divelab/Sys2Bench huggingface dataset:
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 200 units?
Options:
A)50 hours
B)40 hours
C)25 hours
D)12 hours
E)8 hours
Rationale: Here, we're told that 5 machines can produce 20 units in 10 hours....
That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.
20 units/5 machines = 4 units are made by each machine every 10 hours
Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...
10 hours/4 units = 2.5 hours per unit when 1 machine is working.
The prompt asks us how long would it take 20 machines to produce 200 units.
If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 200 units is '10 times' 20, we need '10 times' more TIME.
(2.5 hours)(10 times) = 25 hours
Final Answer:
[Reveal]Spoiler:
C
Answer: C
Question: Two men can complete a piece of work in four days. Two women can complete the same work in eight days. Four boys can complete the same work in five days. If four men, eight women and 20 boys work together in how many days can the work be completed?
Options:
A)1/2 day
B)1/8 day
C)1/3 day
D)8/2 day
E)1/7 day
Rationale: Two men take four days to complete the work four men would take (2 * 4)/4 = 2 days to complete it.
Similarly four women would take two days to complete it and 20 children would take one day to complete it.
All the three groups working togerther will complete 1/2 + 1/2 + 1/1 work in a day
= 2 times the unit work in a day.
They will take 1/2 a day to complete it working together.
Answer: A
Answer: A
Question: It is known that no more than 100 children will be attending a birthday. What is the smallest number of toffees that must be brought to the party so that each child receives the same number of toffees?
Options:
A)15
B)320
C)400
D)150
E)36
Rationale: The number of children is not specified. We are just given that there are no more than 100 children.
If we assume that number of children is 75 then answer will be D.
If we assume that number of children is 100 then answer will be C because only 400 is divisible by 100.
Answer: C
Question: A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 840 in 4 years. The rate of interest per annum is?
Options:
A)2 1/2 %
B)4%
C)5%
D)6 2/3 %
E)6%
Rationale: S.I. on Rs. 800 for 1 year = (840 - 800) = Rs. 40 Rate = (100 * 40)/(800 * 1) = 5%
ANSWER:C
Answer: C
Question: A vehicle has an insurance of 4/5 of its original value. Premium on the vehicle at the rate of 1.3% amounts to 910 Rs. What is the original value of the vehicle?
Options:
A)87,508
B)87,502
C)87,500
D)87,509
E)87,5083
Rationale: Explanation:
No explanation is available for this question!
ANSWER: C
Answer: C
Question: 15.06 * 0.0000001 = ?
Options:
A)15060000
B)0.001506
C)1.506e-06
D)0.1506
E)None of these
Rationale: Explanation:
Clearly after decimal 9 digits should be there.
Option C
Answer: C
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 220 per month. What is his monthly salary?
Options:
A)5500
B)2999
C)2878
D)2990
E)2771
Rationale: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 â€“ 96 =Rs. 4
100 ------ 4
? --------- 220 => 5500
Answer: A
Answer: A
Question: In how many ways can be 7 boys and 7 girls sit around circular table so that no two boys sit next to each other?
Options:
A)(5!)^2
B)(6!)^2
C)6!7!
D)11!
E)(5!)^2*6!
Rationale: first fix one boy and place other 6 in alt seats so total ways is 6!
now place each girl between a pair of boys... total ways of seating arrangement of girls 7!
total is 6!*7!
ANS C
Answer: C
Question: The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#39?
Options:
A)17
B)18
C)19
D)20
E)21
Rationale: First, let's translate the expression 21#39, using the definition given:
21#39 = 21×24×27×30×33×36×39
We need the prime factorization of this product.
Let's factor out 3 from each multiple.
21#39 = 3^7(7×8×9×10×11×12×13)
Now let's replace each consecutive integer with its prime factorization:
21#39 = 3^7(7×2^3×3^2×(2×5)×11×(2^2×3)×13)
Let's group the prime bases:
21#39 = 2^6×3^10×5×7×11×13
The sum of the exponents is 6 + 10 + 1 + 1 + 1 + 1 = 20
The answer is D.
Answer: D
Question: John bought an old Vehicle for $42000. He spent $13000 on repairs and sold it for $64900. What is his profit percent?
