divelab/Sys2Bench huggingface dataset:
Question: here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
Options:
A)1800
B)2130
C)2231
D)4510
E)3560
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
Ans: A
Answer: A
Question: Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 25% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?
Options:
A)23%
B)28%
C)33%
D)38%
E)43%
Rationale: Let x be the number of new biographies added to the library.
Let b be the original number of biographies, so the original number of books was 5b.
0.25(5b+x) = b+x
0.25b = 0.75x
x = 0.33b
The answer is C.
Answer: C
Question: A sum fetched a total simple interest of 4016.25 at the rate of 9 %.p.a. in 5 years. What is the sum?
Options:
A)4462.5
B)8032.5
C)8925
D)None of these
E)Cannot be determined
Rationale: Explanation: Principal = (100 x 4016.25)/(9 x 5)
= 401625/45
= 8925
Answer: Option C
Answer: C
Question: Find the middle one when The sum of three consecutive even numbers is 72?
Options:
A)70
B)60
C)78
D)72
E)62
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 72.
Hence a = 72.
D
Answer: D
Question: A man has a savings account of $500. if he receives $50.6 for every $100 as interest and pays a tax of $15.5 on every $100 how many years will it take for his savings to double.
Options:
A)2.85
B)5
C)4.1
D)3.5
E)5.6
Rationale: Annual increase is (100 + 50.6 - 15.5)*5=675.5
Hence every year there is an increase of 175.5
for his saving to double he needs additional $500
therefore $500/175.5=2.85
correct option is A)
Answer: A
Question: What is the units digit of the product of the first 2 primes?
Options:
A)1
B)2
C)0
D)4
E)5
Rationale: 1*2*=2
Answer : B
Answer: B
Question: John makes $60 a week from his job. He earns a raise andnow makes $84 a week. What is the % increase?
Options:
A)16.12%
B)16.66%
C)16.56%
D)40%
E)18.1%
Rationale: Increase = (24/60)*100 = (4/10)*100 = 40%.
D
Answer: D
Question: What is the sum of all possible 3-digit numbers that can be constructed using the digits 2, 4, and 5 if each digit can be used only once in each number?
Options:
A)2442
B)2552
C)2662
D)2772
E)2882
Rationale: There are 6 possible arrangements of the three numbers.
Then each number will be in the hundreds, tens, and ones place two times each.
The sum is 2(222) + 2(444) + 2(555) = 2442
The answer is A.
Answer: A
Question: Elena purchased Brand X pens for $4.00 apiece and brand Y for $2.40 apiece. If Elena purchased a total of 12 of these pens for $42.00, how many brand X pens did she purchase?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 4x+2.8y=42 --> multiply by 2.5 (to get the integers) --> 10x+7y=105 --> only one positive integers solutions x=5 and y=5 (how to solve: 7y must have the last digit of 5 in order the last digit of the sum to be 5).
Answer: B.
Answer: B
Question: Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest T?
Options:
A) 60
B) 61
C) 62
D) 63
E) 64
Rationale: 60 = 2*2*3*5 factor count =3
61= prime number
62 = 2*31 factor count=2
63=3*3*7 factor count=2
64=2*2*2*2*2*2 factor count=1=T
answer is A.
Answer: A
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
Options:
A)18:11
B)18:18
C)98:18
D)18:10
E)18:12
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer: A
Answer: A
Question: If the price of sugar rises from Rs. 3 per kg to Rs. 5 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
Options:
A)15%
B)20%
C)25%
D)30%
E)40%
Rationale: Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 3 = x × 5 = x = 60 kg.
∴ Reduction in consumption = 40%.
Answer E
Answer: E
Question: Three cubes of sides 5 m, 4 m, and 3 m are melted to form a new cube. Find the surface of the new cube?
Options:
A)236
B)256
C)216
D)246
E)206
Rationale: Volume of the new cube = [ 5(power)3 + 4(power)3 + 3(power)3 ] Cm(power)3
= 125 + 64 + 27 = 216 Cm(power)3 => a(power)3 = 216 Cm(power)3
Answer is C.
Answer: C
Question: A person was asked to state his age in years.His reply was,”Take my age three years hence,multiply it by 3 and then subtract three times my age three years ago and you will know how old I am”.What was the age of the person ?
