divelab/Sys2Bench huggingface dataset:
Question: A bag is filled with pennies and nickels in the ratio of 5 to 3. There are 60 nickles in the bag, how many coins are there in that bag?
Options:
A)40
B)160
C)65
D)70
E)80
Rationale: A ratio of pennies to nickels of 5 to 3 means that we can write the number of pennies and nickels in the form
number of pennies = 5x and number of nickels = 3x
But we know the number of nickels, 60. Hence
3x = 60
Solve for x
x = 20
The total number of coins is given by
5x + 3x = 8x = 8 × 20 =160
Answer : B
Answer: B
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
Options:
A)26.4 m2
B)39.6 m2
C)52.8 m2
D)79.2 m2
E)None of these
Rationale: Explanation:
42/360 * 22/7 * 12 * 12 = 52.8 m2
ANSWER IS C
Answer: C
Question: What is the total cost of 2 sandwiches at $3.49 each and 4 sodas at $0.87 each?
Options:
A)$3.36
B)$6.85
C)$8.46
D)$10.46
E)$11.85
Rationale: Answer = D
2 * 3.49 + 4 * 0.87
= 2 (3.50 - 0.01) + 4 (1.00 - 0.13)
= 7 + 4 - 0.02 - 0.52
= 11 - 0.54
= 10.46
Answer: D
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
Options:
A)4830
B)5120
C)6420
D)8960
E)7960
Rationale: Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m3 = 5120 m3. Answer: Option B
Answer: B
Question: n^(n/2)=4 is true when n=4 in the same way what is the value of n if n^(n/2) =8?
Options:
A)4
B)8
C)2
D)6
E)10
Rationale: n^(n/2)=8Apply logN/2logn=log8nlogn=2log8=log8^2=log64Logn=log64Now apply antilogn=64/nNow n=8.ANSWER:B
Answer: B
Question: Subtracting 5% of A from A is equivalent to multiplying A by how much ?
Options:
A)0.95
B)9.4
C)0.094
D)94
E)None
Rationale: Answer
Let A - 5% of A = AB.
⇒ (95 x A) / 100 = AB
∴ B = 0.95
Correct Option: A
Answer: A
Question: In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 9 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
Options:
A)2/1
B)4/1
C)2/3
D)3/4
E)3/2
Rationale: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+9) = 36/18 = 2/1.
Answer: A.
Answer: A
Question: A dealer purchased an book at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
Options:
A)79%
B)88%
C)100%
D)94%
E)103%
Rationale: C
100%
MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer: C
Question: In the class of 100 students, 70 speak Tamil and 40 speak Telugu. What is the lowest possible number of students who
speak both the languages?
Options:
A)A)8
B)B)10
C)C)20
D)D)30
E)E)32
Rationale: let the student who speaks Tamil-x
let the student who speaks Telugu-y
as (xuy)-(xny)=total
70+40-(xny)=100
=10
B)
Answer: B
Question: In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.67 per Kg?
Options:
A)3 : 1
B)3 : 2
C)4 : 3
D)5 : 3
E)1 : 1
Rationale: Required ratio = 500 : 500 = 3 : 1
Answer E
Answer: E
Question: A pack of 52 playing cards, 2 cards aredrawn together at random. Find the probability of both the cards being king ?
Options:
A)2/124
B)3/234
C)1/221
D)2/314
E)3/431
Rationale: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
C
Answer: C
Question: A school’s annual budget for the purchase of student computers increased by 38% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
Options:
A)10%
B)20%
C)15%
D)18%
E)16%
Rationale: Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $138, price = $1.2 --> the number of computers purchased = 138/1.2 = 115.
Increase in the number of computers purchased = 15%.
Answer: C.
Answer: C
Question: The sum of the present ages of father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
Options:
A)12 years
B)14 years
C)18 years
D)20 years
E)22 years
Rationale: Let the present ages of son and father be x and (60 - x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
6x = 84 => x = 14
Son's age after 6 years = (x + 6) = 20 years.
ANSWER:D
Answer: D
Question: A can do a piece of work in 10 days and B alone can do it in 15 days. How much time will both take to finish the work ?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.