Options:
A)11%
B)15%
C)18%
D)17%
E)13%
Rationale: C
18%
Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100 = 18%
Answer: C
Question: If (2x + 1) times (x + 2) is an odd integer, then x must be:
Options:
A)an odd integer
B)an even integer
C)a prime number
D)a composite number
E)a negative integer
Rationale: Solution:
(2x + 1) times (x + 2) means (2x + 1)(x + 2)
(2x + 1)(x + 2) = 2x^2+5x+2
For 2x^2+5x+2 to be odd, 5x+2 must be odd since 2x^2 is always even.
So 5x must be odd, hence x must be odd.
Therefore x is an odd integer.
Answer: A
Answer: A
Question: What is the speed of the stream if a canoe rows upstream at 9 km/hr and downstream at 12km/hr
Options:
A)1 kmph
B)4 kmph
C)3 kmph
D)2 kmph
E)1.5 kmph
Rationale: Sol.
Speed of stream = 1/2(12 -9) kmph = 1.5 kmph.
Answer E
Answer: E
Question: A right triangle has sides of a, b, and 7, respectively, where a and b are both integers. What is the value of (a + b)?
Options:
A)40
B)42
C)46
D)48
E)49
Rationale: LET a= hypotenuse , b =base ,7 = perpendicular . therefore a^2 -b^2 =7^2 or (a+b)(a-b) = 49
a+b =49/a-b ' a-b cannot be zero ..therefore a+ b =49 where a-b is equal to 1
E
Answer: E
Question: How many positive integers less than 100 are neither multiples of 5 or 6.
Options:
A)a)30
B)b)31
C)c)32
D)d)33
E)e)67
Rationale: To answer this Q we require to know
1) multiples of 5 till 100 = 100/5 = 20
2) Multiples of 6 till 100 = 100/6 = 16.66= 16
add the two 20+16=36 ; subtract common terms that are multiple of both 5 and 6..
LCM of 5 and 6 = 30
Multiples of 30 till 100 = 100/30 = 3.3 = 3
so total multiples of 2 and 3 = 36-3 = 33
ans = 100-33 = 67
E
Answer: E
Question: Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
Options:
A)10.77 a.m
B)10.85 a.m
C)10.27 a.m
D)10.25 a.m
E)20.25 a.m
Rationale: Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs.
Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs
= 2 5/6 = 2 hrs 50 min
Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.
So, Anna reached city A at 10.25 a.m.
Answer:D
Answer: D
Question: How many different positive integers exist between 10^7 and 10^8, the sum of whose digits is equal to 2?
Options:
A)6
B)7
C)5
D)8
E)18
Rationale: So, the numbers should be from 10,000,000 to 100,000,000
The following two cases are possible for the sum of the digits to be 2:
1. Two 1's and the rest are 0's:
10,000,001
10,000,010
10,000,100
10,001,000
10,010,000
10,100,000
11,000,000
7 numbers.
2. One 2 and the rest are 0's:
20,000,000
1 number.
Total = 8 numbers.
Answer: D
Answer: D
Question: 0.0005?=0.01
Options:
A)5
B)0.05
C)0.5
D)50
E)None of these
Rationale: Explanation :
Required Answer = 0.0005/0.01 = 0.05/1 = 0.05. Answer : Option B
Answer: B
Question: A toy store regularly sells all stock at a discount of 20% to 40%. If an additional 25% were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount?
Options:
A)$5.60
B)$7.20
C)$8.80
D)$9.60
E)$15.20
Rationale: The lowest price would have to be calculated by finding the price of the $16 product after the initial 40% reduction, then the final price after 25% was taken off of the already-discounted price. So:
A 40% discount on a $16 product would = 60% of the original $16 price: $16 x .60 = $9.6
Next you have to find the price after an additional 25% had been discounted from the $9.6, which would be 75% of the $9.6: $9.6 x .75 = $7.20
The answer is B
Answer: B
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 63. By how much do the two digits differ?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Let’s first label the original two-digit integer as N. We can then say that N = 10A + B, where A is the tens digit and B is the units digit of N.
If this is hard to see let’s try it with a sample number, say 24. We can say the following:
24 = (2 x 10) + 4
24 = 20 + 4
24 = 24
Getting back to the problem, we are given that if the integer N has its digits reversed the resulting integer differs from the original by 63. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.
