divelab/Sys2Bench huggingface dataset:
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 140 sandwiches were made, how many bologna sandwiches
were made?
Options:
A)15
B)30
C)38
D)42
E)49
Rationale: For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
140 / 20 = 7 sandwiches in one part
For bologna we have 7 parts so:
7 * 7 = 49
Answer is E
Answer: E
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
B)20
C)21
D)10
E)27
Rationale: Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
Then,	((6x + 6) + 4)*10=	11*((5x + 6) + 4)
10(6x + 10) = 11(5x + 10)
5x = 10
x = 2.
Sagar's present age = (5x + 6) = 16 years
Ans- A
Answer: A
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Options:
A)Rs. 375
B)Rs. 400
C)Rs. 600
D)Rs. 800
E)None of these
Rationale: C's 1 day's work = 1/3-(1/6+1/8)=1/3=7/24=1/24;
A's wages: B's wages: C's wages = 1/6:1/8:1/24=4:3:1;
C's share = Rs.(1/8*3200)=Rs.400.
Correct Option: B
Answer: B
Question: A glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution. If 45 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container?
Options:
A)3.0
B)5.0
C)5.5
D)6.5
E)6.75
Rationale: Construct an equation: 15/100=x/45-> x=6.75
Answer: E.
Answer: E
Question: Last year Elaine spent 20% of her annual earnings on rent. This year she earned 25% more than last year and she spent 30% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year?
Options:
A) 182.5
B) 184.5
C) 167.5
D) 172.5
E) 187.5
Rationale: For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.
She would've spent $20 of this on rent.
This year she earned 25% more, or $125.
She would've spent 30% of this on rent, or $37.5
Do $37.5/$20
This will give you 187.5%
E is the correct answer.
Answer: E
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages.
Options:
A)20, 35, 55
B)16, 28, 36
C)20, 35, 45
D)None of these
E)20, 15, 45
Rationale: Answer: Option B
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80 => x = 4
Their present ages are 16, 28 and 36 years respectively.
Answer: B
Question: A man goes 50Km north , then turned left walked 40Km, then turned right ? In which direction he is?
Options:
A)North
B)South
C)East
D)West
E)None
Rationale: 5okm-north-->north
left-west--->west
turned right-north--->north
ANSWER:A
Answer: A
Question: Grace has enough money to buy 45 bricks. If the bricks each cost 10 cents less, Grace could buy 5 more bricks. How much money does Grace have to spend on bricks?
Options:
A)$100
B)$50
C)$45
D)$40
E)$30
Rationale: 45 bricks at $1 each = 45*$1.00 = $45.
50 bricks at ($1 - $0.10) each = 50*$0.90 = $45
This gives us C
Answer: C
Question: The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 20 years is:
Options:
A)111 × 1827 miles
B)1174× 10^11 miles
C)346 × 1012 miles
D)247 × 1012 miles
E)587 × 1012 miles
Rationale: The distance of the light travels in one years is:
5,870,000,000,000 = 587 * 10 ^10
The distance of the light travels in 20 years is:
= 2*10 * 587 * 10^10
= 1174 × 10^11 miles.
Answer :B
Answer: B
Question: What is the units' digit of the following expression (13)^5*(13)^10*(17)^5?
Options:
A)0
B)1
C)3
D)5
E)9
Rationale: We do not have to do any calculations or find units digit of remaining numbers...
all three terms - 13,13,17 - are ODD and since the PRODUCT contains 3, the units digit of the product will remain 3
C
Answer: C
Question: If the cost price is 86% of the selling price, then what is the profit percent?
Options:
A)5%
B)11%
C)16%
D)21%
E)19%
Rationale: Let S.P. = $100
C.P. = $86
Profit = $14
Profit% = 14/86 * 100 = 25/6 = 16% approximately
Answer is C
Answer: C
Question: A can do a piece of work in 4 days. B can do it in 9 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Options:
A)22 days
B)36/5 days
C)67 days
D)17/7 days
E)18 days
Rationale: C = 1/2 - 1/4 - 1/9 = 5/36
=> 36/5 days
Answer:B
Answer: B
Question: A side of beef lost 50 percent of its weight in processing. If the side of beef weighed 750 pounds after processing, how many pounds did it weigh before processing?
Options:
A)191
B)355
C)737
D)840
E)1,500
Rationale: Let weight of side of beef before processing = x
(50/100)*x = 750
=> x = (750 * 100)/50 = 1500
Answer E
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)356
B)278
C)127
D)279
E)150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m
Answer: E
Answer: E
Question: In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race?
