divelab/Sys2Bench huggingface dataset:
Question: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 70 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
Options:
A)15
B)20
C)40
D)42
E)68
Rationale: Car Y began travelling after 72 minutes or 1.2 hours.
Let t be the time for which car Y travelled before it stopped.
Both cars stop when they have travelled the same distance.
So,
35(t+1.2) = 70t
t=1.2
Distance traveled by car X from the time car Y began traveling until both cars stopped is
35 x 1.2
= 42 miles
Answer:- D
Answer: D
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
Options:
A)228878
B)27771
C)28867
D)28,000
E)267781
Rationale: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
Answer:D
Answer: D
Question: On flipping 3 coins together what is the outcomes for at least three head and three tail?
Options:
A)1/7
B)2/8
C)3/11
D)4/13
E)5/13
Rationale: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {HHH,TTT}
2/8
B
Answer: B
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
Options:
A)276
B)209
C)285
D)267
E)123
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2
Answer: C
Answer: C
Question: John takes 6 hrs to print 32 pages. Peter takes 5hrs to print 40 pages. In how many hours they will print 110 pages together ?
Options:
A)7 hours 15 minutes
B)8 hours 15 minutes
C)9 hours
D)10 hours 15 minutes
E)11 hours 15 minutes
Rationale: Ram can type 32/6 pages per hour
Shaam can type 8 pages per hourThey can type 32/6 + 8 = 40/3 pages per hour
So they will take 110/40 × 3 = 33/4 hours or 8 hours 15 minutes
B)
Answer: B
Question: Convert 40miles into yards?
Options:
A)25630 yards
B)35200 yards
C)39520 yards
D)42560 yards
E)70400 yards
Rationale: 1 mile = 1760 yards
40 miles = 40*1760 = 70400 yards
Answer is E
Answer: E
Question: A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 540 ?
Options:
A)249
B)498
C)676
D)269
E)1,002
Rationale: slope of 2 and a y-intercept of 2
y-coordinate is 540
y = 2x + 2
538 = 2x
x = 269
Answer:
D. 269
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)288 metres
B)557 metres
C)887 metres
D)150 metres
E)123 metres
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer: D
Answer: D
Question: Which one of the following numbers is exactly divisible by 11?
Options:
A)235641
B)245642
C)315624
D)415624
E)415625
Rationale: (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0.
So, 415624 is divisible by 11
ANSWER:D
Answer: D
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 5 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
Options:
A)20
B)25
C)30
D)40
E)50
Rationale: Ans.(B)
Sol. Number of choices to go by ship = 5 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 5 x 5 = 25 ways
Answer: B
Question: What is the average of first 21 multiples of 7 ?
Options:
A)55
B)66
C)77
D)88
E)99
Rationale: Explanation:
Required average = 7(1+2+….+21) / 21
(7/21)X ( (21×22) / 2 ) (because sum of first 21 natural numbers)
= 77
Answer: C
Answer: C
Question: The digit sum of the year 2007 is 2 + 0 + 0 + 7 = 9, which is a square number. How many years during the twenty-first century have a square digital sum?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: The twenty-first century runs from the year 2001 to 2100 inclusive, so with the
exception of the year 2100, for which the digital sum is three anyway, the first two
digits of all the other years are fixed as 20. Hence for the sum of all the digits to be
square the sum of the last two digits number be two less than a perfect square.
As the maximum sum of the last two digits is 18, the greatest sum will be 20.
Therefore we can obtain digital sums of 4, 9, or 16, with the last two digits adding to
2, 7, or 14 respectively.
4: 2002, 2011, 2020
9: 2007, 2016, 2025, 2034, 2043, 2052, 2061, 2070
16: 2059, 2068, 2077, 2086, 2095
That is, there are sixteen years during the twenty-first century for which the digital
sum is square.
ANSWER:D
Answer: D
Question: If x=kc and y=kt,then y+x =?