10B + A = reversed integer
Since we know the resulting integer differs from the original by 63 we can say:
10B + A – (10A + B) = 63
10B + A – 10A – B =63
9B – 9A = 63
B – A = 7
Since B is the tens digit and A is the units digit, we can say that the digits differ by 7.
The answer is E.
Answer: E
Question: 5 cylinders are built successively, the first is 4 meters tall and the following cylinders are each 4 meters taller than the previous. If the perimeter is 10pi m, what is the total surface area of the 5 cylinders, excluding the bases of each cylinder?
Options:
A)725pi sq m
B)1025pi sq m
C)600pi sq m
D)125pi sq m
E)850pi sq m
Rationale: s.a. = h x p + 2 x a
we need to excude the bottom area, so the formula becomes:
s.a. = h x p + a
p = 2 pi x r, so 10 pi = 2 pi x r
r = 5
since we have 5 cylinders with different heights the equation becomes
s.a. = ( 4 + 8 + 12 + 16 + 20 ) x 10pi + 5 x pi x r ^2
60 x 10 pi + 5 pi x 5^2
600 pi + 125 pi = 725 pi sq. m.
Answer is A
Answer: A
Question: The length of a rectangular plot is 10 meters more than its width. If the cost of fencing the plot at $15.50 per meter is $682, what is the length of the plot in meters?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: perimeter = 2L + 2W = 2L + 2(L-10) = 4L - 20
cost of fencing = (4L - 20) * 15.50 = 62L - 310 = 682
62L = 992
L = 16 meters
The answer is D.
Answer: D
Question: Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 250 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?
Options:
A)1,300
B)1,000
C)900
D)700
E)650
Rationale: Given: Atleast 1 juice was liked by the participants. --> Neither = 0
Assume, I -->No overlap between the sets
II --> Overlap between 2 sets
III --> Overlap between 3 sets
I + 2*(II) + 3*(III) = 100 + 200 + 700
I + 2*(250) + 3*(50) = 1000
I = 350
Total number of shoppers who took the taste test = I + II + III = 350 + 250 + 50 = 650
Answer: E
Answer: E
Question: In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score P that Lindsey could have received on her midterm exam?
Options:
A)52%
B)64%
C)72%
D)76%
E)80%
Rationale: If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%.
Answer: A
Question: If three eighth of a number is 141. What will be the approximately value of 32.08% of this number?
Options:
A)90
B)120
C)160
D)60
E)100
Rationale: x * 3/8 = 141 => x= 376
376 * 32.08/100 = 120
ANSWER:B
Answer: B
Question: A searchlight on top of the watch-tower makes 1 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 20 seconds?
Options:
A)1/4
B)1/3
C)1/2
D)2/3
E)3/4
Rationale: 1 revolutions per minute = 1 revolution every 60 seconds
So no matter what anybody appearing at the tower cannot stay in the dark for more than 60 seconds. This will be our total number of possibilities i.e the denominator.
P(man in dark for at least 20 seconds) = 1 - P (man in dark for max of 20 seconds) = 1 - 20/60 = 1 - 1/3 = 2/3
or the other way would be:
P(man in dark for at least 20 seconds) is like saying he can be in dark for 5,6,7...all the way to 60 seconds because that is the max. In this approach it would be 20/60 seconds = 1/3.
Answer is B
Answer: B
Question: 85% of a number is added to 24, the result is the same number. Find the number?
Options:
A)330
B)267
C)278
D)160
E)882
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Answer: D
Question: 36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
Options:
A)76
B)55
C)44
D)12
E)91
Rationale: Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1}
From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12.
Answer:D
Answer: D
Question: IF
6= I
7= E
8= I
9= I
10=E
THEN 11=?
Options:
A)I
B)J
C)K
D)L
E)M
Rationale: IF
6= I... Second letter of ONE.
7= E.... Second letter of TWO.
8= I
9= I
10= E
THEN 11=L... Second letter of Eleven
ANSWER:D
Answer: D
Question: A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different colors r patterns can be floor be parqueted?
Options:
A) 104
B) 213
C) 3^5
D) 705
E) 726
Rationale: Total number of squares we need to fill = 6
Number of colors we have r= 3
Therefore, total number of patterns = 3*3*3*3*3*3 = 729
However, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).
