divelab/Sys2Bench huggingface dataset:
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 72% of the required amount. What is the net difference in the expenditure on that product?
Options:
A)12.5%
B)10%
C)15%
D)17%
E)19%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.72 x 1.25 = 0.9
Decrease in price = (0.1/1) × 100 = 10%
B)
Answer: B
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
Options:
A)5/21
B)5/27
C)5/97
D)5/22
E)5/39
Rationale: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252 = 5/21
Answer: A
Answer: A
Question: A small beaker is 1/2 filled with salt water. Another beaker, which has five times the capacity of the small beaker, is 2/5 filled with fresh water. After dumping all of the salt water from the small beaker into the large beaker, to what fraction of its capacity will the large beaker be filled?
Options:
A)5/6
B)4/5
C)3/4
D)2/3
E)1/2
Rationale: 1/2 of the small beaker is 1/10 of the large beaker.
1/10 + 2/5 = 1/2
The answer is E.
Answer: E
Question: A football coach must choose 6 freshers from a team of 12 players. How many different ways can the coach choose the freshers?
Options:
A)500
B)650
C)729
D)800
E)924
Rationale: Choose 6 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{6}}= 924
E
Answer: E
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 4 muffins remained. How many guests did Monica plan on?
Options:
A)3.
B)5.
C)4.
D)6.
E)7.
Rationale: 5N +2 = 4 + 6(N-1)
Solving N= 4
Hence C
Answer: C
Question: Eleven bags are bought for Rs.1000 and sold at 10 for Rs.1400. What is the gain or loss in percentage?
Options:
A)10%
B)21%
C)24%
D)20%
E)None of these
Rationale: Explanation:
As selling price is Rs.1400 for 10 bags, each bag is sold at Rs.140.
Hence, the profit is Rs.100 after selling 10 bags plus the selling price of 1 bag = 100 + 140 = Rs.240.
%profit = 240/1000 *100
= 24%
ANSWER C
Answer: C
Question: A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?
Options:
A)144
B)378
C)217
D)299
E)277
Rationale: Explanation:
Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
B's share = = Rs. 144.
Answer: A) 144
Answer: A
Question: Mr. keth sold two pipes at $3 each. Based on the cost, his profit one was 30% and his loss on the other was 15%. On the sale of the pipes. Find the amount of his profit or loss?
Options:
A)lost 10 cents
B)lost 50 cents
C)broke even
D)gained 60 cents
E)gained 40 cents
Rationale: 30 % profit on $ 3
= $ 30/100 ×3
= $ 0.30× 3
= $ 0.90
Similarly, 15% loss on $ 3
= $ 15/100 × 3
= $ 0.15 ×3
= $ 0.45
Therefore, in one pipe his profit is $ 0.90 and in the other pipe his loss is $ 0.45
so profit by amount $0.40.
Answer is E
Answer: E
Question: Including Cara and Dan, there are seven members on the board of directors for a company. If the board is to be split up into a four-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan?
Options:
A)1/5
B)1/4
C)1/3
D)1/2
E)2/5
Rationale: The number of possible subcommittees with Cara is 6C3=20.
The number of possible subcommittees with Cara and Dan is 5C2=10.
The fraction of Cara's subcommittees which include Dan is 10/20=1/2.
The answer is D.
Answer: D
Question: In a deck of cards there are 52 cards numbered from 1 to 13. There are 4 cards of each number in the deck. If you insert 10 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it?
Options:
A)1/4.
B)7/31.
C)5/29.
D)4/13.
E)1/3.
Rationale: 4+10 tens/52+10 total cards=14/62=7/31
B
Answer: B
Question: A certain number when divided by 65 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
Options:
A)4
B)5
C)6
D)8
E)9
Rationale: Explanation:
65 + 25 =90/15 =6 (Remainder)
C
Answer: C
Question: Which of the following must be divisible by 2 if z is a positive integer?
Options:
A)z^2*(z−5)
B)(z^2−2)
C)z(z+2)^3
D)(z−1)*z*(z+1)
E)z^2*(z−5)
Rationale: option D) (z−1)*z*(z+1) which represents the product of three consecutive integers
the product of 3 consecutive integers is divisible by both 2 and 3.
Answer is D
Answer: D
Question: A sum of money is borrowed and paid back in two annual installments of Rs. 882 each allowing 5% C.I. The sum borrowed was?