Options:
A)k(t+c)
B)k(c-t)
C)c(k-t)
D)t(k-c)
E)k(1-t)
Rationale: Just put in the given values of y and x
y - x = kt - kc
Now take k common
y - x = k(t + c)
You get (A) as your answer.
Answer: A
Question: Simplify: 997 x 997
Options:
A)999991
B)994009
C)999994
D)997009
E)999009
Rationale: 997 x 997 = (1000 - 3)(1000 - 3)
= 1000000 +9-3000-3000
= 994009
Answer is B
Answer: B
Question: If |r|=−r, which of the following must be true?
Options:
A)x≥0
B)r≤0
C)x2>x
D)x3<0
E)2x<x
Rationale: |r| =-r means absolute value of r is equal to negative of r. Since absolute value cannot be negative hence negative of r should result in a non negative number. It means r is a non positive number i.e. r<0. Answer is B
Answer: B
Question: If the selling price of 80 articles is equal to the cost price of 40 articles, then the loss or gain percent is:
Options:
A)30%
B)35%
C)50%
D)55%
E)40%
Rationale: Let C.P. of each article be Re. 1.
Then, C.P. of 80 articles = Rs. 80;
S.P. of 80 articles = Rs. 40.
Loss % = 40/80 * 100 = 50%
ANSWER:C
Answer: C
Question: The measures of the 2 acute angles of a triangle are in the ratio of 1 : 8. What arethe measures of the 2 angles?
Options:
A)20°
B)80°
C)110°
D)120°
E)140°
Rationale: If the ratio of the two angles is 1:8, then the measures of two angles can be written as x and 8x. Also the two acute angles of a triangle is equal to 90°. Hence
x + 8x = 90
9x = 90
x = 10
Measures of the two acute angles are
x = 1 × 10 = 10°
8x = 8 × 10 = 80°
B
Answer: B
Question: For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/8 + 8^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
Options:
A)1/3
B)1/5
C)1/6
D)1/7
E)1/8
Rationale: For all positive integers n and m,
A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,
note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)
B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.
A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}
A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)
The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...
missing numbers are 1/8, 1/13, 1/16, ....
B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)
here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values
The largest reciprocal that present in B(25) but not in A(5) is 1/3
Answer A
Answer: A
Question: There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value R of 100th term?
Options:
A)126
B)192
C)232
D)252
E)342
Rationale: (1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer R is 342. The correct answer is E.
Answer: E
Question: A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 46 instead of 96 then find the correct average marks up to two decimal places.
Options:
A)73.41
B)74.31
C)73.42
D)73.43
E)Cannot be determined
Rationale: Total marks = 35 x 72 =2520
Corrected total marks = 2520 - 46 + 96 =2570
Correct Average = 2570/35 = 73.42
Answer : C
Answer: C
Question: If x is an even integer, then which of the following is a true statement?
Options:
A)x is a prime number
B)(x2 + 4) is an even integer
C)x is a Composite number
D)(x2 - 1) is an even integer
E)None of these
Rationale: Explanation:
(x2 + 4) is an even integer
Answer: Option B
Answer: B
Question: Each of five different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?
Options:
A)1/8
B)1/6
C)1/4
D)3/8
E)1/25
Rationale: I was just going over probability questions.
can some one explain me what's wrong in my approach here.
Probability of choosing one right key out of 5 is 1/5.
Probability of choosing another right key is 1/5.
since the question is asking for 2 right keys , probability is multiplication of both = 1/5 * 1/5 = 1/25.
Ans E
Answer: E
Question: If a man can cover 30 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
A)118 km
B)162 km
C)1767 km
D)1887 km
E)405 km
Rationale: 30 m/s = 30 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 30 * 18/5 * 15/4 km = 405 km.
Answer: E
Answer: E
Question: A grocery store recently raised the price of flour by 25% over the original price. If the owner then had a sale advertising 10% off, what would be the sale price if the original price was $20?