Time taken to finish the job = XY / (X + Y)
= 10 x 15 / (10 + 15)
= 150 / 25
= 6 days
Answer: B
Answer: B
Question: N is a positive integer. When N + 1 is divided by 4, the remainder is 3. What is the remainder when N is divided by 3?
Options:
A)1
B)2
C)3
D)0
E)4
Rationale: N+1 = 4a+3
i.e. N+1 = 7, 10, 13, 16, ... etc.
i.e. N = 6, 9, 12, 15, ... etc.
When N is divided by 3 Remainder is always 0
Answer: D
Answer: D
Question: Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Options:
A)12 minutes
B)17 minutes
C)27 minutes
D)97 minutes
E)26 minutes
Rationale: Part filled by A in 1 min. = 1/20
Part filled by B in 1 min. = 1/30
part filled by (A + B) in 1 min. = 1/20 + 1/30 = 1/12.
Both the pipes can fill the tank in 12 minutes.
Answer: A
Answer: A
Question: A three-person committee must be chosen from a group of 7 professors and 12 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?
Options:
A)A)70
B)B)743
C)C)749
D)D)1,260
E)E)1,980
Rationale: Total number of ways to select at least one professor = Number of ways to select 3 people from 12 students and 7 professors - Number of ways to select 3 people from 12 student (i.e. without including any professor)
= 19C3 - 12C3 = 969 - 220 = 749
ANSWER:C
Answer: C
Question: In a certain aquarium, the number of red fish is three times the number of the green fish, and the number of blue fish is half the number of the red fish. If the ratio of green fish to red fish were to be doubled, and the ratio of red fish to blue fish were to be doubled, then the ratio of blue fish to green fish in that aquarium would be
Options:
A)3:2
B)1:1
C)1:2
D)3:4
E)3:8
Rationale: Lots of little places to make a mistake or panic here. =)
R = 3G
B = R/2
G/R = 1/3 ----> Doubled G/R = 2/3
R/B = 2 ----> Doubled R/B = 4
B/G = (B/R)*(R/G) = (1/4)*(3/2) = 3/8
ANSWER:E
Answer: E
Question: Find the value of m 82519 x 9999 = m?
Options:
A)724533811
B)353654655
C)825107481
D)725117481
E)477899932
Rationale: 82519 x 9999 = 82519 x (10000 - 1)
= 82519 x 10000 - 82519 x 1
= 825190000 - 82519
= 825107481
C
Answer: C
Question: In a group of 100 cars, 47 cars do not have air conditioning. If at least 55 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes?
Options:
A)45
B)47
C)49
D)51
E)53
Rationale: Lets assume AC=53(includesonly AC carsandcars with AC and racing stripes)
lets assume RS(racing stripes)>=55(includescars with AC and racing stripesandonly racing stripes).
Now since we want to maximize(only AC) we have to see to it thatcars with AC and racing stripesis minimal(assume 0) But since RS>=55.. we have to assign atleast 8 tocars with AC and racing stripes.
Hence AC=53-8=45.
The answer is A
Answer: A
Question: In a club there are no more than 20 persons. What is the smallest number of fruits that must be brought to the club so that each person receives the same number of fruits?
Options:
A)26
B)75
C)80
D)45
E)33
Rationale: The number of persons is not specified. We are just given that there are no more than 20 persons.
If we assume that number of persons is 15 then answer will be B.
If we assume that number of persons is 20 then answer will be C because only 80 is divisible by 20.
Answer: C
Question: The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?
Options:
A)87
B)91
C)100
D)96
E)101
Rationale: number of pens = 1001
number of pencils = 910
Required number of students = H.C.F. of 1001 and 910 = 91
Answer is B
Answer: B
Question: The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare be Rs. 333.18, find its base and height.
Options:
A)B=900;H=300
B)B=900;H=302
C)B=900;H=338
D)B=900;H=329
E)B=900;H=122
Rationale: Explanation:
Area of the field = Total cost/rate = (333.18/25.6) = 13.5 hectares
Let altitude = x metres and base = 3x metres.
Then,
Base = 900 m and Altitude = 300 m.]
