.When c is divided by d the remainder is 12.
If a,b,c,d are all positive integers then which of these may be the value of b+d?
Options:
A)23
B)24
C)25
D)26
E)27
Rationale: In the original question, we're told that, when a is divided by b the remainder is 13
So, b must be greater than 13.
In other words, b COULD equal 14, 15, 16, 17, ....
We're also told that, c is divided by d the remainder is 12
So, d must be greater than 12.
In other words, d COULD equal 13, 14, 15, 16, ....
So, the smallest possible value of b+d is 14+13
In other words, b+d COULD equal 27
Answer:E
Answer: E
Question: The age of Somu is one-third his father's. 10 years back he was one-fifth of his father's age. What is his persent age ?
Options:
A)11
B)13
C)14
D)12
E)20
Rationale: Explanation :
Let Somu's age be x and that of his father be 3x.
So, x - 10 = 3x - 10/5 = x = 20
Answer : Option E
Answer: E
Question: A secret can be told only 2 persons in 5 minutes .the same person tells to 2 more persons and so on . How long will take to tell it to 768 persons ?
Options:
A)35 min
B)36 min
C)37 min
D)39 min
E)45 min
Rationale: at start one person will tell to 2 persons, it will take 5 min, now that 1+2 = 3 persons will tell this to next 6 persons, then 1+2+6 = 9 persons will tell to next 18 persons, then 1+2+6+18 = 27 persons to 54 similarly 1+2+6+18+54 = 81 persons will tell this to 162 persons similarly 1+2+6+18+54+162 = 243 persons will tell this to 486 persons, upto this step total persons who have listened this secret = 2+6+18+54+162+486 = 728, and total time taken upto this step = 5*6 = 30 min, now next 5 min will be sufficient to tell this message to next 40 persons so total time taken = 35 min
ANSWER:A
Answer: A
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 12 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
Options:
A)19:2
B)18:3
C)11:1
D)11:5
E)11:4
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 15/2 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 15/2 + 7/2 = 11 litres
As 16 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 11 : 5
Answer:D
Answer: D
Question: Look at this series: J14, L16, __, P20, R22, ... What number should fill the blank?
Options:
A)S24
B)N18
C)M18
D)T24
E)T28
Rationale: In this series, each set contains alphabet and numbers.
Alphabet increasing by 2alphabets : J L N P R
Numbers increasing by 2 : 14 16 18 20 22
Finally : J14 L16 N18 P20 R22
ANSWER:B
Answer: B
Question: After decreasing 24% in the price of an article costs Rs.1140. Find the actual cost of an article?
Options:
A)1500
B)6789
C)1200
D)6151
E)1421
Rationale: CP* (76/100)
= 1140
CP= 15 * 100 => CP
= 1500
Answer: A
Answer: A
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
Options:
A)2888
B)2690
C)2668
D)9261
E)2312
Rationale: A = 8000(21/20)3 = 9261.Answer:D
Answer: D
Question: A farmer is planting a row consisting of 3 unique apple trees and 4 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?
Options:
A)288
B)576
C)1,024
D)1,152
E)10,080
Rationale: 2 possible arrangements are possible
AOAOAOAO
OAOAOAOA
2 unique type of trees are present consisting of 4 trees each
3 apple trees can be arranged in 4! ways
4 orange trees can be arranged in 4! ways
as 2 arrangements are possible
total arrangements = 2 *3! * 4! = 288
correct answer option A
Answer: A
Question: Two trains of equal lengths take 10 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)13 sec
B)12 sec
C)16 sec
D)15 sec
E)18 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/20 = 6 m/sec.
Relative speed = 12 + 6 = 18 m/sec.
Required time = (120 + 120)/18 = 13 sec.
Answer:A
Answer: A
Question: A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 90% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?
Options:
A)1.8 lakh
B)1.5 lakh
C)1.9 lakh
D)8.1 lakh
E)6.1 lakh
Rationale: Explanation:
Total cost of 4 cars = 1+2 = 3 lakh
Total SP of 4 cars = 3 x 1.9 = 5.7 lakh
SP of 1 car = 1.2 lakh
SP of rest 3 cars = 5.7 - 1.2 = 4.5 lakh
Average SP of all the 3 cars = 1.5 lakh
Answer: B)
Answer: B
Question: Due to 10% decrease in the price of sugar and John can buy 2kg more sugar in Rs100 , then find the CP of sugar?