Options:
A)18 years
B)20 years
C)24 years
D)32 years
E)43 years
Rationale: Solution
Let the present age of the person be x years.
Then,3(x+3)-3(x-3)=x ⇔ (3x + 9)-(3x-9)=x ⇔ x = 18.. Answer A
Answer: A
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)Rs. 2000
B)Rs. 2200
C)Rs. 2400
D)Rs. 3400
E)Data inadequate
Rationale: Explanation:
Let C.P. be Rs. x.
Then,	1920 - x	/ x	x 100 =	x - 1280/ x	x	100
=> 1920 - x = x - 1280
=> 2x = 3200
=> x = 1600
Required S.P. = 125% of Rs. 1600 = Rs.(125/100 x1600)=Rs 2000.
ANSWER IS A
Answer: A
Question: How many two-element subsets of {2,4,6,8} are there that do not contain the element 4?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Required subsets are = {2,6}, {2,8}, {6,8}= 3
Answer: C
Answer: C
Question: A man swims downstream 48 km and upstream 42 km taking 6 hours each time; what is the speed of the current?
Options:
A)3 kmph
B)0.5 kmph
C)13 kmph
D)6.5 kmph
E)7:3kmph
Rationale: Explanation:
48 --- 6 DS = 8
? ---- 1
42 ---- 6 US = 7
? ---- 1 S = ?
S = (8 - 7)/2 = 0.5
Answer: Option B
Answer: B
Question: A train running at the speed of 50 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
A)125
B)272
C)278
D)277
E)112
Rationale: Speed =50*(5/18) m/sec = 125/9 m/sec
Length of Train (Distance) = Speed * Time
(125/9) * 9
= 125 meter
Answer: A
Answer: A
Question: 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days Z do they need to finish the same job?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Let Rate of one worker be R
=> (6*R)*8 = 1 (Rate * Time = work)
=> R = 1/48
=> Work remaining after 3 days
1 - (3*6)/48 = 30/48
After 4 ppl joined in
((6+4)*Time)/48 = 30/48
Time Z= 3 days to finish the task
IMO A
Answer: A
Question: The average weight of a class is x pounds. When a new student weighing 50 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?
Options:
A)85
B)86
C)88
D)90
E)92
Rationale: When the student weighs 80 pounds the average weight is x - 1 pounds;
When the student weighs 110 pounds the average weight is x + 4 pounds.
So, the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 30/5 = 6 students (including the new one). So, initially there were 5 student.
Total weight = 5x + 80 = 6(x-1) --> x = 85 pounds.
Answer: A.
Answer: A
Question: There are 10 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.
Options:
A)90
B)85
C)75
D)95
E)82
Rationale: First of all you should remember that there is a difference in left and right sock.
now no. of way to select any of the sock = 10
and for second = 9
so total methods = 10*9 = 90
ANSWER:A
Answer: A
Question: How many two-digit numbers are there whose remainder when divided by 10 is 1, and whose remainder when divided by 7 is 6?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 2 digit numbers whose remainder when divided by 10 is 1 are
11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91
Out of above , numbers whose remainder when divided by 6 is 5 are
11 , 41 and 71
Answer D
Answer: D
Question: Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 1000 Km?
Options:
A)10.
B)25.
C)30.
D)38
E)50.
Rationale: Total distance - 1000KM
Time ratio A:B - 3:1
Speed Ratio A : B - 3 : 1
So distance(speed*time) ratio will be - 3*3 : 1*1 - 9:1
So total distance traveled by B - 100 KM
Time taken by B (18:00-16:00 =2) - 2 hours
Speed of B - 50 KMPH
ANSWER:E
Answer: E
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
Options:
A)200
B)88
C)77
D)66
E)51
Rationale: Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: A
Answer: A
Question: If A and B are positive integers, and the remainder obtained when A is divided by B is the same as the remainder obtained when B is divided by A, which of the following is a possible value of AB?
Options:
A) 62
B) 55
C) 49
D) 34
E) 24
Rationale: I am not too sure on this. I guess it is possible only when A and B are both same. If they are both same, AB must be a perfect square.
49 is a perfect square.
