divelab/Sys2Bench huggingface dataset:
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?
Options:
A)125786
B)158799
C)564323
D)344567
E)220030
Rationale: (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
E
Answer: E
Question: If you write down all the numbers from 1 to 100, then how many times do you write 2 ?
Options:
A)A)11
B)B)18
C)C)20
D)D)21
E)E)22
Rationale: Explanation:
Clearly, from 1 to 100, there are ten numbers with 2 as the unit's digit- 2, 12, 22, 32, 42, 52, 62, 72, 82, 92; and ten numbers with 2 as the ten's digit - 20, 21, 22, 23, 24, 25, 26, 27, 28, 29.
So, required number = 10 + 10 = 20.
Answer: C
Answer: C
Question: I forgot the last digit of a 7-digit telephone number. If 1 randomly dial the final 3 digits after correctly dialing the first four, then what is the chance of dialing the correct number?
Options:
A)1/1002
B)1/1028
C)1/1000
D)1/1287
E)1/1289
Rationale: Explanation:
It is given that last three digits are randomly dialled. then each of the digit can be selected out of 10 digits in 10 ways.
Hence required probability = = 1/1000
Answer: C) 1/1000
Answer: C
Question: In a 200 meters race, A beats B by 20 meters, while in a 100 meters race, B betas C by 5 meters. A beats C in a kilometer race by
Options:
A)105 meters
B)225 meters
C)205 meters
D)145 meters
E)None
Rationale: When A = 200, B = 180.
When B = 100, C = 95.
Make B = 900. A will be 1000. C will be 855.
Answer: D.
Answer: D
Question: A boat goes 100 km downstream in 10 hours, and 60 m upstream in 15 hours. The speed of the stream is?
Options:
A)3
B)22 1/4
C)22 1/2
D)22 1/1
E)22 1/3
Rationale: 100 --- 10 DS = 10
? ---- 1
60 ---- 15 US = 4
? ----- 1 S = (10 - 4)/2
= 3 kmp Answer: A
Answer: A
Question: If the price of 357 apples is Rs.1517.25, what will be the approximate price of 49 dozens of such apples?
Options:
A)Rs. 2500
B)Rs. 2300
C)Rs. 2200
D)Rs. 1400
E)Rs. 1600
Rationale: Explanation:
Price of 357 apples = Rs.1517.25
price of 1 apple = Rs. 1517.25/357
price of 49 dozens apples = Rs (49×12×1517.25/357)≈Rs. 2500
Answer: Option A
Answer: A
Question: Two cards are drawn together from a pack of 52 cards. The probability that one is a club and other is a diamond, is:
Options:
A)29/34
B)47/100
C)3/20
D)13/102
E)None of these
Rationale: Explanation :
One card drawn.
Probability of being it club or diamond = (13x2)/52.
Another card drawn.
Now, Probability of being it of other suit(the suit among the two, not selected in first draw) = 13/51.
Hence, probability of event = ((13x2)/52)x(13/51)= 13/102.
Answer : D
Answer: D
Question: Which of the following equations describes a line that is perpendicular to y = x/2 + 5?
Options:
A)y = x − 5
B)y = −3 − 2x
C)y = 5x
D)y = 5x - 1
E)y = 1/x + 5
Rationale: Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y = x/2 + 5 is 1/2 so the slope of a perpendicular line will be -2.
The answer is B.
Answer: B
Question: If b < 2 and 2x - 2b = 0, which of the following must be true?
Options:
A)x > -3
B)x < 2
C)x = 3
D)x < 3
E)D. x > 3
Rationale: 2x - 2b = 0
Therefore, 2x = 2b
As, b<2
2x < 2(2)
i.e x < 2
Answer : B
Answer: B
Question: By investing in 16 % stock at 64, one earns Rs. 1500. The investment made is:
Options:
A)5760
B)7667
C)4445
D)4566
E)3344
Rationale: Explanation:
To earn Rs., investment = Rs. 64.
To earn Rs. 1500, investment = = Rs. 5760.
Answer: C) 5760
Answer: C
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
Options:
A)2 1/0
B)2 1/8
C)2 1/5
D)2 1/3
E)2 1/2
Rationale: Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours.
Answer:E
Answer: E
Question: In a forest 140 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
Options:
A)150
B)750
C)1,250
D)1,400
E)2,500
Rationale: The percentage of tagged deer in the second sample = 5/50*100=10%.