Options:
A)Rs.1648
B)Rs.1640
C)Rs.1289
D)Rs.1282
E)Rs.1633
Rationale: Principal = (P.W. of Rs. 882 due 1 year hence) + (P.W. of Rs. 882 due 2 years hence)
= [882/(1 + 5/100) + 882/(1 + 5/100)2]
= (882 * 20)/21 + (882 * 400)/441
= Rs.1640.
Answer:B
Answer: B
Question: Six lights begin to flash together at 12:00 noon and flash respectively at intervals of 4, 5, 6, 7, 8, and 9 seconds. Not including the flash at 12:00 noon, how many more times will all six lights flash together before 4:00 pm (i.e. four hours later)?
Options:
A)3
B)5
C)7
D)9
E)11
Rationale: The least common multiple is 2*2*2*3*3*5*7=2520.
14400 seconds / 2520 = 5 + remainder.
The answer is B.
Answer: B
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
Options:
A)388
B)277
C)266
D)280
E)191
Rationale: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Answer: D
Question: Vishal and Raghu jointly started a business. Vishal invested three times as Raghu did and invested his money for double time as compared to Raghu. Raghu 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)Rs. 28,000
B)Rs. 18,000
C)Rs. 14,000
D)Rs. 8,000
E)None of these
Rationale: Explanation:
Investments ratio is = 3:1
Time period ratio is = 2:1
As they are proportional to gain
------
Gain ratio of Vishal and raghu = 6:1
But given Raghu got Rs. 4000,
=? 1 ----- 4000
7 ----- ?
=> Rs.28,000
The total gain = Rs.28,000
ANSWER IS A
Answer: A
Question: Sahil took a loan for 6 years at the rate of 5% per annum on Simple Interest, If the total interest paid was Rs. 1230, the principal was
Options:
A)4100
B)4200
C)4300
D)4400
E)None of these
Rationale: Explanation:
S.I.=P∗R∗T /100=>P=S.I.∗100/ R∗T
By applying above formula we can easily solve this question, as we are already having the simple interest.
=>P=1230∗100/ 6∗5
=>P=4100
Option A
Answer: A
Question: In March, Kurt ran an average of 2 miles an hour. If by June he had increased his pace by 10 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June?
Options:
A)3590/60^2
B)2410/60^2
C)1790/60^2
D)3586/60
E)60^2/3590
Rationale: Kurt ran at an average of 2 miles/hour in march. So to run 1 mile he would take 1/2 hours = (60 * 60)/2 seconds = 1800 seconds.
If he increases his speed by 10 seconds, he will complete a mile in 1790 seconds. Converting in hours = 1790/(60 * 60) = 1790/(60^2)
ANSWER: C
Answer: C
Question: Rs.8000 become Rs.8820 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
Options:
A)6 years
B)8 years
C)9 years
D)3 years
E)2 years
Rationale: 8820 = 8000(21/20)N
(21/20)^2 = (21/20)N => N = 2
. At the end of two years what will be the comp.Answer: E
Answer: E
Question: A can do a certain job in 20 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
Options:
A)7 1/2 days
B)8 days
C)12 1/2 days
D)9 days
E)None of them
Rationale: Ratio of times taken by A and B = 160 : 100 = 8 : 5.
Suppose B alone takes x days to do the job.
Then, 8 : 5 :: 20 : x = 8x = 5 x 20 =x = 12 1/2 days.
Answer is C.
Answer: C
Question: The length and breadth of a rectangle are raised in the proportion 3:4 and 4:5 correspondingly. What is the proportion of the previous place to the new?
Options:
A)2:3
B)3:5
C)5:7
D)7:9
E)None of these
Rationale: Explanation :
-> If the real length = 3a
And the real breadth = 4a
Area = (3a)*(4a)
=12 a2
-> New Length is 4a and New breadth is 5a
New area is (4a)*(5a)
= 20 a2
Ratio of previous place to new place = 12 a2 : 20 a2
= 12 : 20
= 3 : 5
Answer : B
Answer: B
Question: A ship sails out to a mark at the rate of 18 kmph. and sails back at the rate of 14 kmph. The average rate of sailing is ?
Options:
A)5 km/hr
B)12 km/hr
C)16 km/hr
D)25 km/hr
E)None
Rationale: Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 18 x 14 ) / (18 +14 ) km/hr.
= 16 km/hr.