Options:
A)s. 5(5/9)
B)s. 2(2/9)
C)s. 2(1/9)
D)s. 3(2/7)
E)s. 4(2/9)
Rationale: Here r = 10 % ,x = 100 and A = 2 kg
Actual price of sugar = 10*100/((100-10 )*2) = Rs. 5(5/9)
A
Answer: A
Question: Find the mean proportional between 36 & 49?
Options:
A)A)42
B)B)61
C)C)63
D)D)65
E)E)67
Rationale: Formula = √a×b
A = 36 and B = 49
√36×49 = 6 × 7 = 42
A
Answer: A
Question: At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/3 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
Options:
A)12 greater
B)17 fewer
C)92 fewer
D)36 fewer
E)44 fewer
Rationale: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/3* 480 =160
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 160-68 =92>>> therfore answer is 92 fewer
C
Answer: C
Question: The area of a triangle is with base 4m and height 5m?
Options:
A)11
B)10
C)288
D)87
E)22
Rationale: 1/2 * 4 * 5 = 10 m2 ,Answer: B
Answer: B
Question: Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rajan?
Options:
A)2000
B)2100
C)2200
D)2300
E)2400
Rationale: Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000
=>4:5:3
=>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...]
=> 12:5:6
Share of Rajan => 4600*12/23 = 2400
ANSWER:E
Answer: E
Question: In a 200 Meter race A beats B by 35 Meters in 7 seconds. A's time over the cause is?
Options:
A)47 sec
B)40 sec
C)45 sec
D)33 sec
E)35 sec
Rationale: B covers 35m in 7seconds
B take time =(200*7)/35=40
A takes time =40-7=33 sec
ANSWER:D
Answer: D
Question: At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 15th highest price and the 22nd lowest price among the prices of the items sold, how many items were sold at the garage sale?
Options:
A)34
B)35
C)36
D)37
E)38
Rationale: There were 14 items sold at a higher price than the radio and 21 items sold at a lower price than the radio. Including the radio, there were 14 + 21 + 1 = 36 items sold.
The answer is C.
Answer: C
Question: If the average (arithmetic mean) of a and b is 110, and the average of b and c is 150, what is the value of a − c?
Options:
A)−220
B)−100
C)100
D)−80
E)It cannot be determined from the information given
Rationale: Question: a - c = ?
(a + b)/ 2 =110 ===> a + b = 220
(b + c)/2 = 150 ===> b + c = 300
(a + b) - (b + c) = 220 - 300 ===> a + b - b - c = - 80 ===> a - c = - 80
Answer: D
Answer: D
Question: A mixture of 150 liters of wine and water contains 15% water. How much more water should be added so that water becomes 25% of the new mixture?
Options:
A)10
B)30
C)20
D)15
E)17
Rationale: Number of liters of water in150 liters of the mixture = 15% of 150 = 15/100 * 150 = 22.5 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (22.5 + P) and total volume of mixture is (150 + P).
(22.5 + P) = 25/100 * (150 + P)
90+4P = 150+P
P = 20 liters.
Answer: C
Answer: C
Question: If n = 5^11 – 5, what is the units digit of n?
Options:
A)0
B)1
C)4
D)6
E)8
Rationale: Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 5^3 - 5. Now 5^3 has last digit 5. we subtract 5 from 5=0 is the answer. Option A
Answer: A
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
Options:
A)6
B)7
C)9
D)2
E)1
Rationale: 9 a.m.
Answer:C
Answer: C
Question: The length of a rectangle is reduced by 15%. By what % would the width have to be increased to maintain the original area?
Options:
A)10%
B)20%
C)17.6%
D)30%
E)35%
Rationale: Sol. Required change = (15*100)/(100-15)=17.6%
C
Answer: C
Question: he total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
Options:
A)55
B)65
C)75
D)85
E)95
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2 = 75.