So, 140 tagged deers comprise 10% of total # of deers --> total # of deers = 140*10 = 1,400.
Answer: D.
Answer: D
Question: To create paint with a certain shade of gray, one must combine 2.3 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?
Options:
A)152.1
B)156.4
C)347.1
D)694.4
E)705.6
Rationale: Since the ratio of Black to White is 2.3 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.
Now between A and B:
Black:White = 2.3:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. B is more than half so can not be the answer, A fits the criteria hence should be the correct answer. No calculation needed whatsoever.
Answer: A
Question: A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 14 cups of tea are prepared, 7 in one way and 7 in other. Find the different possible ways of presenting these 14 cups to the expert.
Options:
A)2532
B)2432
C)3032
D)3432
E)None
Rationale: Solution:
Since, there are 7 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,
[14!/(7!x7!)]= 3432
Answer: Option D
Answer: D
Question: If December 3rd, 1999 is a Friday, what day is January 6th, 2000?
Options:
A)Wednesday
B)Thursday
C)Friday
D)Saturday
E)Sunday
Rationale: There is difference of 34 days from Dec. 3rd 1999 to Jan. 6th 2000.
34/7 has a remainder of 6.
Jan. 6th is: Friday + 6 days = Thursday
The answer is B.
Answer: B
Question: A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 7 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
Options:
A)10
B)7
C)9
D)5
E)12
Rationale: Relative speed = Speed of A + Speed of B (âˆ´ they walk in opposite directions)
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour and 2 times in 1/2 hour
Time duration from 7 am to 9.30 am = 2.5 hour
Hence they cross each other 12 times before 9.30 am
Answer : E
Answer: E
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
Options:
A)32
B)52
C)62
D)72
E)35
Rationale: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
ANSWER B
Answer: B
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
Options:
A)12
B)24
C)34
D)48
E)54
Rationale: Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.Answer: Option D
Answer: D
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
Options:
A)288
B)200
C)289
D)267
E)261
Rationale: The number of ways to select two men and three women
= 5C2 * 6C3
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
Answer:B
Answer: B
Question: The width of a rectangle is 10 meter and its area is 150 square meter. If length of the rectangle is increased then its new area is 4/3 times of the original area. What is the new perimeter of the rectangle?
Options:
A)48 m
B)52 m
C)54 m
D)60 m
E)None of these
Rationale: Let length of new rectangle be x m
Then x×10=150×4/3=200 or, x=20 m
Hence new perimeter=2(10+20)=60 m
ANSWER:D
Answer: D
Question: A train 600 m long passed a pole in 12 sec. How long will it take to pass a platform 450 m long?
Options:
A)19
B)20
C)21
D)22
E)23
Rationale: Speed = 600/12
= 50 m/sec.
Required time
= (600 + 450)/50
= 21 sec.
Answer:C
Answer: C
Question: The traffic lights at 3 different roads change after every 48 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.
Options:
A)9:22:12
B)9:42:15
C)10:15:24
D)9:54:12
E)10:01:20
Rationale: LCM of 48,72,108 = 432 = 7mnts 12sec
The lines will change every 7m 12sec
The light will change again after 9:15 AM is = 9:15+0:07:12 = 9:22:12
Answer is A
Answer: A
Question: What is the units digit of (147^17)^48 ?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: The units digit of the exponents of 7 repeat in a cycle of four, which is {7,9,3,1}. The number 17 has the form 4n+1 so the units digit is 7 inside the bracket. The exponent 48 has the form 4n, so the units digit is 1. The answer is A.
Answer: A
Question: The cost price of 4 notebooks is equal to the selling price of 6 notebooks. What is the % profit or loss.
Options:
A)32.3 %
B)33.3 %
C)12.3 %
D)23.3 %
E)13.3 %
Rationale: Let the cost price of 1 notebooks be Rs 1
Cost of 6 notebooks = Rs 6
Selling price of 6 apples = 4
Gain/loss = 6 - 4 = 2
%=2/6âˆ—100= 33.3
Answer: B
Answer: B
Question: Bill is golfing with three friends and can either buy generic golf tees that are packaged by the dozen or the higher quality Aero flight tees that come by the pair. What is the minimum number of packages of Aero flight tees Bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome, if he will buy no more than 2 packages of the generic golf tees?