Thus our answer should be :729 - 3 = 726
Answer : E
Answer: E
Question: We all know that square root of number 121 is 11.
But do you know what si the square root of the number "12345678987654321" ?
Options:
A)222222222
B)111111111
C)333333333
D)777777777
E)444444444
Rationale: B
It's a maths magical square root series as :
Square root of number 121 is 11
Square root of number 12321 is 111
Square root of number 1234321 is 1111
Square root of number 123454321 is 11111
Square root of number 12345654321 is 111111
Square root of number 1234567654321 is 1111111
Square root of number 123456787654321 is 11111111
Square root of number 12345678987654321 is 111111111 (answer)
Answer: B
Question: Joe went on a diet 3 months ago when he weighed 222 pounds. If he now weighs 198 pounds and continues to lose at the same average monthly rate, in approximately how many months will he weigh 170 pounds?
Options:
A) 3
B) 3.5
C) 4
D) 4.5
E) 5
Rationale: 222 - 198 = 24 pounds lost in 3 months
24/3 = 8, so Joe is losing weight at a rate of 8 pounds per month.
...in approximately how many months will he weigh 170 pounds?
A simple approach is to just list the weights.
Now: 198 lbs
In 1 month: 190 lbs
In 2 months: 182 lbs
In 3 months: 174 lbs
In 4 months: 166 lbs
Since 170 pounds is halfway between 174 and 166, the correct answer must be 3.5 months.
Answer: B
Answer: B
Question: The average of first 10 even numbers is?
Options:
A)17
B)199
C)16
D)11
E)123
Rationale: Sum of 10 even numbers = 10 * 11 = 110
Average = 110/10 = 11
Answer:D
Answer: D
Question: There are 5 balls are in a bag; 2 are red balls and the other 3 are green balls. If 2 magazines are to be selected at random from the 5 balls, what is the probability that at least one of the green ball will be selected?
Options:
A)11/10
B)3/10
C)5/10
D)7/10
E)9/10
Rationale: Total probability=5C2=10
3C2 +3C1*2C1=3+6=9
therefore the probability that at least one of the green ball will be selected= 9/10
answer is E
Answer: E
Question: Look at this series: 23, 22, 24, 23, 25, 24, ... What number should come next?
Options:
A)20
B)26
C)28
D)21
E)22
Rationale: In this simple alternating subtraction and addition series; 1 is subtracted, then 2 is added, and so on.
23-1 = 22
22+2 = 24
24-1 = 23
23+2 = 25
25-1 = 24
24+2 = 26
Answer is B
Answer: B
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and B together can do it in 2 hours. How long will C alone take to do it?
Options:
A)12hours
B)10hours
C)6hours
D)8hours
E)4hours
Rationale: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + B)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
C's 1 hour work = (7/12 - 1/2) = 1/12
C alone will take 12 hours to do the work.
Answer:A
Answer: A
Question: If the sum of three consecutive positive odd integers is A, then the sum of the next three consecutive odd integers in terms of A is:
Options:
A)A+3
B)A+9
C)A+18
D)2A + 3
E)3A
Rationale: In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median
I.e. Median = A/3 = Mean = Second Integer
First Integer = A/3 - 2
Second Integer = A/3
Third Integer = A/3 + 2
i.e.
Fourth Integer = A/3 + 4
Fifth Integer = A/3 + 6
Sixth Integer = A/3 + 8
Now Mean of next 3 Integers = Median = A/3 + 6
i.e. Sum of Next 3 integers = (A/3 + 6)*3 = A+18
Answer: option C
Answer: C
Question: The average of 35 numbers is 25. If each number is multiplied by 5, find the new average?
Options:
A)125
B)777
C)255
D)199
E)261
Rationale: Sum of the 35 numbers = 35 * 25 = 875
If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5.
Thus, the new average = 25 * 5 = 125.Answer: A
Answer: A
Question: In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1?