Ans:C
Answer: C
Question: Farm A had an average output of 300 kgs of wheat per acre. Farm B had an average output of 350 kgs of wheat per acre. It is known that Farm B's area is 15 acres less than Farm A's. It is also known that Farm B in total harvested 3000 kgs of wheat more than Farm A. What is the area of Farm A?
Options:
A) 130 acres
B) 135 acres
C) 145 acres
D) 164 acres
E) 180 acres
Rationale: The area of Farm A = x acres;
The area of Farm B = x-15 acres.
Total output of Farm A = 300x kgs;
Total output of Farm B = 350(x-15) kgs.
Farm B in total harvested 3000 kgs of wheat more than Farm A: 300x+3000=350(x-15) --> x=164 acres.
Answer: D.
Answer: D
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 162.The amount of the bill is
Options:
A)Rs. 1386
B)Rs. 1350
C)Rs. 1575
D)Rs. 2268
E)None of these
Rationale: Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.162.
∴ x 16 x9/ 12x 1/100}= 162 or x = 1350.
∴ P.W. = Rs. 1350.
Answer B
Answer: B
Question: If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle?
Options:
A)76
B)27
C)19
D)50
E)11
Rationale: Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(i)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(ii)
Solving (i) and (ii), we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.
Answer: D
Answer: D
Question: In one hour,a boat goes 11 km along the stream and 5 km against the stream.The speed of the boat in still water (in km/hr) is :
Options:
A)3
B)5
C)8
D)9
E)10
Rationale: Solution
Speed in still water =1/2(11+5)kmph.= 8 kmph. Answer C
Answer: C
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years (20% per anum) and received $600 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $655 as interest. What was the value of his total savings before investing in these two bonds?
Options:
A)3000
B)5000
C)6000
D)8000
E)9000
Rationale: So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $300, thud 0.2x = $300 --> x = $1,500.
Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,500 = $3,000.
Answer: A
Answer: A
Question: A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 38 now, the son age 5 years back was
Options:
A)14
B)17
C)11
D)19
E)99
Rationale: Let the son's present age be x years .Then, (38 - x) = x x= 19.
Son's age 5 years back = (19 - 5) = 14 years
Answer: A
Answer: A
Question: A certain company employs 6 senior officers and 3 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?
Options:
A)8
B)24
C)58
D)60
E)210
Rationale: Number of ways to select 3 senior officers from 6 of them = 6C3 = (6 x 5 x 4)/3! = 20 ways
Next we can determine the number of ways to select 1 junior officer.
number of ways to select 1 junior officer from 3 of them = 3C1 = 3 ways
Thus the number of ways to select 3 senior officers and 1 junior officer is 20 x 3 = 60 ways.
Answer: D
Answer: D
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)12
B)15
C)24
D)27
E)52
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds.
Answer:D
Answer: D
Question: A certain tax rate is $82 per $100.00. What is the rate, expressed as a percent?
Options:
A)82%
B)8.2%
C)0.82%
D)0.082%
E)0.0082%
Rationale: Here in question it is asking $.82 is what percent of $ 100.Suppose $ .82 is x% of 100 means
100* (x/100) = 82
Hence x = 82 %
So answer is A
Answer: A
Question: A number when divided b the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is:
Options:
A)1220
B)1250
C)22030
D)220030
E)None of these
Rationale: Required number = (555+445)*2*110+30 = 220000+30= 220030.
Answer: D
Answer: D
Question: Twenty two years ago,a father was three times as old as his son.Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :
Options:
A)132
B)76
C)108
D)105
E)86
Rationale: Let the present ages of the father and son be 2x and x years respectively.
then,(2x-22)=3 (x-22)
x=44.
Required sum =(2x+x)=3x=132 years.
Answer is A
Answer: A
Question: If 0.5% of A =75 paise, then the value of A is ?
Options:
A)Rs. 150
B)Rs. 17
C)Rs. 1.70
D)Rs. 4.25
E)None
Rationale: Answer
∵ 0.5/100 of A = 75/100
∴ A = Rs. (75 / 0.5) = Rs. 150
Correct Option: A
Answer: A
Question: Two boys starting from the same place walk at a rate of
5kmph and 5.5kmph respectively.what time will they take to be
8.5km apart, if they walk in the same direction
Options:
A)17 hrs
B)11 hrs
C)19 hrs
D)7 hrs
E)21 hrs
Rationale: The relative speed of the boys = 5.5kmph – 5kmph = 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs
Answer is A.