Options:
A)16
B)10
C)28
D)4
E)2
Rationale: At least 20 golf tees for each member of his foursome = total of at least 4*20 = 80 tees.
2 packages of the generic golf tees, that are packaged by the dozen = 2*12 = 24 tees.
So, Bill must by at least 16 Aero tees. They come by the pair, hence he must by at least 56/2 = 28 packages of Aero flight tees.
Answer: C.
Answer: C
Question: A father was as old as his son's present at the time of your birth. If the father's age is 42 years now, the son's age 5years back was?
Options:
A)10 years
B)12 years
C)14 years
D)16 years
E)20 years
Rationale: Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21.
Son's age 5 years back (21 - 5) = 16 years.
D
Answer: D
Question: The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n3/3 + cn2 + n/6, where c is a constant. What is the sum of the first 15 positive perfect squares?
Options:
A)1,010
B)1,164
C)1,240
D)1,316
E)1,476
Rationale: For n=1,
1=1/3 + c + 1/6
1=1/2 + c
=> c = 1/2
15*15*15/3 + 1/2*15*15 + 15/6=1240
ANSWER:C
Answer: C
Question: What is the range of all the roots of |x^2 - 1| = x ?
Options:
A)4
B)3
C)2
D)1
E)0
Rationale: we get 2 quadratic equations here ..
1) x^2-x-1=0 ....... roots 2 , -1
2) x^2+x-1=0 ........ roots -2, 1
Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations .
So value of x for given equation .... x=2 or x=1
I guess range is 2-1 =1
D
Answer: D
Question: Find value of X: 5216 × 51 = X
Options:
A)265016
B)343546
C)266016
D)353546
E)457632
Rationale: Normal way of multiplication may take time. Here is one alternative.
5216×51=(5216×50)+5216=(5216×1002)+5216=5216002+5216=260800+5216=266016
C
Answer: C
Question: By walking at 3/4th of his usual speed, a man reaches office 16 minutes later than usual. What is his usual time?
Options:
A)48min
B)50min
C)65min
D)60min
E)70min
Rationale: let T be the usual time.
time spent=4T/3
therefore, 4T/3=T+16
4T=3T+48...therefor T=48min
ANSWER:A
Answer: A
Question: When an amount was distributed among 14 boys, each of them got rs 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys. What was the amount?
Options:
A)Rs. 5040
B)Rs. 6040
C)Rs. 7040
D)Rs. 5440
E)Rs. 8040
Rationale: If 18 boys got Rs x, then
18x = 14*(x+80)= 14x+1120
or
4x =1120
x= 280
so total amt = 280*18 = Rs. 5040
ANSWER:A
Answer: A
Question: If the remainder is 10 when positive integer n is divided by 14, what is the remainder when n is divided by 7?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Assume x is quotient here,
n=14x+7 ----------(1)
and n=7x+ ?
We can also write equation (1) as:
n=(14x+7)+3.
ie 7(2x+1)+3 ie the first term is perfectly divisible by 7.
So,the remainder left is 3.
So,answer (D) is right choice.
Answer: D
Question: A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?
Options:
A)20 hours
B)19 hours
C)90 hours
D)80 hours
E)70 hours
Rationale: Explanation:
Part filled without leak in 1 hour = 1/9
Part filled with leak in 1 hour = 1/10
Work done by leak in 1 hour
=1/9âˆ’1/10=1/90
We used subtraction as it is getting empty.
So total time to empty the cistern is 90 hours
ANSWER IS C
Answer: C
Question: In my bungalow in Bangalore I have a beautiful rose garden.
The four sides of the garden are known to be 20, 16, 12 and 10 rods. And it is also knownthat it has the greatest possible area for those area?
Options:
A)189.2
B)177.2
C)153.9
D)200.1
E)194.4
Rationale: E
194.4 square roots will be the answer
Half the sum of the side is 29 and from this we deduct the sides in turn, which gives us 9, 13, 17, 19, which when multiplied together make 37791, The square root of this number is 194.4.