Answer: A)
Answer: A
Question: A florist has 2 azaleas, 3 buttercups, and 5 petunias. The florist puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?
Options:
A)31/45
B)23/45
C)14/45
D)11/15
E)8/15
Rationale: The probability that two of the same flowers were chosen:
P(AA) = 2/10 * 1/9 = 2/90
P(BB) = 3/10 * 2/9 = 6/90
P(PP) = 5/10 * 4/9 = 20/90
The sum of these probabilities is 14/45
P(two flowers are different) = 1 - 14/45 = 31/45
The answer is A.
Answer: A
Question: Find the least number with which 16200 should be multiplied, to make it a perfect cube.
Options:
A)23
B)28
C)45
D)20
E)11
Rationale: Explanation:
16200 = 23 * 34 * 52
A perfect cube has a property of having the indices of all its prime factors divisible by 3.
Required number = 32 * 5 = 45
Answer:C
Answer: C
Question: In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 440, how many purple chips were selected?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 440 = 1*5*8*11
The factor of 8 must come from the purple point value, so there is 1 purple chip.
The answer is A.
Answer: A
Question: Three numbers are in the ratio 3:5:7. The largest number is 49. What is the difference between smallest and largest number?
Options:
A)16
B)20
C)24
D)28
E)32
Rationale: The three numbers are 3x, 5x, and 7x.
The largest number is 49 = 7*7, so x = 7.
The smallest number is 3*7 = 21.
49 - 21 = 28
The answer is D.
Answer: D
Question: A girl has 8 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?
Options:
A)A)96
B)B)102
C)C)108
D)D)110
E)E)112
Rationale: The girl can select one jeans in 8 ways.
The girl can select one shirt in 12 ways.
The number of ways in which he can select one jeans and one shirt is 8 * 12 = 96 ways.
A
Answer: A
Question: What is the sum of the different positive prime factors of 1020?
Options:
A)13
B)17
C)20
D)25
E)27
Rationale: I think answer is E: 27
1020 = 2*2*3*5*17
Sum of theDIFFERENTpositive prime factors = 2 + 3 + 5 + 17 = 27
Answer: E
Question: The distance between two stars is 1.8 × 10^4 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)
Options:
A)8.8 x 10^2
B)6.6 x 10^2
C)2.2 x 10^3
D)5.5 x 10^3
E)8.8 x 10^4
Rationale: 1.8 × 10^4 ly / (3.26 ly/parsec) = (1.8/3.26) x 10^4 = 0.55 x 10^4 = 5.5 x 10^3 parsec
The answer is D.
Answer: D
Question: A tradesman by means of his false balance defrauds to the extent of 28%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)44%
B)48%
C)94%
D)45%
E)64%
Rationale: g% = 28 + 28 + (28*28)/100
= 64%
Answer: E
Answer: E
Question: What is the minimum value of z for which z^2 + z - 3/2 > 0 is not true?
Options:
A) -5/2
B) -3/2
C) -3
D) 1/4
E) 1/2
Rationale: I think C -3 is the best ans...
Answer: C
Question: Let Q represent a set of seven distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?
Options:
A)1
B)2
C)3
D)5
E)7
Rationale: Q = p1+p2+p3+p4+p5+p6+p7 = even (and all primes are distinct)
if the least prime is 2 then we have sum of Q =even.
Ans. C. 3
Answer: C
Question: John purchased a fridge and a mobile for Rs.5000 &Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
Options:
A)Rs. 100
B)Rs. 150
C)Rs. 200
D)Rs. 260
E)Rs. 280
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C
Answer: C
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.
Options:
A)306.08
B)306.00
C)306.04
D)306.02
E)306.01
Rationale: A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
Answer: C
Answer: C
Question: Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
Options:
A)16 years
B)18 years
C)20 years
D)Cannot be determined
E)None of these
Rationale: (x-6)/(y-6)=6/5
(x+4)/(y+4)=11/10
after solving we get y=16
ANSWER:A
Answer: A
Question: A man bets on no. 16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes?
Options:
A)37:2
B)Either ;35:1
C)39:3
D)41:31
E)31:12
Rationale: Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.