Options:
A)25
B)45
C)55
D)70
E)30
Rationale: Day 1&2 = 80; Only Day 1&2 (80-20) = 60,
Day 2&3 = 70; Only Day 2&3 (70-20) = 50,
Only Day 1 = 175 - (60+50+20) = 45
Answer:B
Answer: B
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Options:
A)Rs.200
B)Rs.220
C)Rs.250
D)Rs.300
E)Rs.350
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
C
Answer: C
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 16000, then find the annual income of A?
Options:
A)Rs. 537600
B)Rs. 180000
C)Rs. 201600
D)Rs. 504000
E)None of these
Rationale: B's monthly income = 16000 * 112/100 = Rs. 17920
B's monthly income = 2 parts ----> Rs. 17920
A's monthly income = 5 parts = 5/2 * 17920 = Rs. 44800
A's annual income = Rs. 44800 * 12 = Rs. 537600
ANSWER:A
Answer: A
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 4 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)15 a.m
B)10 a.m
C)7 a.m
D)02 a.m
E)05 a.m
Rationale: Suppose they meet x hours after 4 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 7 a.m.
Answer:C
Answer: C
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 25% profit by using a false weight. What weight does he substitute for a kilogram?
Options:
A)800 1/7 grams
B)800 grams
C)800 8/3 grams
D)883 1/3 grams
E)800 1/3 grams
Rationale: If the cost price is Rs.100, then to get a profit of 25%, the selling price should be Rs.125.
If 125kg are to be sold, and the dealer gives only 100kg, to get a profit of 25%.
How many grams he has to give instead of one kilogram(1000 gm).
125 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/125 =800 grams.
Answer:B
Answer: B
Question: A man's speed with the current is 21 km/hr and the speed of the current is 4.3 km/hr. The man's speed against the current is
Options:
A)9.2
B)10.3
C)11.5
D)12.4
E)13
Rationale: Man's rate in still water = (21 - 4.3) km/hr = 16.7 km/hr.
Man's rate against the current = (16.7 - 4.3) km/hr = 12.4 km/hr.
Answer:D
Answer: D
Question: The sum of two numbers is 21 and the sum of their squares is 527. Find the product of the numbers.
Options:
A)48
B)41
C)46
D)43
E)96
Rationale: Let a and b be the two numbers(a+b)^2=a^2+2ab+b^2Given (a+b)=21 a^2+b^2=527So, 21^2=527+2ab2ab=527-4412ab=86ab=43Ans D
Answer: D
Question: If a, b, and c are consecutive positive integers and a > b > c, which of the following must be true?
I. c - a = 2
II. abc is an odd integer.
III. (a + b + c)/3 is an integer.
Options:
A) I only
B) II only
C) I and III only
D) II and III only
E) I, II, and III
Rationale: Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true.
Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is false.
Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.
Answer: C.
Answer: C
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 96km/h, what is the circumference of the tire?
Options:
A)7 meters
B)9 meters
C)4 meters
D)5 meters
E)3 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 96,000 m : C is the circumference
C = 4 meters
correct answer C
Answer: C
Question: Approximately what percent of the employees with 5 or more years of employment are NOT taking either workshop?
Options:
A)86%
B)64%
C)50%
D)14%
E)7%
Rationale: Total = n(A) + n(B) - Both + None
None = Total - n(A) - n(B) + Both
Calculate "none" for each case
None(5+ yrs Line) = 200 - 50 - 40 + 30 = 140
None(5+ yrs Staff) = 160 - 40 - 50 + 20 = 90
Employees not taking either workshop/Total number of employees = (140 + 90)/(200 + 160) = 230/360 = About 64%
ANSWER:B
Answer: B
Question: A and B undertake to do a piece of work for $600. A alone can do it in 6days while B alone can do it in 8days. With the help of C, they finish it in 3days. Find the share of A?
Options:
A)$100
B)$150
C)$300
D)$250
E)$350
Rationale: C's 1day work = (1/3)-(1/6 + 1/8) = 1/24
A:B:C= 1/6 : 1/8: 1/24 = 4:3:1
A's share = 600*4/8 = $300
Answer is C
Answer: C
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 171.The amount of the bill is
Options:
A)Rs. 1386
B)Rs. 1764
C)Rs. 1425
D)Rs. 2268
E)None of these
Rationale: Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.171.
∴ x 16 x9/ 12x 1/100}= 171 or x = 1425.
∴ P.W. = Rs. 1425.
Answer C
Answer: C