Options:
A)2min 10 sec
B)2min 30 sec
C)2min 40 sec
D)2min 50 sec
E)2min 20 sec
Rationale: 100 m = 15 sec
1 m = 15/100 sec
1000 m = 15/100*1000
=150 sec
=2min 30 sec
ANSWER:B
Answer: B
Question: The set X = {6,7,8,9}. The set Y = {2,3,4,5}. We will randomly choose one element x from set X and one element y from set Y. What is the probability that x / y will be an integer?
Options:
A)5/16
B)3/16
C)7/8
D)5/8
E)3/8
Rationale: The total number of x and y pairs is 4*4=16.
There are five pairs such that x / y is an integer.
The probability that x / y is an integer is 5/16.
The answer is A.
Answer: A
Question: The average age of 32 students in a group is 14 years. When teacherâ€™s age is included to it, the average increases by one. What is the teacherâ€™s age in years?
Options:
A)31
B)36
C)47
D)51
E)None
Rationale: Sol.
Age of the teacher = ( 33 Ã— 15 â€“ 32 Ã— 14 ) years = 47 years.
Answer C
Answer: C
Question: Today John is 3 times older than Mark. If in 12 years, John will be one year younger than twice the age of Mark on that day, how old is John today?
Options:
A)13
B)33
C)36
D)38
E)39
Rationale: t
Given after 12yrs john will be 1 year younger than twice mark's age
i.e 3M+12 = 2(M+12)-1
M=11
=>John's current age = 3M = 33
Answer is B
Answer: B
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Options:
A)4
B)5
C)7
D)8
E)2
Rationale: C
7
1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/10 + 10/140) = (1/14 + 1/14) = 1/7
5 women and 10 children will complete the work in 7 days.
Answer: C
Question: A can do a piece of work in 30 days; B can do the same in 50 days. How many days will it take the work to get finished if A and B work together?
Options:
A)18.75
B)20.25
C)21.52
D)23.45
E)24.58
Rationale: A completes 1/30th of the work in one day and B completes 1/50th.
(1/30)+(1/50)=(1/x)
8/150=1/x => x=150/8=18.75days
Answer: A
Answer: A
Question: 8th Dec 2007 was Saturday, what day of the week was it on 8th Dec, 2006?
Options:
A)Sunday
B)Tuesday
C)Friday
D)Tuesday
E)None of these
Rationale: Explanation :
Given that 8th Dec 2007 was Saturday
Number of days from 8th Dec, 2006 to 7th Dec 2007 = 365 days
365 days = 1 odd day
Hence 8th Dec 2006 was = (Saturday - 1 odd day) = Friday. Answer : Option C
Answer: C
Question: Present ages of Solomon and Arnald are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Arnald present age in years?
Options:
A)A)24
B)B)25
C)C)26
D)D)27
E)E)28
Rationale: Let the present ages of Solomon and Arnald be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Arnald present age = 4x = 24 years.
ANSWER:A
Answer: A
Question: In a school 10% of the boys are same in number as 1/5th of the girls. what is the ratio of boys to the girls in the school?
Options:
A)5:2
B)2:3
C)1:2
D)3:7
E)2:5
Rationale: 10% of B = 1/5 G
10B/100 = G/5
B = G/2
B/G = 1/2
B:G = 1:2
Answer is C
Answer: C
Question: The compound interest on rs.30000 at 7% per annum is Rs.4347. The period is
Options:
A)2
B)6
C)78
D)8
E)9
Rationale: Explanation:
Amount = Rs.(30000+4347) = Rs.34347
let the time be n years
Then,
n = 2years
Answer: A) 2 years
Answer: A
Question: The sum of ages of 4 children born 4 years different each is 48 yrs. What is the age of the Elder child?
Options:
A)8
B)9
C)16
D)17
E)18
Rationale: Let the ages of children be x, (x + 4), (x + 8), (x + 12) years.
Then, x + (x + 4) + (x + 8) + (x + 12) = 48
4x = 24
x =6
x+12= 6+12= 18
Answer : E
Answer: E
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)278 m
B)265 m
C)123 m
D)270 m
E)289 m
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer:D
Answer: D
Question: The average age of a group of 12 students is 20years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is
Options:
A)22
B)23
C)24
D)25
E)26
Rationale: total age of 12 std=20*12
total age of 16 std=21*16
total age of 4 std=(21*16)-20*12=96
avg of 4 std =(96)/4=24
ANSWER:C
Answer: C
Question: A certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 10 times per hour, and both clocks chirp for the first time at 2:03 PM, at what time will the first clock have chirped three times as many times as the second clock can chirp per hour?