Either ;35:1
B)
Answer: B
Question: Q' = 3Q - 3, what is the value of (3')' ?
Options:
A) 0
B) 10
C) 20
D) 30
E) 40
Rationale: (3')'=(3*3-3)'=6'=6*6-6=30
Answer D
Answer: D
Question: There are 7 players in a bowling team with an average weight of 103 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
Options:
A)95 Kg.
B)99 Kg.
C)89 Kg.
D)90 Kg.
E)92 Kg.
Rationale: The New average will be= (103*7+110+60)/9= 99 kgs
B is the answer
Answer: B
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 20 miles behind the slower one. How far apart are the two trains at 5 o'clock?
Options:
A)60 miles
B)70 miles
C)90 miles
D)120 miles
E)400 miles
Rationale: Answer = B. 70 miles
Relational speed = 130 - 100 = 30 miles per hour
In 3 hours, difference = 30 * 3 = 90 miles
Fast train trailing 20 miles, so effective difference = 90 - 20 = 70 miles
Answer: B
Question: Two dice are rolled. What is the probability that the sum on the top face of both the dice will be greater than 9?
Options:
A)3/8
B)2/3
C)1/2
D)1/3
E)1/6
Rationale: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
Hence, total number of outcomes possible two dice are rolled, n(S) = 6 × 6 = 36
E = Getting a sum greater than 9 when the two dice are rolled = {(4, 6), {5, 5}, {5, 6}, {6, 4}, {6, 5}, (6, 6)}
Hence, n(E) = 6
P(E) = n(E)/n(S)=6/36=1/6
Answer: E
Question: When positive integer N is divided by positive integer J, the remainder is 8. If N/J = 150.25, what is value of J?
Options:
A)16
B)26
C)32
D)132
E)20
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 150.25
Here 150 is the quotient.
Given that Remainder = 8
So, 150.25 = 150 + 8/J
So, J = 32
Answer: C
Answer: C
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
Options:
A)3/8
B)3/2
C)3/5
D)3/9
E)3/2
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Answer: B
Question: If 625^(-x) + 25^(-2x) + 5^(-4x) = 11, what is the value of x?
Options:
A)-4
B)-1/4
C)0
D)1/4
E)4
Rationale: We're told that 625^(-X) + 25^(-2X) + 5^(-4X) = 15. We're asked for the value of X.
Since each of the calculated terms MUST be positive (regardless of what the exponent is), we can use thebasesto our advantage.....
With Answer A, we'd have 625^4, which is MUCH BIGGER than 15 (and we'd be adding to that big number). Eliminate A.
With Answer E, we'd have 625^(-4), which would create a TINY fraction (and we'd add some other fractions to it, so the total would be MUCH TOO SMALL). Eliminate E.
With Answer D, we'd have 625^(-1/4), which will also be a fraction (just not as tiny as the one in answer E), but the total would still be TOO SMALL. Eliminate D.
With Answer C, anything to the '0 power' is 1, so we'd have 1+1+1 = 3. This is not 15. Eliminate C.
D
Answer: D
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is:
Options:
A)31 kg
B)32 kg
C)33 kg
D)35 kg
E)None of these
Rationale: Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (45 x 2) = 90 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv)
Subtracting (i) from (iv), we get : B = 35.
B’s weight = 35 kg.
Answer: D
Answer: D
Question: What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?
Options:
A)0
B)1
C)11
D)9
E)7
Rationale: In this type of questions we can separately divide each number with 12 and get remainder and then multiply remainder then divide by 12 ...the remainder which comes now will be the answer.
1271 div by 12==>remainder = 11
1275 div by 12 ==>rema = 3
1285 div by 12 ==> remain = 1
1277 div by 12 ==> rema = 5
now multiply the remainder = 165
165 div by 12 rem = 9
ANSWER:D
Answer: D
Question: Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 100% more than Bert had in savings, and separately, the same price was also 60% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.
Options:
A)1:5
B)2:5
C)3:5
D)4:5
E)1:1
Rationale: Suppose bert had 100 so price becomes 200 , this 200 = 1.6 times R's saving .. so R's saving becomes 125
So required ratio is 100:125=4:5
ANSWER:D
Answer: D
Question: What is the probability that Terry and Tim will get selected for a job they both applied for in a company, given that their chances of getting selected is 3/8 and 2/7 respectively?