ANSWER:C
Answer: C
Question: A three-digit positive integer is chosen at random. What is the probability that the product of its digits is even?
Options:
A)1/2
B)31/36
C)49/54
D)7/8
E)11/12
Rationale: P(three odd digits) = 5/9*5/10*5/10 = 5/36 (first digit cannot be 0, so we have a total of 9 digits, 4 even and 5 odd).
Therefore, P(at least one even digit) = 1 - 5/36 = 31/36.
Answer B.
Answer: B
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Options:
A)186
B)167
C)120
D)168
E)619
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer: C:
Answer: C
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)37
B)38
C)30
D)77
E)27
Rationale: US = 25
DS = 35
M = (35 + 25)/2
= 30
Answer:C
Answer: C
Question: How many seconds will a train 100 meters long take to cross a bridge 160 meters long if the speed of the train is 36 kmph?
Options:
A)26
B)72
C)25
D)82
E)27
Rationale: Explanation:
D = 100 + 160 = 260
S = 36 * 5/18 = 10 mps
T = 260/10 = 26 sec
Answer: Option A
Answer: A
Question: Find all rational zeros of P(x) = x3*cubic* - 7x + 6.
Options:
A)1,2,-3
B)2,2,-5
C)1,4,-7
D)4,3,-1
E)3,3,-8
Rationale: P(x) = x3*cubic* - 7x + 6 : given
leading coefficient 1 and its factors are : +1,-1
constant term is 6 and its factors are : +1,-1,+2,-2,+3,-3,+6,-6
possible rational zeros : +1,-1,+2,-2,+3,-3,+6,-6
test : P(1) = 0, P(2) = 0 and P(-3) = 0
x = 1, x = 2 and x = -3 are the zeros of P(x).
correct answer is A) 1,2,-3
Answer: A
Question: How much water must be added to 48 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre?
Options:
A)10 litres
B)12 litres
C)15 litres
D)18 litres
E)None of these
Rationale: C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3
∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4
∴ Quantity of water to be added to 48 litres of milk
= (1⁄4 × 48) litres = 12 litres.
Answer B
Answer: B
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
A)150 meter
B)250 meter
C)200 meter
D)480 meter
E)153 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer:A
Answer: A
Question: What is the number of triangles that can be formed whose vertices are the vertices of an octagon but have only one side common with that of octagon?
Options:
A)22
B)32
C)88
D)29
E)01
Rationale: Explanation:
When the triangles are drawn in an octagon with vertices same as those of the octagon and having one side common to that of the octagon, the figure will appear as shown in (Fig. 1).
Now, we shall first consider the triangles having only one side AB common with octagon ABCDEFGH and having vertices common with the octagon (See Fig. 2).Such triangles are ABD, ABE, ABF and ABG i.e. 4 in number.
Similarly, the triangles having only one side BC common with the octagon and also having vertices common with the octagon are BCE, BCF, BCG and BCH (as shown in Fig. 3). i.e. There are 4 such triangles.
This way, we have 4 triangles for each side of the octagon. Thus, there are 8 x 4 = 32 such triangles.
Answer: B) 32
Answer: B
Question: Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:
Options:
A)5 %
B)12/11 %
C)2 %
D)5 5/11 %
E)10/6%
Rationale: Explanation:
Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
Gain % =(300/5500*100)%=5 5/11 %
ANSWER:D
Answer: D
Question: The product of two positive integers is 575 and their difference is 2. What is the bigger number?
Options:
A)21
B)23
C)25
D)27
E)29
Rationale: Let's use trial and error to find the two numbers.
27*25 = 675 (too high)
25*23 = 575
The answer is C.
Answer: C
Question: Raja and David invested in a business. They earned some profit which they divided in the ratio of 2:4. If RAM invested Rs.10, 000, the amount invested by David is:
Options:
A)Rs. 21000
B)Rs. 22000
C)Rs. 20000
D)Rs. 23000
E)Rs. 24000
Rationale: Invested by David = 10000/2*4 = 20000
ANSWER : C
Answer: C