Options:
A) $21.00
B) $21.50
C) $22.00
D) $22.50
E) $23.00
Rationale: sale price = (original price + 25% increase) - 10% decrease
price = [20 * (125/100)] * (90/100) = 20 * (1.25) * (.90) = 25 * .9 = 22.50
The answer is D.
Answer: D
Question: Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
Options:
A)27
B)28
C)31
D)35
E)46
Rationale: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation
larger number – smaller number = 7
which is equivalent to
Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.
C
Answer: C
Question: A train passes a man standing on the platform. If the train is 140 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)7 sec
E)7 Â½ sec
Rationale: D
7 sec
D = 140
S = 72 * 5/18 = 20 mps
T = 140/20 = 7 sec
Answer: D
Question: The average of five results is 45 and that of the first four is 45. The fifth result is?
Options:
A)45
B)88
C)77
D)66
E)51
Rationale: 5 * 45 â€“ 4 * 45
= 45
Answer: A
Answer: A
Question: Priya bought a fish last week. She was going to measure it but realized that her ruler was not long enough. She was able to measure the head and discovered that it was 12cm long; she then measured the tail and found that it was the length of the head plus one third of the length of the body. If the body was the length of the head plus the tail, what is the total length of the fish?
Options:
A)58
B)45
C)72
D)63
E)36
Rationale: Let us take H=Length of the head
T=Length of the tail
B=length of the body
Given that H=12 cms.
T=H+1/3 B => T=12+1/3B
Let this be the first equation
B=H+T
substituting the value of H and T here we will get
B=12+12+1/3B
=> B=24+1/3B
Therefore,B=36 cm
Substituting this in T we get
T=12+1/3(36)
T=12+12 =24
So now that you got all the values add
H=12 cm
B=36 cm
T= 24 cm
and the answer is 72 cm
ANSWER:C
Answer: C
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
Options:
A)7 1/2 years
B)20 years
C)15 years
D)38 years
E)30 years
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years
ANSWER:B
Answer: B
Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 O’clock, the true time is –
Options:
A)4 p.m.
B)59 7⁄12 minutes past 3
C)58 7⁄11 minutes past 3
D)2 3⁄11 minutes past 4
E)None of these
Rationale: Time from 7 a.m. to quarter pas 4
= 9 hours 15 min. = 555 min.
Now, 37⁄12 min. of this watch = 3 min. of the correct watch.
555 min.of this watch = (3×12/37×555) min.
= (3×12/37×55560) hrs. = 9 hrs. of the correct watch.
Correct time is 9 hours after 7 a.m. i.e., 4 p.m.
Answer A
Answer: A
Question: 15 beavers, working together in a constant pace, can build a dam in 4 hours. How many hours will it take 20 beavers that work at the same pace, to build the same dam?
Options:
A)2.
B)4.
C)5.
D)6
E)3.
Rationale: Total Work = 15*4 = 60 Beaver hours
20 Beaver * x =60 Beaver hours
x=60/20=3
ANSWER:E
Answer: E
Question: A boy and a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected?
Options:
A)1/3
B)2/5
C)3/5
D)4/7
E)5/9
Rationale: Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)
= = 2/5
B
Answer: B
Question: 5!/(5-3)!=?
Options:
A)36
B)46
C)56
D)59
E)60
Rationale: 5!/(5-3)!=5!/2!=5*4*3 = 60. Hence, the correct answer is E.
Answer: E
Question: A seven-digit phone number is divisible by 8. After adding the two digits of the area code the number is not divisible by 8, which of the following cannot be the area code?
Options:
A)07.
B)05.
C)08.
D)04.
E)02.
Rationale: Given that 7 digit number is divisible by 8
we know any number will not be divisible by 8 if the sum of all digits of the number is not the multiple of 8.