Answer: A
Question: It takes 35 identical printing presses 15 hours to print 500,000 papers. How many hours would it take 25 of these printing presses to print 500,000 papers?
Options:
A)18
B)20
C)21
D)24
E)25
Rationale: 35 printing presses can do 1/15 of the job each hour.
25 printing presses can do 5/7*1/15 = 1/21 of the job each hour.
The answer is C.
Answer: C
Question: In a company, 54 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?
Options:
A)55%
B)60%
C)65%
D)70%
E)75%
Rationale: The percent of employees who are unionized and men is 0.7*0.6 = 42%
The percent of employees who are unionized and women is 60 - 42 = 18%
46% of all employees are women, so non-union women are 46%-18% = 28%
40% of all employees are non-union.
The percent of non-union employees who are women is 28%/40% = 70%
The answer is D.
Answer: D
Question: Cost price of 12 mangoes is equal to the selling price of 9 mangoes and the discount on 10 mangoes is equal to the profit on 5 mangoes. What is the percentage point difference between the profit percentage and discount percentage?
Options:
A)1.5 %
B)1.75 %
C)1.85 %
D)2 %
E)None of these
Rationale: Cost price of 12 mangoes is equal to the selling price of 9 mangoes,
Let the C.P. of one mango = Re. 1
C.P. of 9 mangoes = Rs. 9
S.P. of 9 mangoes = Rs. 12
Profit % of 9 mangoes = 3/9 x 100 = 33.33 %
Profit % of 1 mango = 33.33/9 = 3.703 %
Profit % of 5 mangoes = 3.703 x 5 = 18.51 %
Given, the discount on 10 mangoes is equal to the profit on 5 mangoes,
Discount on 10 mangoes = 18.51 %
Discount on 1 mango = 1.851 %
Therefore, Profit % of 1 mango - Discount on 1 mango = 3.703 - 1.851 = 1.85 %
ANSWER:C
Answer: C
Question: The area of a square pond is A square feet and the perimeter is p feet. If 2A=4p+18, what is the perimeter of the pond, in feet?
Options:
A)28
B)36
C)40
D)56
E)84
Rationale: You can also solve this via using the given numbers in the answer choices!
Of course you need to be aware of the basic properties as outlined by the other posts above (a = x^2 and p = 4x)
Starting with D you will notice that x=14 is way too big for your area (14^2) and will not satisfy: 2A=4p+18 or A=2p+9
--> Eliminate D and E
Now pick B (its either too big, then its A, or too small then you know its C or it is B itsself)
And picking B indeed solves the problem! (36/4 --> 9; a= 9^2 = 81 and 81=2x36+9)
Answer: B
Question: A train covers a distance of 18 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)177
B)168
C)120
D)882
E)180
Rationale: Speed = (18/10 * 60) km/hr = (108 * 5/18) m/sec = 30 m/sec.
Length of the train = 30 * 6 = 180 m.Answer:E
Answer: E
Question: Arun is 4 years older than Sachin, and Jai is 5 times older than Arun. If S is Sachin’s age and J is Jai’s age, what is the relationship between S and J?
Options:
A)J = 5S + 20
B)J = 5S + 10
C)J = 5S + 5
D)J = 5S − 20
E)J = 5S − 5
Rationale: A=S+4 and J=5A --> J=5S+20
Answer A
Answer: A
Question: The number of new words that can be formed by rearranging the letters of the word 'MOTHER' is
Options:
A)288
B)767
C)719
D)287
E)112
Rationale: Explanation:
Number of words which can be formed = 6! - 1 = 720 - 1 = 719.
Answer: C
Answer: C
Question: A trumpet section includes six musicians. If they hold an audition to determine chair order within the section, and there are to be no ties, how many distinct chair orders can result?