Options:
A)2:30 PM
B)2:45 PM
C)3:00 PM
D)3:15 PM
E)3:30 PM
Rationale: The question is asking when the first clock will have chirped 30 times (3*10 chirps).
The first clock chirps once every 3 minutes.
If the first chirp is at 2:03, then the 30th chirp is at 90 minutes after 2:00.
The answer is E.
Answer: E
Question: A man goes downstream at 11 kmph, and upstream8 kmph. The speed of the stream is
Options:
A)1.5kmph
B)4kmph
C)16kmph
D)2.5kmph
E)26kmph
Rationale: Speed of the stream = 1/2(11-8)kmph
=1.5kmph.
correct option :A
Answer: A
Question: How many integers between 100 and 170, inclusive, cannot be evenly divided by 3 nor 5?
Options:
A)36
B)38
C)40
D)42
E)44
Rationale: The total numbers between 100 and 170, inclusive, is 71.
3*34=102 and 3*56=168 so the number of multiples of 3 is 23.
5*20=100 and 5*34=170 so the number of multiples of 5 is 15.
However, the multiples of 15 have been counted twice.
15*7=105 and 15*11=165 so the number of multiples of 15 is 5.
Thus the total number is 71-23-15+5=38.
The answer is B.
Answer: B
Question: A chemical supply company has 60 liters of a 30% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?
Options:
A)12
B)15
C)20
D)24
E)30
Rationale: 60 liters of a 30% HNO3 solution means HNO3 = 18 liters in 60 liters of the solution.
Now, let x be the pure HNO3 added.
As per question,
18 + x = 50% of (60 + x)
or x =24. Hence, D
Answer: D
Question: On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of?
Options:
A)16 2/37%
B)16 2/3%
C)16 6/3%
D)12 2/3%
E)16 3/3%
Rationale: Clearly, the retailer gets 1 dozen out of 6 dozens free.
Equivalent discount = 1/6 * 100 = 16 2/3%.Answer: C
Answer: C
Question: How many 4 digit number contain number 2 ?
Options:
A)3168
B)3268
C)3368
D)3468
E)3568
Rationale: total 4 digit no. = 9*10*10*10 = 9000
not containing 2 = 8*9*9*9 = 5832
total 4 digit number contain 2 = 9000 - 5832 = 3168
ANSWER:A
Answer: A
Question: Denise is trying to open a safe whose combination she does not know. IF the safe has 4000 possible combinations,and she can try 50 different possibilities,what is the probability that she does not pick the one correct combination.
Options:
A)1
B)0.9875
C)0.8875
D)3/160
E)0
Rationale: If Denise does not pick the correct combination in first 50 try, then the correct combination is one of remaining 3950. So Probability = 3950/4000 = 0.9875.
answer is B
Answer: B
Question: The ratio of male to female in a class is 3:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?
Options:
A)a)160 degree
B)b) 168 degree
C)c)191 degree
D)d)180 degree
E)e)204 degree
Rationale: here is my approach => males => 3x and females =3x => total =6x
now 6x=> 360
therefore 3x => 180 degree .
P.S => 3x is nothing but total number of students with the given prefee
aNSWER D
Answer: D
Question: A boat whose speed is 15 k/hr in still water goes 30 k/he downwards and come back in total 4 hr 30 min what is the speed of stream in k/hr ?
Options:
A)1km/hr
B)2km/hr
C)3km/hr
D)4km/hr
E)5km/hr
Rationale: If the speed of stream=x
Speed in downstream=15+x , Speed in Upstream=15-x,
Total time=4 hr 30 min=9/2 hr
[30/(15+x) + 30/(15-x)]=9/2,Solving x=5
x=5km/hr
ANSWER:E
Answer: E
Question: Find the odd man out
4, 9, 16, 25, 36, 50, 64, 81
Options:
A)4
B)9
C)25
D)36
E)50
Rationale: as 50 is only odd number.
ANSWER:E
Answer: E
Question: 16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
Options:
A)33
B)77
C)20
D)99
E)71
Rationale: 16 * 25 = 20 * x => x
= 20 days
Answer: C
Answer: C
Question: Of all the players in a professional baseball league, 1/2 are foreign-born, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreign-born?
Options:
A)100%
B)75%
C)66 2/3%
D)50%
E)25%
Rationale: Assume that the total number of players is 100.
