divelab/Sys2Bench huggingface dataset:
Question: If u, v, and w are three different positive integers whose sum is prime, which of the following statements could be true?
Options:
A)The average (arithmetic mean) of u, v, and w is prime.
B)Each of u + 3, v + 3, and w + 3 is prime.
C)Each of u + v, u + w, and v + w is prime.
D)Each of u, v, and w is prime.
E)u + v = w
Rationale: the question asks could be!!!!
this means that if at least one option works, it is the answer.
3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that D is the answer.
Answer: D
Question: The 106th term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is
Options:
A)h
B)k
C)l
D)o
E)r
Rationale: a is one time, b,2 times so on...
so 106=n(n+1)/2..
0r n(n+1)= 212 ... now 15*16=240...14*15<212 so n= 15. and 15th alphabet is O. ans D
Answer: D
Question: A person took some amount with some interest for 2 years, but increase the interest for 1%, he paid Rs.140/- extra, then how much amount he took?
Options:
A)s.5500/-
B)s.6000/-
C)s.4000/-
D)s.7000/-
E)s.8000/-
Rationale: Explanation:
2 years = Rs.140/-
year = 140/2
Rate of Interest = 1%
100/1% × 140/2 = Rs.7000/-
P = Rs.7000/-
Answer: Option D
Answer: D
Question: What is the ratio of 4/7 to the product 3*(7/3)?
Options:
A)4:49
B)1:3
C)3:21
D)1:7
E)3:49
Rationale: 4/7 / 21/3 = 4/49...
IMO option A.
Answer: A
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
Options:
A)2%
B)3%
C)5%
D)8%
E)9%
Rationale: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =(80/1600)x100 % = 5%
answer : C
Answer: C
Question: How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?
Options:
A)13
B)25
C)87
D)49
E)63
Rationale: Explanation:
Required numbers are 24, 30, 36, 42, ..., 96
This is an A.P. in which a = 24, d = 6 and l = 96
Let the number of terms in it be n.
Then tn = 96 a + (n - 1)d = 96
24 + (n - 1) x 6 = 96
(n - 1) x 6 = 72
(n - 1) = 12
n = 13
Required number of numbers = 13.
A)
Answer: A
Question: The present ratio of students to teachers at a certain school is 70 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?
Options:
A)2
B)8
C)10
D)12
E)15
Rationale: We are given that the ratio of students to teacher is 70 to 1. We can rewrite this using variable multipliers.
students : teachers = 70x : x
We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:
Students/Teachers  25/1 = (70x + 50)/(x + 5)
If we cross multiply we have:
25(x + 5) =70x + 50
25x + 125 = 70x + 50
1.667 = x
x~2
Since x is the present number of teachers, currently there are 2 teachers.
Answer A.
Answer: A
Question: workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.60 lacs . How many workers were they?
Options:
A)220
B)230
C)1200
D)560
E)590
Rationale: N * 50 = (360000 - 300000) = 60000
N = 60000 / 50
= 1200
C
Answer: C
Question: If |b| ≥ 1 and x= -| a| b, then which one of the following is necessarily true?
Options:
A)a -xb < 0
B)a -xb ≥ 0
C)a -xb > 0
D)a -xb ≤ 0
E)None of these
Rationale: Explanation :
x = –|a| b
Now a – xb = a – (– |a| b) b
= a + |a| b2
∴ a – xb = a + ab2 … a 0 ≥ OR a – xb
= a - ab2 …a < 0
= a(1 + b2) = a(1 – b2).
Consider first case:
As a ≥ 0 and |b| ≥ 1, therefore (1 + b2) is positive.
∴ a (1 + b2) ≥ 0
∴ a – xb ≥ 0
Consider second case.
As a < 0 and |b| ≥ 1, therefore (1 – b2) ≤ 0
∴ a (1 – b2) ≥ 0 (Since –ve × -ve = +ve and 1 – b2 can be zero also), i.e. a – xb ≥ 0
Therefore, in both cases a – xb ≥ 0.
Answer : B
Answer: B
Question: Mr. loyd wants to fence his Square shaped land of 120Sqft each side.If a pole is laid every 12ft how many poles do he need?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: If each side is 120 feet..then total perimeter is 120*4=480
poles every 12 feet hence no of poles= 480/12=40
ANSWER:C
Answer: C
Question: In a zoo, the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same five years ago. If the increase in the number of cheetahs in the zoo since then is 3, then what is the increase in the number of pandas?