194.4 square roots will be the answer
Answer: E
Question: Consider a Number 3.1n6
n represent the hundredths digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
Options:
A)4
B)3
C)1
D)2
E)5
Rationale: In this ques we are given the thousandth digit as 6, so the hundreth digit can take any value from 0-9. For the hundreth digit i considered 2 set of values (i) 0, 1, 2, 3 and (ii) 4, 5, 6, 7, 8, 9. Given that the thousandth digit is 6, the hundreth digit has to go up by 1, and correspondingly, the tenth digit should increase by one.i.e 0-9.say 2
D
Answer: D
Question: In a certain kindergarten, every child has got either a dog or a cat or both. 18 children have got dogs only and 6 children have got both dogs and cats. If there are 30 children in the kindergarten, how many of them have cats?
Options:
A)6
B)12
C)14
D)16
E)20
Rationale: A : Only Cats
B : Both Cats and Dogs
C : Only Dogs
As per question, A + B + C =30
C = 18
B = 6, so A = 6. Hence, A + b = 12. Answer is B
Answer: B
Question: I. j; k; m; n; p
II. j - 10; m; m; m; p + 15
III. j + 2; k + 1; m; n - 1; p - 2
If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation H in which of the following?
Options:
A) I, III, II
B) II, I, III
C) II, III, I
D) III, I, II
E) III, II, I
Rationale: Range of 1st Set = (p-j)
Range of 2nd Set = P+15 - j +10 = (p-j) +25
Range of 3rd Set = P -2 - j - 2 = (p-j) - 4
R2 > R1 > R3 ==> SD2 > SD1 > SD3
Since, H=Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B
Answer: B
Question: When the price of an article is reduced by 30%, the sales increases by 50%. The percentage change in the total amount of receipts is?
Options:
A)5% decrease
B)5% increase
C)10% decrease
D)15% decrease
E)none of these
Rationale: We have, receipts = Price x Sales
Therefore, net % change in receipts
= (x + y + xy/100) %
= [ - 30 + 50 + (-30 x 50)/100]%
= 5% increase.
ANSWER:B
Answer: B
Question: The average (arithmetic man) of three integers a, b, and c is exactly half the median. If a < b < c and a = 0, what is the value of c/b?
Options:
A)2
B)3/2
C)4
D)5
E)Cannot be determined from the information given.
Rationale: The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=1b/2 --> since a=0, then (0+b+c)/3=1b/2 --> c=3b/2 --> c/b=3/2.
Answer: B.
Answer: B
Question: Bob invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest?
Options:
A)5%
B)10%
C)12%
D)15%
E)20%
Rationale: First divide $550/2 years to get 275$/yr non-compounding interest.
Next, subtract from the total compound after 2 years to see the interest gained in the second year. This can be done because the same amount has been invested in both accounts and the interest gained for the first year will be the same. So, $605-$275= $330.
To find the difference in interest gained, $330-$275= $55 increase in interest after the first year through compounding.
From this information we can set up the equation $275 * X% = $55... 55/275=1/5=20% giving us answer choice E.
Answer: E
Question: For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6,7,9,-10?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.
1*(-3)=-3=negative;
-3*2=-6=negative;
5*(-4)=-20=negative.
-6*7 = -42 > negative
9 * -10 = -90 > negative
So there are 5 pairs of consecutive terms.
Answer: E
Answer: E
Question: Tough and Tricky questions: Decimals.
The value of x is derived by summing a, b, and c and then rounding the result to the tenths place. The value of y is derived by first rounding a, b, and c to the tenths place and then summing the resulting values. If a = 5.43, b = 2.98, and c = 3.76, what is y – x?
Options:
A)0
B)0.04
C)0.05
D)0.1
E)0.2
Rationale: To find x, we first sum a, b, and c, then round to the tenths place. 5.43 + 2.98 + 3.76 = 12.17, which rounds to 12.2.
To find y, we first round a, b, and c to the tenths place and them sum them. so 5.4 + 3.0 + 3.8 = 12.2.
We are looking for y - x, which gives us 12.2 - 12.2 = 0, or
answer choice A.
Answer: A
Question: If a certain sample of data has a mean of 15 and a standard deviation of 2, which of the following is not within 2 standard deviations?
Options:
A)11
B)15
C)10
D)12
E)14
Rationale: If a data distribution is normal then the 68% data values are within one standard deviation of the mean (i.e., μ ± σ), and about 95 percent are within two standard deviations (μ ± 2σ).
Here, mean = 15 and standard distribution is 2.