Options:
A)2/21
B)2/25
C)3/28
D)5/28
E)3/25
Rationale: Explanation:
P(Terry) = 3/8
P(Tim) = 2/7
E = {Terry and Tim both get selected}
P(E) = P(Terry)*P(Tim)
= 3/8 * 2/7
= 3/28
ANSWER: C
Answer: C
Question: Find the area of circle whose radius is 14m?
Options:
A)288
B)154
C)616
D)168
E)178
Rationale: 22/7 * 14 * 14
= 616
Answer: C
Answer: C
Question: There are 12 yes or no questions. How many ways can these be answered?
Options:
A)1324
B)6234
C)3651
D)4562
E)4096
Rationale: Each of the questions can be answered in 2 ways (yes or no)
Therefore, no. of ways of answering 12 questions = 212 = 4096 ways.
Ans:E
Answer: E
Question: The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum E of all the digits of the integers from 0 to 99 inclusive?
Options:
A)450
B)810
C)900
D)1000
E)1100
Rationale: We want the sum of the digits from 0 to 99, so I approximated:
0-9 ->45-> (9+0)*10/2
40-49 ->85(13+4)*10/2
90-99 ->135(18+9)*10/2
We can see at a glance that theweightgoes up as the numbers go up (meaning the difference between 85 and 45 is 40, while 135-85 is 50, this means that the second part of this sequence carries more weight for our result), so we know that the final answer has to be more than 850 (85*10) but close to it, and that's just E=900:the answer is C.
Answer: C
Question: A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Options:
A)5 : 6
B)6 : 5
C)8 : 3
D)3 : 8
E)None of these
Rationale: Explanation :
Let the rate upstream of the boat = x kmph
and the rate downstream of the boat = y kmph
Distance travelled upstream in 8 hrs 48 min = Distance travelled downstream in 4 hrs.
Since distance = speed × time, we have
x × (8(4/5)) = y × 4
x × 44/5 = y × 4
x × 11/5 = y --------- (equation 1)
Now consider the formula given below
Hence, speed of the boat = (y+x)/2
speed of the water = (y−x)/2
Required Ratio = left(fracy+x2right):left(fracy−x2right)left(fracy+x2right):left(fracy−x2right)
= (y + x):(y − x)
∵ (Substituted the value of y from equation 1)
= left(frac11x5+xright):left(frac11x5−xright)left(frac11x5+xright):left(frac11x5−xright)
= (11x + 5x) : (11x − 5x)
= 16x : 6x
= 8 : 3 Answer : Option C
Answer: C
Question: A rectangular floor that measures 6 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters. If the carpet squares cost $15 apiece, what is the total cost for the number of carpet squares needed to cover the floor?
Options:
A) $200
B) $240
C) $480
D) $225
E) $1,920
Rationale: The width of the rectangular floor(6 m) is a multiple of one side of the square(2 m), and the length of the floor(10 m) is also a multiple of the side of the square. So the number of carpets to cover the floor is (6/2)*(10/2)=15.
The total cost is 15*15=$225.
The answer is, therefore, D.
Answer: D
Question: The successive discounts 20% and 15% are equal to a single discount of?
Options:
A)26
B)22
C)32
D)82
E)61
Rationale: Explanation:
Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.
Answer: C
Answer: C
Question: 21 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.
Options:
A)19
B)20
C)21
D)22
E)23
Rationale: in case of cycle no of handshakes = no of persons
hence ans = 21
ANSWER:C
Answer: C
Question: If A,B,C,D,E,F,G,H,I,J are in an increasing Arithmetic Progression as such. Then Which of the following operations will result in only mean being modified but not the median.
A) A is removed
B) A and J are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and E are removed
Options:
A)1) A and B
B)2) A and E
C)3) A,C,E
D)4) All of them
E)5) None of them
Rationale: There are 10 equidistant numbers on the number line.
Mean and median will be the average of middle two numbers.
If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. But there is no change possible where mean will change and median will not change.
Answer: E
Answer: E