Options:
A) 2
B) 3
C) 9
D) 10
E) 15
Rationale: One short cut to solve the problem is
c:p = 1:3
c increased to 4
=> 1:3 = 4:x
=> x = 12
=>p increased by 9
C is the answer
Answer: C
Question: The area of a circle is increased by 800%. By what percent has the radius of the circle increased?
Options:
A) 100%
B) 400%
C) 300%
D) 600%
E) 200%
Rationale: The area of the circle is increased by 800%, thus the area is increased 9 times.
The area of a circle it proportional to the square of the radius (area=πr^2), therefore the radius must increase 3 times (diameter increase 3 times = area increase 9 times), which is increase by 200%.
Answer: E.
Answer: E
Question: A pilotless cargo carrier brings water, air and dry food to a space station. A third of the cargo's weight is water and the ratio, by weight, of air to dry food is 2:3. If the cargo contains 1,800 pounds of water, how many pounds of air does it contain?
Options:
A)1,200
B)1,300
C)1,440
D)3,000
E)3,240
Rationale: Let the capacity of the cargo be x
W + A + D = X
Given X/3 = W => X = 3*1800 = 5400
Now W+A+D = 5400
Now A+D = 5400 - 1800 => 3600
Given A/D = 2/3
Now air will 2/5*3600 =>1440.
ANSWER:C
Answer: C
Question: John found that the average of 15 numbers is 40. If 11 is added to each number then the mean of number is?
Options:
A)51
B)45
C)65
D)78
E)64
Rationale: (x+x1+...x14)/15 = 40
51
Option A
Answer: A
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,800 nuts and 1,800 bolts?
Options:
A)1,250 seconds
B)1,500 seconds
C)1,750 seconds
D)2,700 seconds
E)3,000 seconds
Rationale: I used the Rate formula (R=\frac{1}{T})
Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}
Rate of 1st machine = Rate of 2nd machine
After this I got lost.
Please can you help how to approach using algebra?
I wouldn't complicate:
1 machine needs 1,800*1 seconds to produce 1,800 bolts, so 2 need half of that, so 1,800/2 seconds.=900
1 machine needs 1,800*2 seconds to produce 1,800 nuts, so 2 need half of that, so 1,800*2/2 seconds.=1800
total =2700 sec
D
Answer: D
Question: Vanessa, Mike and Sarah have missed a total of 17 days of school this year. Vanessa and Mike have missed 14 days total, and Mike and Sarah have missed 12 days total. How many days of school did Vanessa miss alone?
Options:
A)9
B)4
C)5
D)2
E)3
Rationale: Vanessa + Mike + Sarah = 17
V+M=14
M+S=12 <<Use this formula & plug into the original formula, to get Vanessa's total
V + (M + S) = 17
V + 12 = 17
Subtract 12 from both sides
V = 5
Answer: C
Answer: C
Question: Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $540. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $720. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear?
Options:
A)12
B)11
C)10
D)15
E)16
Rationale: Let X be pair of shoes and Y be pair of boots.
22x+16y = 540 ... eq1
8x +32y = 720....eq 2.
Now multiply eq 1 by 2 and sub eq 2.
44x = 1080
8x = 720.
36x = 360 => x = 10.
Sub x in eq 2.... we get 80 + 32y = 720... then we get 32y = 640 then y = 20
Differenece between X and Y is 10
Answer : C
Answer: C
Question: Molly's age in 18 years will be five times her age six years ago. What is Molly's present age?
Options:
A)8
B)9
C)10
D)12
E)14
Rationale: Let x be Molly's present age.
x + 18 = 5(x-6)
x = 12
The answer is D.
Answer: D
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1123
B)1234
C)1345
D)1450
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: E
Question: What is the difference between the local value of 1 and 2 in the number 2124?
Options:
A)70
B)75
C)20
D)80
E)60
Rationale: Explanation:
100 â€“ 20 = 80
Answer: D
Answer: D
Question: The average age of 10 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years. Find the average age of the women?
Options:
A)21
B)32
C)30
D)41
E)37
Rationale: 10 + 12+ 10 * 2
= 42/2
= 21
Answer:A
Answer: A
Question: Gambling with 4 dice, what is the probability of getting an even sum?