Options:
A)240
B)125
C)720
D)100
E)25
Rationale: We have a word problem using permutations. We must identify the number of total items in the group. There are six possible musicians who could be placed in the first chair, five possible musicians for the second, four for the third, three for the fourth, and two for the fifth and one for the sixth. To determine the number of possible orderings, we multiply these numbers, which we can express as 6!. Now 6! = (6)(5)(4)(3)(2)(1) = 720=C
Answer: C
Question: What approximate value should come in place of the question mark (?) in the following equation ?
1⁄7 of 1596 + 3015 = ? – 2150
Options:
A)7200
B)48000
C)5380
D)58000
E)6300
Rationale: ? ≈ 1 × 230 + 3000 + 2150
= 230 + 3000 + 2150 = 5380
Answer C
Answer: C
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $6 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans?
Options:
A)9%
B)10%
C)11%
D)35%
E)15%
Rationale: You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So
3(15) = 45 - Fox
2(18) = 36 - Pony
The total discount discount is $6 and you are asked to find the percent discount of pony jeans,
so 45(18 - X)/100 + 36(X)/100 = 6 or 45*18 -45*x + 36*x =6*100 or 9x = -6*100 +45*18
x=210/6= 35%
D
Answer: D
Question: if log 2 = 0.30103, the number of digits in 2128 is
Options:
A)22
B)39
C)88
D)28
E)11
Rationale: Explanation:
log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4
ie, its characteristic = 38
Hence, number of digits in 2128 = 38+1 = 39
Answer: Option B
Answer: B
Question: The perimeter of one face of a cube is 32 cm. Its volume will be:
Options:
A)125cm3
B)400cm3
C)512cm3
D)625cm3
E)None of these
Rationale: Explanation:
Edge of cude = 32/4 = 8 cm
Volume = a*a*a = 8*8*8 = 512 cm cube
Option C
Answer: C
Question: A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out?
Options:
A)32 m3
B)36 m3
C)40 m3
D)44 m3
E)None
Rationale: Sol.
Volume = Πr2h = (22/7 x 1 x 1 x 14)m3
= 44 m3.
Answer D
Answer: D
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is?
Options:
A)52:59
B)52:53
C)52:83
D)52:93
E)53:53
Rationale: Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
Answer:B
Answer: B
Question: Round off the given number to nearest hundreds
4765
Options:
A)4800
B)4900
C)5000
D)4600
E)4700
Rationale: the given number is 4765
its tens digit is 6. so replace each of the tens and ones digit by 0 and increase the hundreds digit by 1 to get the rounded off number to the nearest hundred.
correct answer (A)
Answer: A
Question: What would be the local minimum for the function represented as f(x,y) = x2 +ay+y2 -3x ?
Options:
A)(1,1)
B)(2,-1)
C)(-1,1)
D)(2,2)
E)(3,2)
Rationale: f(x,y) = x2 + ay + y2 - 3x
= 4 - a + 1 - 6
= -a-1
So the above value will be the minimum if u check for all other options also. therefore, the answer is (2,-1)
ANSWER:B
Answer: B
Question: There are 25 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Options:
A)156
B)167
C)157
D)352
E)702
Rationale: The total number of stations = 27
From 27 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in ²⁰P₂ ways.
²⁰P₂ = 27 * 26
= 702.
Answer: E
Answer: E
Question: An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discountoffered on it, find its SP?
Options:
A)Rs. 60
B)Rs. 65
C)Rs. 72
D)Rs. 78
E)Rs. 85
Rationale: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
C
Answer: C
Question: There are 59 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?
Options:
A)2
B)4
C)8
D)29
E)32
Rationale: lets assign variables to all the areas in Venn Diagram of Three.
three different Units are DOG, Cat, Snake= Total = 59
Only Dog= d=15
Only Cat = c=10
Only Snake = s
Exactly Dog and Cat= 5
Exactly Dog and Snake = x
Exactly Cat and Snake = y
all three= 3
so 59=15+10+5+3+x+y+s
we need to know total snakes= x+y+s+3 = 29
answer:D
Answer: D
Question: 3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
Options:
A)15/7 days
B)15/4 days
C)25/4 days
D)15/9 days
E)15/2 days
Rationale: 3M = 6W ---- 20 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 20 32 -----?
6 * 20 = 32 * x => x = 15/4 days
Answer: B
Answer: B