1/2 are foreign born, so 50 are foreign born. 75 players are pitchers out of which 1/3 are foreign born. 25 players are foreign born and pitchers. The other 25 who are foreign born are thus not pitchers.
Thus out of 25 non pitchers, 25 are foreign born. Answer: A - 100%
ANSWER:A
Answer: A
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
Options:
A)17 kmph
B)50 kmph
C)18 kmph
D)17 kmph
E)11 kmph
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10)
= 50 kmph.
Answer:B
Answer: B
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/3 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
Options:
A)(a) 14/23
B)(b) 7/15
C)(c) 10/21
D)(d) 17/35
E)(e) 1/2
Rationale: This problem is very good example how easy and quick plug-in method might be.
Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;
Let the price of small cup be $6, then the price of larges cup would be 7/3*6=$14;
Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$14=$56;
Fraction of total revenue from large cups: 56/(36+56)=14/23.
Answer: A.
Answer: A
Question: A monkey start climbing up a tree 17 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.
Options:
A)15 hrs
B)18 hrs
C)19 hrs
D)17 hrs
E)16 hrs
Rationale: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.
similarly in 14hrs it wil be 14ft.
Bt since the height of the tree is 17ft, so if the monkey hops up the tree in the next hr i.e 15th hr then it reaches at the top of the tree.
hence it takes 15 hrs for monkey to reach at the top
ANSWER:A
Answer: A
Question: If x is an integer, which of the following is a possible value of K=(x^2 +2x – 7)/9?
Options:
A)-2.4
B)0.268
C)1.166 repeating
D)4.555 repeating
E)8.125
Rationale: x is an integer, which of the following is a possible value of K=(x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.125
when this is multiplied by 9, x is not an integer
Answer choice D seems to fit.D
Answer: D
Question: Of the 550 people attending a conference, 300 have signed up for the Marketing workshop and 400 have signed up for the Accounting workshop. If 110 of the people attending did not sign up for either workshop, then the number of people who signed up for both the Marketing and the Accounting workshops is:
Options:
A)245
B)260
C)275
D)280
E)300
Rationale: Since the information in the prompt refers to the 'standard' 5 groups, you can use the Overlapping Sets Formula to get to the solution:
Total = Gp.1 + Gp.2 - Both + Neither
550 = 300 + 400 - Both + 110
550 = 810 - Both
Both = 260
Final Answer:
B
Answer: B
Question: A spends 90% of his salary and B spends 85% of his salary. But savings of both are equal. Find the income of B, if sum of their incomes is Rs. 5000.
Options:
A)2000
B)2400
C)2125
D)2400
E)None
Rationale: Explanation:
Let the incomes of A and B are x, y respectively.
Savings of A = (100 - 90)% (x) = 10% (x)
Savings of B = (100 - 85)% (y) = 15% (y)
Given, both saves equal amount.
Therefore, 10% (x) = 15% (y) ⇒xy=15%/10%=3/2
Therefore, x : y = 3 : 2
Hence, B's salary = 2/(2+3) x 5000 = Rs. 2000.
Correct Option: A
Answer: A
Question: A box contain a certain number of balls, marked successively from 1 to n. If there are 55 different ways that two balls can be selected from the box such that the ball with number 3 marked on it is not selected, then what is the value of n?
Options:
A)6
B)8
C)9
D)12
E)14
Rationale: Total ways of selecting 2 balls out of n balls = nC2
We're told that one balls marked as 3 cannot be selected.
So total number of balls left now = (n-1)
Hence total ways of selecting 2 balls out of (n-1) balls = (n-1)C2
Given that (n-1)C2 = 55
So, [(n-1)(n-2)]/[2 * 1] = 55
So, n^2-3n+2 = 110
So, n^2-3n-108 = 0
So, n = 12 or -9 (rejected)
Hence option 4.
ANSWER:D
Answer: D
Question: What is the tens digit of 6^19?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:
The tens digit of 6^2=36 is 3.
The tens digit of 6^3=216 is 1.
The tens digit of 6^4=...96 is 9.
The tens digit of 6^5=...76 is 7.
The tens digit of 6^6=...56 is 5.
The tens digit of 6^7=...36 is 3 again.
etc...
19 has the form 5n+4, so the tens digit of 6^19 is 9.
The answer is E.
Answer: E
Question: A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew ¼ of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs. 760. What is A's share in the profit?