Options:
A)3/4
B)1/2
C)2/3
D)1/4
E)1/3
Rationale: Even sum can be obtained in following cases:
EEEE - one case. Each E can take 3 values (2, 4, or 6), so total for this case is 3^4;
OOOO - one case. Each O can take 3 values (1, 3, or 5), so total for this case is 3^4;
EEOO - 4!2!2!=64!2!2!=6 cases (EOEO, OOEE, ...). Each E can take 3 values (2, 4, or 6) and each O can also take 3 values (1, 3, or 5), so total for this case is 6*3^2*3^2=6*3^4
Total # of outcomes when throwing 4 dice is 6^4.
P=3^4+3^4+6∗3^4/6^4=1/2
Answer: B.
Answer: B
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)288
B)266
C)500
D)277
E)121
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: C
Answer: C
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Options:
A)10 sec
B)11 sec
C)77 sec
D)99 sec
E)67 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec
Answer: A
Answer: A
Question: The ratio of 4 seconds to 8 hours
Options:
A)1:80
B)1:6000
C)1:600
D)1:7200
E)1:500
Rationale: 1 hour =3600 sec
then 8 hours =8*3600=28800
so ,4:28800=1:7200
ANSWER:D
Answer: D
Question: At the end of the first quarter, the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 55 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?
Options:
A)24%
B)25%
C)30%
D)33%
E)40%
Rationale: Another method is to use the formula for 2 successive percentage changes:
Total = a + b + ab/100
55 = 25 + b + 25b/100
b = 24
Answer (A)
Answer: A
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
Options:
A)3/19
B)3/31
C)9/42
D)4/49
E)4/51
Rationale: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Answer: C
Question: What is the HCF of 2/3, 4/15 and 6/5
Options:
A)7/45
B)2/45
C)4/15
D)8/45
E)2/15
Rationale: Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 15, 5) = 2/15
Answer: Option E
Answer: E
Question: The ratio of cost price to the market price of an article is 4: 5. What is the profit percentage if the ratio of the profit percentage on selling the article to the discount allowed on it is 5: 4?
Options:
A)10%
B)12%
C)12.5%
D)15%
E)16%
Rationale: lets assume mp=100 and cp=80
p/d=5/4
therefore d= p*(4/5)
now cp + profit = mp- discount= sp
80+ p(80/100)=100-(p*(4/5)*(100/100))
solving for p we get p=12.5%
ANSWER:C
Answer: C
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)78
B)66
C)20
D)26
E)29
Rationale: M = 15
S = 5
DS = 15 + 5
= 20
AnswerC
Answer: C
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
Options:
A)5
B)8
C)9
D)3
E)2
Rationale: US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer:A
Answer: A
Question: A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger?
Options:
A)46
B)36
C)18
D)22
E)23
Rationale: Explanation:
Distance to be covered = 240+ 120 = 360 m
Relative speed = 36 km/hr = 36×10/36 = 10 m/s
Time = distance/speed = 360/10 = 36 seconds
Answer: Option B
Answer: B
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)3
B)8
C)9
D)4
E)2
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: B
Question: 80 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
Options:
A)35
B)32
C)36
D)40
E)52
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 80 = 35
ANSWER:A
Answer: A
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)22
B)10
C)28
D)27
E)19
Rationale: Explanation:
4/12 + x/15 = 1
x = 10
Answer:B
Answer: B
Question: Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in e hours. In terms of x and e, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
Options:
A)x/(x+y)
B)y/(x+y)
C)xy/(x+y)
D)xy/(x-y)
E)xe/(e-x)
Rationale: Pick some smart numbers for x and e.
Say x=1 hour and e=2 hours (notice that e must be greater than x, since the time for machine A to do the job, which is e hours, must be more than the time for machines A and B working together to do the same job, which is x hours).
In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.
Now, plug x=1 and e=2 in the options to see which one yields 2. Only option E fits.
Answer: E.
Answer: E
Question: A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 56 km downstream
Options:
A)2 hours
B)4 hours
C)5 hours
D)6 hours
E)7 hours
Rationale: Explanation:
Speed of the boat in still water = 24 km/hr
speed of the stream = 4 km/hr
Speed downstream = (22+5) = 28 km/hr
Distance travelled downstream = 56 km
Time taken = distance/speed = 56/28 = 2 hours
Answer: Option A
Answer: A
Question: A, B, C together started a business. A invested Rs.1000 for 5 months B invested Rs.1500 for 6 months and C Rs.2000 for 3 months. If they get a total profit of Rs.3000. Find the share of A?