Hence looking at the option we can say that the number that should be added to the seven digit number must be 08 as adding it will make it divisible by 8... hence answer is C
Answer: C
Question: A man has 'n' magical eggs whose average weight is 'k' gm. Each of the 'n' eggs produces 'n' eggs next day such that the average weight of 'n' eggs produced is same as that of the parental egg for each 'n' groups individually i.e. each egg produces 'n' eggs of next generation and average weight of all the 'n' eggs of next generation is same as the weight of the mother egg. This process is continued without any change in pattern. What is the total weight of all the eggs of rth generation, where the initial number of eggs with man are considered as the eggs of first generation.
Options:
A)rnk
B)rnk
C)nkr
D)nrk
E)None of these
Rationale: Solution: The weight is increasing in form of GP so the total weight of eggs in the end of rth will be nrk.
Answer: Option D
Answer: D
Question: How many integers k greater than 100 and less than 800 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: Not sure if this is the shortest.. But this is how I did this
There are 6 sets of integers with hundreds and units digits exchanged that satisfies k + 99.
1. 102 | 201 (satisfies k+99, where k = 102)
2. 203 | 302 (satisfies k+99, where k = 203)
3. ...
4. ...
5. ...
6. 607 | 708
Each set has 10 such numbers.
1. 102 | 201 (still k+99 holds good)
2. 112 | 211
3. 122 | 221
4. 132 | 231
5. ...
6. ...
7. ...
8. ...
9. 182 | 281
10. 192 | 291
Therefore, 6 sets with 10 such number in each set will give 6 x 10 = 60 integers.
B
Answer: B
Question: Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?
Options:
A)-33
B)33
C)35
D)36
E)-35
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.
Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.
So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.
Solving this equation for d+ed+e gives d+e=−66d+e=−66.
Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.
Hence, the answer is A: -33
Answer: A
Question: The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).
Options:
A)178.99 cm
B)178.29 cm
C)118.29 cm
D)578.29 cm
E)173.29 cm
Rationale: Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm
= 180 * 35 cm - 166 cm + 106 cm/35 = 180 cm - 60 /35 cm
= 180 cm - 1.71 cm = 178.29 cm.
Answer: B
Answer: B
Question: Maria earned a profit of 30% on selling an article for Rs.6110. What was the cost price of the article?
Options:
A)Rs.5725
B)Rs.4080
C)Rs.5250
D)Rs.4700
E)None of these
Rationale: Explanation:
30% profit means, SP= 130% of CP
i.e. 130% of CP= Rs.6110. Therefore, CP = 6110x100/130 = Rs.4700.
Answer: Option D
Answer: D
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 45% on his income, while Mindy pays a rate of only 15% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate?
Options:
A)19%
B)21%
C)23%
D)25%
E)27%
Rationale: Let x be Mork's income, then Mindy's income is 4x.
The total tax paid is 0.45x + 0.6x = 1.05x
1.05x / 5x = 0.21
The answer is B.
Answer: B
Question: The inner circumference of a circular race track, 14m wide is 440m. Find the radius of the outer circle.
Options:
A)84
B)12
C)67
D)28
E)21
Rationale: Explanation:
let inner radius be r meters.
{\color{Black} Then,2\Pi r=440\Rightarrow r=440\times \frac{7}{22}\times \frac{1}{2}=70m}
Radius of outer circle = 70 + 14 = 84m
Answer: A) 84m
Answer: A
Question: Tom planted vegetables in a rectangular garden that was 28 feet long and 15 feet wide. He used
1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?
Options:
A)195 sq. ft.
B)196 sq. ft.
C)197 sq. ft.
D)198 sq. ft.
E)199 sq. ft.
Rationale: area of garden is 28 x 15 = 420 sq. ft.
1/3 x 420 = 140 sq. ft. for corn
1/5 x 420 = 84 sq. ft. for peas
140 + 84 = 224 sq. ft. used
420 - 224 = 196 sq. ft. left over
correct answer A
Answer: A
Question: A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in --- hours.