Correct Option: C
Answer: C
Question: A businessman earns $28800 in December, thus decreasing his average annual (January to December) earnings by $1300. His average annual earnings would be
Source: CMAT Preparation
Options:
A)$29000
B)$33500
C)$40200
D)$41000
E)$43100
Rationale: (x - 28,800)/11 - x/12 = 1,300
x = 517,200
x/12 = 43,100
Answer: E.
Answer: E
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings?
Options:
A)88
B)16
C)128
D)37
E)12
Rationale: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer:D
Answer: D
Question: A merchant has selected two items to be placed on sale, one of which currently sells for 25 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?
Options:
A)52 %
B)40%
C)30%
D)20%
E)10%
Rationale: Expensive item = $100;
Cheap item = $75;
We must increase $75 to $100, so by $25, which is approximately 30% increase: (100-75)/75 = 1/3 = ~0.33
Answer: C.
Answer: C
Question: The ages of two persons differ by 16 years. 6 years ago, the elder one was
3 times as old as the younger one. What are their present ages of the elder person?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Let present age of the elder person =x and
present age of the younger person =x−16
(x−6)=3(x−16−6)
x−6=3x−66
2x=60
x=60/2=30 Answer: Option C
Answer: C
Question: How many prime numbers D exist such that 90 < D < 106 and D is a factor of 99999919?
Options:
A)1. Zero
B)2. One
C)3. Two
D)4. Three
E)5. More than three
Rationale: I found that considering the constraint..D is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.C
Answer: C
Question: A man bring 2 cats to his home to eliminate all the mice. They do a half of the work in 5 days, then the man brings 3 more cats. If they hunt at the same rate, how many days will take to hunt all the mice, since the first day?
Options:
A) 7 days
B) 8 days
C) 9 days
D) 10 days
E) 11 days
Rationale: We have that: 2 cats----- 5 days, (2+3) C ----- X d, that is: (X d/ 2C) = (5 d/5P), then: X d = (5 d/5C)2C = 2d. Is to say, the 5 cats hunt the same quantity in 2 days; as it is only 1/2 of the work, all the mice would be hunt in: M = 5 d + 2 d = 7 days. Answer A.
Answer: A
Question: next term in series 3,32,405
Options:
A)5144
B)6144
C)7144
D)7582
E)8547
Rationale: first term 3*1^2=3
second term 4*2^3=32
third term 5*3^4=405
fourth term 6*4^5=6144
ANSWER:B
Answer: B
Question: Find the invalid no.from the following series 3, 7, 15, 31, 63, 123, 255
Options:
A)3
B)7
C)27
D)63
E)123
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 123 is wrong.
E
Answer: E
Question: A shopkeeper fixes the marked price of an item 40% above its cost price. The percentage of discount allowed to gain 8% is
Options:
A)23.85%
B)22.85%
C)21.85%
D)20.85%
E)None of these
Rationale: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 140
Required gain = 8%,
So Selling price = Rs 108
Discount = 140 - 108 = 32
Discount% = (32/140)*100 = 22.85%
Option B
Answer: B
Question: A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40,000 liters of petrol is used daily, the suply fails in 90 days.If 32,000 liters of petrol is used daily, it fails in 60 days. How much petrol can be used daily with out the supply ever failing?
Options:
A)64000 liters
B)56000 liters
C)78000 liters
D)60000 liters
E)None of these
Rationale: Explanation:
Let x liter be the per day filling and v litr be the capacity of the reservoir, then
90x + v = 40000 × 90 -----(1)
60x + v= 32000 × 60 ------(2)
solving eq.(1) and (2) , we get
x = 56000
Hence , 56000 liters per day can be used without the failure of supply.
Answer: B
Answer: B
Question: A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colour.
Options:
A)52/55
B)3/55
C)41/44
D)3/44
E)None of these
Rationale: Explanation:
Total cases =12C3=12∗11∗10/3∗2∗1=220
Total cases of drawing same colour =5C3+4C3+3C3
5∗4/2∗1+4+1=15
Probability of same colur ==15/220=3/44
Probability of not same colur =1−3/44=41/44
Option C
Answer: C
Question: A man can row 7.5 km/hour in still water & he finds that it takes him twice aslong to row up as to row down the river. Find the rate of stream?