Options:
A)750
B)3000
C)2777
D)2999
E)17212
Rationale: 2*5:3*6:4*3
10 : 18 : 12 => 5 : 9 : 6
5/20 * 3000 = 750
Answer:A
Answer: A
Question: Rs.320 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)388
B)266
C)120
D)240
E)267
Rationale: 4x 5x 6x
100 50 25
400x + 250x + 150x = 32000
x = 40
6x = 240
Answer: D
Answer: D
Question: Tough and Tricky questions: Work/Rate Problems.
If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 15 workers to do this same job?
Options:
A)14
B)11
C)7
D)7/3
E)9/7
Rationale: 70 Workers = 3 hours then,
1 Worker = 3*70 Hours
30 Workers = (3*70) /(15) = 14 Answer. A
Answer: A
Question: Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 40 percent of the cards for himself and split the remaining cards evenly among his 4 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 4 younger brothers to get an equal number of cards?
Options:
A)110
B)112
C)116
D)118
E)122
Rationale: This question can be easily solved by looking at the options.
Assuming number of cards to be x
We need to find the option for which (1/4)*(2x/5) is an integer
Or x/10 is an integer.
Hence we need the lowest multiple of 10 from the given options.
Let us start from the lowest value:
Option A: 110. This is not a multiple of 10
Option B: 112 = 10*11. This is a multiple of 10. Hence the correct answer.
Correct Option: A
Answer: A
Question: A train passes a man standing on the platform. If the train is 130 meters long and its speed is 72 kmph, how much time it took in doing so?
Options:
A)6 Â½ sec
B)6 Â½ sec
C)9 Â½ sec
D)8 Â½ sec
E)7 Â½ sec
Rationale: B
6 Â½ sec
S = 72 * 5/18 = 20 mps
T = 130/20 = 6 Â½ sec
Answer: B
Question: In an election between two candidates, 10% of votes are were declares invalid. First candidate got 1800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was?
Options:
A)10000
B)12000
C)13000
D)14000
E)15000
Rationale: 100 % - 10 % = 90 %
54%-36%=18%
18% ------> 1800 ( 18 × 100 = 1800)
100% -------> 10000 votes (100 × 100 = 10000)
A)
Answer: A
Question: John had a stock of 1000 books in his bookshop. He sold 20 on Monday, 120 on Tuesday, 200 on Wednesday,250 on Thursday and 300 on Friday. What percentage of the books were not sold?
Options:
A)68%
B)74%
C)76%
D)62%
E)89%
Rationale: Let N be the total number of books sold. Hence
N = 20 + 120 + 200 + 250+ 300= 890
Let M be the books NOT sold
M = 1000 - N = 1200 - 890 = 798
Percentage
Books not sold / total number of books = 890/1000 = 0.89= 89%
correct answer E
Answer: E
Question: There are cats got together and decided to kill the mice of 999919. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?
Options:
A)941,1009
B)991,1001
C)991,1009
D)791,1009
E)931,1009
Rationale: 999919 can be written as 1000000 – 81
= 10002 – 92 ie of the form a2-b2=(a+b)(a-b)
=(1000+9)*(1000-9)
= (1009)*(991)
Given that number of cats is less than number if mice.
So number of cats is 991 and number of mice were 1009
Answer C
Answer: C
Question: In an election between two candidates, 75 % of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes.
Options:
A)16800
B)15800
C)16700
D)15700
E)15000
Rationale: Explanation:
Let the total number of votes enrolled are x.
Number of votes cast = 75% of x
Valid votes = 98% of 75% of x
Now, as 9261 is the 75% of valid casted votes so,
75% of 98% of 75% of x = 9261 [imporant]
=>75Ã—98Ã—75Ã—x/100Ã—100Ã—100=9261
=>x=16800
ANSWER IS A
Answer: A
Question: Two trains which have lengths of 150 m are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
Options:
A)7.6
B)7.1
C)6.8
D)7.2
E)6.4
Rationale: D = 150m + 150m = 300m * 1/1000 = 0.3 kms
RS = 70 + 80 = 150 kmph
T = (0.3/150) * 3600 = 7.2 sec
ANSWER:D
Answer: D
Question: In the parking lot there are 38 vehicles, 21 of them are buses, and the rest are cars. The color of 23 vehicles is red, of which 15 are buses. How many cars can be found in the parking lot which are not colored red?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: The number of cars is 38-21 = 17.