Options:
A)310
B)330
C)370
D)350
E)None of these
Rationale: Explanation :
Ratio of the initial capital of A and B = 4 : 5
Hence we can take the initial capitals of A and B as 4x and 5x respectively
Ratio in which profit will be divided
= (4x*3) + (3/4)*(4x)*7 : (5x*3)+ (4/5)*(5x)*7
= 12+21 : 15+28
= 33 : 43
A's share = 760 * 33/76 = 330.Answer : Option B
Answer: B
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good
Options:
A)20/63
B)4/56
C)8/7
D)6/9
E)4/9
Rationale: Explanation:
Required probability = (âµCâ‚ƒ . â´Câ‚)/â¹Câ‚„ = (10 * 4)/126 = 20/63
Answer: A
Answer: A
Question: Two men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?
Options:
A)5 days
B)8 days
C)6 days
D)3 days
E)2 days
Rationale: 2M + 3W ----- 35 h
4M + 4W ------- 21 h
7M -------? d
70M + 105W = 84M +84M
21W = 14M => 2M = 3W
4 * 35 = 7 * x => x = 20 hours
20/4 = 5 days
Answer: A
Answer: A
Question: The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10,
respectively. Due to a dramatic increase in the surrounding temperature, the composition of the
compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the
changed compound, if the total weight is 232 lbs, how much does substance x weigh?
Options:
A)48
B)36
C)24
D)12
E)10
Rationale: x:y=4:6
if the ratio is halevd then x:y=2:6
The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.
x:y=2:6=12:36 ( multiplied the ration with 6/6 to have a common co eff x in both the rations x:y and x:z)
so x:y:z= 12:36:10
and we know x + y + z = 232 lbs
from the ratio of x ,y and z we have x=12k y=36k z=10K
put it in the equation we have 12k+36k+10k=232
k=4
Hence x=12(4)=48
Ans A
Answer: A
Question: Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 kmph. The second goes at a speed of 8 kmph in the first hour and increases its speed by 1/2 kmph each succeeding hours. After how many hours will the second car overtake the first, if both cars go non stop?
Options:
A)8 hours
B)7 hours
C)6 hours
D)9 hours
E)None
Rationale: Explanation :
The second car overtake the first car in x hours
Distance covered by the first car in x hours = Distance covered by the second car in x hours
10x = x/2[2a + (x-1)d] 10x = x/2[2*8 + (x-1)1/2] x = 40 -31 = 9
Answer – D
Answer: D
Question: What is the smallest of six consecutive odd integers whose average (arithmetic mean) is z + 2?
Options:
A)z - 5
B)3
C)z - 3
D)z
E)z + 1
Rationale: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2
And 1st integer= 3rd integer- 4
let's say 3rd integer = n and 4th integer = n+2
2n+2/2= z+2
n= z+1
1st integer= z+1-4= z-3
C is the answer
Answer: C
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)Rs. 16.80
B)Rs. 15
C)Rs. 18
D)Rs. 19
E)Rs. 19.70
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30100
Let the cost of the tax free items = x
Given that tax rate = 6%
âˆ´ (25âˆ’30100âˆ’x)6100=30100â‡’6(25âˆ’0.3âˆ’x)=30â‡’(25âˆ’0.3âˆ’x)=5
x=25âˆ’0.3âˆ’5
=19.70
correct answer - E
Answer: E
Question: How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 35% solution?
Options:
A)A)6.7
B)B)38.5
C)C)9.6
D)D)12.5
E)E)7.9
Rationale: Amount salt in 100kg solution = 10*100/100 = 10 kg
Let x kg of pure salt be added
then(10+x)/(100+x)=35/100
200+20x=700+7x
13x = 500
x = 28.5
Answer is B
Answer: B
Question: If each digit in the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} is used exactly once, in how many ways can the digits be arranged?
Options:
A)356,580
B)358,680
C)360,780
D)362,880
E)364,980
Rationale: 9! = 362,880
The answer is D.
Answer: D
Question: A and B can do a piece of work in 4 days, B and C in 6 days, C and A in 3 days. How long will C take to do it?
Options:
A)8 days
B)10 days
C)12 days
D)4 days
E)12 days
Rationale: 2c = 1/6 + 1/3 – 1/4 = 1/4
c = 1/8 => 8 days
Answer:A
Answer: A
Question: What is the time required for a bike to cover a distance of 450 km with a speed of 90 kmh?
Options:
A)5 hours
B)3 hours
C)8 hours
D)6 hours
E)4 hours
Rationale: Time= Distance / Speed
Time = 450 / 90 = 5
Answer: A
Answer: A