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12
Work done by B in 1 hour = 7/12 – 1/2 = 1/12 => B alone can complete the work in 12 hours
Answer is B.
Answer: B
Question: What is the probability that the sum of two dice will yield a 4, and then when both are thrown again, their sum will again yield a 4? assume that each die has 3 sides with faces numbered 1 to 3.
Options:
A)1/144
B)1/36
C)1/9
D)1/6
E)1/3
Rationale: Solution -
Rolling dices is an independent event.
The combinations to get 4 are (1,3), (3,1), (2,2), and total combinations of both dices is 9.
The probability of getting 4 in first attempt is 3/9=1/3.
Probability of getting 4 again in second attempt = (1/3)*(1/3) = 1/9. ANS C
Answer: C
Question: The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 1500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
A)29997
B)28088
C)13500
D)19000
E)2799
Rationale: Money paid in cash = Rs. 1500
Balance payment = (15000- 1500) = Rs. 13500 .Answer:C
Answer: C
Question: If green means red, red means yellow, yellow means blue, blue means orange and orange means green, what is the colour of clean sky ?
Options:
A)Blue
B)Green
C)Yellow
D)Orange
E)Pink
Rationale: Explanation:
The colour of clean sky is 'blue' and as givne, 'yellow' means 'blue'.
so, the colour of clear sky is 'yellow'.
Answer: C) Yellow
Answer: C
Question: The vertex of a rectangle are (1, 0), (9, 0), (1, 6) and (9, 6) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?
Options:
A)3
B)2
C)1/4
D)3/5
E)5/6
Rationale: If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (5, 3). The slope of a line passing through (0,0) and (5, 3) is 3/5.
The answer is D.
Answer: D
Question: If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+2 ?
Options:
A)-1
B)3
C)-4
D)-1/2
E)-1/3
Rationale: let we put values. a=1, b=3, c=5
5-3-1=1
1+2 =3
Answer :B
Answer: B
Question: There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices.
Options:
A)120
B)116
C)140
D)20
E)10
Rationale: Solution: The number of triangle can be formed by 10 points = 10C3.
Similarly, the number of triangle can be formed by 4 points when no one is collinear=4C3.
In the question, given 4 points are collinear, Thus, required number of triangle can be formed,
= 10C3-4C3 = 120-4 = 116.
Answer B
Answer: B
Question: Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 5 fantasy books, there are 8 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?
Options:
A)6
B)20
C)24
D)35
E)36
Rationale: For every 2 history books, there are 7 fantasy books:
Originally H:F = 2:7 = 10:35.
For every 5 fantasy books, there are 8 reference books:
F:R = 5:8 = 35:56
H:F:R = 10:35:56
After the changes, H:F:R = 20:35:56
There are fewer than 60 fantasy books, so there are 35 fantasy books.
The number of history books is 20.
The answer is B.
Answer: B
Question: A grocer purchased 80 kg of sugar at 13.50 per kg and mixed it with 120 kg sugar at 16 per kg. At what rate should he sell the mixture to gain 19%?
Options:
A)17 per kg
B)17.85 per kg
C)16.5 per kg
D)16 per kg
E)None of these
Rationale: C.P. of 200 kg of mixture = (80 × 13.50 + 120 × 16)
= 3000.
S.P. = 119% of 3000 = (119⁄100 × 3000) = 3570
∴ Rate of S.P. of the mixture = (3570⁄200) per kg
= 17.85 per kg.
Answer B
Answer: B
Question: The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
Options:
A)61.4.
B)51.7
C)51.4
D)51.1
E)51.2
Rationale: Let the required means score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 52 * 100
= 1600 + 775 + 55x = 5200
= 55x = 2825
= x = 565/11 =51.4.
Answer:C
Answer: C
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/5%
B)16 2/9%
C)16 5/3%
D)16 2/3%
E)16 3/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: D