The number of red cars is 23-15=8.
The number of cars which are not red is 17-8=9.
The answer is C.
Answer: C
Question: A person spends 1/5th of his income on the education of his children, and 20% of the remaining on food. If he is left with Rs.576 find his income?
Options:
A)900
B)906
C)988
D)917
E)902
Rationale: X * 4/5 * 80/100 = 576
X = 14400/16
X = 900
Answer: A
Answer: A
Question: On a certain plane, 2/5 of the passengers speak Hindi and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?
Options:
A)12
B)15
C)60
D)74
E)80
Rationale: Assume the total members = x
Hindi = .4x
Hebrew = .75x
Hindi + Hebrew = 1.15x, but this is not possible hence 15 people speak both languages.
Only Hindi= .25x, Only Hebrew = .6x, both = .15x
Since these are all people, all of these should be whole numbers.
Checking the options:
A. 12. Only Hebrew = 12*0.6 = 7.2 We do not get the people as whole numbers. INCORRECT
B. 15. Only Hindi= 0.25*15 Again we do not get the people as whole numbers. INCORRECT
C. 60 Only Hindi= .25*60 = 15, Only Hebrew = .6*60 = 36, both = .15*60 = 9. We have the people as whole numbers. CORRECT
D.74
E. 80
Since we have to find the lowest number, no need to calculate for the rest of the options.
Correct Option: C
Answer: C
Question: The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is?
Options:
A)33
B)38
C)15
D)36
E)81
Rationale: Explanation:
P.W = 2562-122 =Rs.2440
\inline \fn_jvn Rate=\frac{100\times 122}{2440\times \frac{1}{3}}
=15%
Answer: C) 15%
Answer: C
Question: In a particular 100 meter race, 4 athletes are participating that are numbered 1-4. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?
Options:
A)8
B)12
C)16
D)20
E)24
Rationale: The total number of ways for the athletes to finish is 4! = 24.
#4 will be ahead of #2 in exactly half of these possibilities.
24/2 = 12
The answer is B.
Answer: B
Question: There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women?
Options:
A)8/12
B)6/16
C)4/16
D)6/10
E)4/10
Rationale: w = m+4
w+m = 20
m+4+m = 20
2m = 16
m = 8
w = 12
ratio:8:12
Ans: A
Answer: A
Question: How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 13 inches than that of a rectangular sheet of paper measuring 6.5 inches by 11 inches?
Options:
A)50%
B)87%
C)100%
D)187%
E)200%
Rationale: Let's just look at the dimensions (no calculation needed).
With dimension 11 the same, the other dimension 13 is twice 6.5
Then the area will be double which means 100% greater.
The answer is C.
Answer: C
Question: Sudhir started a business with Rs.20,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be
Options:
A)3:2
B)2:3
C)4:3
D)3:4
E)1:1
Rationale: 20000*12:60000*(12-8)
=240000 :240000
=1:1
ANSWER:E
Answer: E
Question: The amount of time that three people worked on a special project was in the ratio of 4 to 3 to 5. If the project took 120 hours, how many more hours did the hardest working person work than the person who worked the least?
Options:
A)25 hours
B)30 hours
C)20 hours
D)26 hours
E)32 hours
Rationale: Let the persons be A, B, C.
Hours worked:
A = 4*120/12 = 40 hours
B = 3*120/12 = 30 hours
C = 5*120/12 = 50 hours
C is the hardest worker and B worked for the least number of hours. So the difference is 50-30 = 20 hours.
Answer : C
Answer: C
Question: Certain stocks in January were 10% less than they were in February and 20% greater than they were in March. What was the percentage decrease in the stocks from February to March?
Options:
A)5%
B)10%
C)20%
D)25%
E)50%
Rationale: Let J,F,M be the values of the stock in Jan,Feb and March.
Thus, per the question, J = 0.9F = 1.2M ----> M =0.75F
Thus the % decrease from F to M = (F-M)/(F) *100 = (F-0.75F)/F * 100 = 0.25*100 = 25 %, D is the correct answer.
Answer: D