Numbers which are within two standard distribution will be in the range of 15±(2*2) i.e. 11 to 19.
Only only which does not follow this range is 10
Answer is C
Answer: C
Question: In the manufacture of a certain product, 9 percent of the units produced are defective and 5 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
Options:
A)0.15%
B)0.45%
C)0.8%
D)1.25%
E)2.0%
Rationale: 0.09*0.05 = 0.0045 = 0.45%
The answer is B.
Answer: B
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Options:
A)50
B)87
C)17
D)98
E)16
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer: A
Answer: A
Question: Find the remainder W when 12^190 is divided by 1729 ?
Options:
A)12
B)1
C)1728
D)1717
E)4
Rationale: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder W -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D
Answer: D
Question: A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
Options:
A)525
B)665
C)412
D)235
E)856
Rationale: Answer: Option B
8 * 84 = 672 â€“ 7 = 665
Answer: B
Question: Two trains for Palwal leave Kanpur at 10 a.m and 10:30 am and travel at the speeds of 60 Kmph and 75 Kmph respectively. After how many kilometers from Kanpur will the two trains be together?
Options:
A)150
B)160
C)170
D)180
E)190
Rationale: Let two train meet at X km distance.
Time taken by first train to cover X km=x/75 h
Time taken by 2nd train to cover X km=x/60 h
Now, x/60 - x/75=1/2
thus, x=150.
ANSWER:A
Answer: A
Question: Which of the following values is the greatest?
Options:
A)11% of 89
B)22% of 78
C)33% of 67
D)44% of 56
E)55% of 45
Rationale: Now, 89 < 78*2 < 67*3 < 56*4 < 45*5;as we can see option E, has the highest value for 11% , hence the answer must be E.
ANSWER:E
Answer: E
Question: If the number is divided by 3, it reduced by 30. The number is
Options:
A)A)51
B)B)50
C)C)45
D)D)40
E)E)36
Rationale: Explanation:
Let the number be x. Then,
x - (x/3) = 30 => 2x/3 = 30
=> x = 45
Answer: Option C
Answer: C
Question: The least number which when increased by 6 each divisible by each one of 24, 32, 36 and 54 is :
Options:
A)858
B)859
C)869
D)4320
E)None of these
Rationale: Solution
Required number = (L.C.M. of 24, 32, 36, 54) - 5 = 864 - 6 = 858. Answer A
Answer: A
Question: Tom covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
Options:
A)15 Kmph
B)29 Kmph
C)25 Kmph
D)30 Kmph
E)34 Kmph
Rationale: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distance of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
A
Answer: A
Question: Find the fourth proportion to 5,6,15
Options:
A)18
B)12
C)6
D)9
E)2
Rationale: Explanation:
5:6 :: 15:x
=> 5/6 = 15/x
=> x = 15*6/5
=> x = 18
Answer:A
Answer: A
Question: In what time will a train 20 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)2.8 sec
C)0.5 sec
D)2.3 sec
E)1.5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 20/40
= 0.5 sec.
Answer:C
Answer: C
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 84, 60, then the average marks of all the students is
Options:
A)54.48
B)54.68
C)54.6
D)54.58
E)65.56
Rationale: Explanation:
(55Ã—50)+(60Ã—84)+(45Ã—60) / 55+60+45
10490 / 160=65.56
Option E
Answer: E
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 3/4 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Options:
A)6/22
B)5/22
C)7/22
D)4/22
E)3/22
Rationale: # of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 12*1=12 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 12+28/5=88/5 --> deluxe/total=28/5 / 88/5= 28/88 =7/22
C
Answer: C
Question: If the ratio of x to y is 3 to 7, then (y-x)/(x+y)?
Options:
A)-7/3
B)-3/7
C)4/10
D)1
E)7/3
Rationale: I believe this problem can be solved using algebra.
The ratio of x to y is 3 to 7 means
(x/y)=(3/7)
Cross-multiply
3x = 7y
x = (3/7)*y
Then, substitute x in the original equation in the problem with the value we just found.
(y - (3/7)*y) / ((3/7)*y + y)
= ((4/7)*y) / ((10/7)*y)
Simplify by canceling the y in the numerator with the y in the denominator.
(4/7) / (10/7)
= (4/7) * (10/7)
The 7s cancel each other out, and you are left with 4/10.
Answer: C