Options:
A)2 km/hr
B)2.5 km/hr
C)3 km/hr
D)4 km/hr
E)4.3 km/hr
Rationale: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream =x
Then speed downstream =2x
we have, 12(x+2x) = speed in still water
⇒12(3x)=7.5⇒3x=15⇒x=5
i.e., speed upstream = 5 km/hr
Rate of stream =12(2x−x)=x2=52=2.5 km/hr
B
Answer: B
Question: A bag contains 6 black and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)3/4
B)1/3
C)1/7
D)1/8
E)4/3
Rationale: Let number of balls = (6 + 3) = 9.
Number of white balls = 3.
P (drawing a white ball) =3/9=1/3.
Option B.
Answer: B
Question: If a chair was sold for $ 990 at a loss of $ 110. Find the cost price of the chair.
Options:
A)$ 1000
B)$ 1100
C)$ 1200
D)$ 1300
E)$ 1400
Rationale: Selling Price = $ 990,
Loss = $ 110
Cost Price = Selling Price + Loss
Cost Price = 990 + 110
= $ 1100
Therefore, cost price of the chair = $ 1100
Answers: B
Answer: B
Question: a, b, c and d are four consecutive numbers. If the sum of a and dis 111, what is the product of b and c?
Options:
A)2652
B)2578
C)2534
D)3080
E)4234
Rationale: Here d = a + 3
a + a + 3 = 111
2a = 108
a = 54
So, numbers are 54, 55, 56 and 57
∴ b × c= 55 × 56 = 3080
D
Answer: D
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
Options:
A)22277
B)26782
C)22882
D)15000
E)28761
Rationale: The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000
= Rs.15000
Answer: D
Answer: D
Question: It costs $18 for the first 1/2 hour to rent a bike. After the first 1/2 hour it costs $10 per hour. If a certain customer uses the bike for 2 hours, how much will it cost him?
Options:
A)$12
B)$45
C)$33
D)$95
E)$30
Rationale: 2 hours = 120 minutes
First 30 min ------> $18
Time left is 90 min...
Now, 60 min costs $ 10
1 min costs $ 10/60
90 min costs $ 10/60*90 => $ 15
So, Total cost will be $15 + $18 => $ 33
The answer will be (C) $ 33
Answer: C
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35,x
Options:
A)23
B)26
C)38
D)35
E)45
Rationale: (C)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 35 + 3 = 38.
Answer: C
Question: In an examination a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
Options:
A)10
B)11
C)8
D)9
E)12
Rationale: Let the number of papers be x. Then,
63x + 20 + 2 = 65x
= 2x = 22
= x = 11.
ANSWER B
Answer: B
Question: A basketball player succeeds with 40% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
Options:
A)0.343
B)0.472
C)0.555
D)0.657
E)0.784
Rationale: P(missing all 3 free throws) = 0.6^3 = 0.216
P(succeeding at least once) = 1 - 0.216 = 0.784
The answer is E.
Answer: E
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Options:
A)5
B)6
C)8
D)4
E)1
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
Answer: C
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Y of races we need to conduct to get the top 3 fastest horses?
Options:
A)5
B)7
C)8
D)10
E)11
Rationale: Y=7 is the correct answer.
Good solution Buneul.B
Answer: B
Question: A, B, C subscribe Rs. 50000/- for a business. A subscribes Rs. 4000/- more than B and B Rs. 5000/- more than C. out of a total profit of Rs. 35,000/- A receives:
Options:
A)Rs. 8400/-
B)Rs. 11900/-
C)Rs. 13600/-
D)Rs. 14700/-
E)None of these
Rationale: Explanation:
Let the investments of C, B and A be Rs. X,
Rs. (x + 5000) and (x + 9000) = 50000
3x = 36000
X = 12000
C = Rs. 12000/- , B = Rs. 17000/- and A = Rs. 21000/-
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
A’s share = Rs. (35000 * 21/50) = Rs. 14700/-
Answer: Option D
Answer: D
Question: Which of the following values is the greatest
Options:
A)a) 11% of 89
B)b) 22% of 78
C)c) 33% of 67
D)d) 65% of 45
E)e) 44% of 56
Rationale: Are you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says D.
Answer: D
Question: The average age of 22 students in a group is 12 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years?
Options:
A)31
B)36
C)35
D)53
E)57
Rationale: age of the teacher=(23*13-22*12)
=35 years.
ANSWER:C
Answer: C
Question: Raju age after 4 years will be 10 times his age 5 years back, What is the present age of Raju
Options:
A)9 years
B)10 years
C)7 years
D)6 years
E)8 years
Rationale: Explanation:
Clearly,
x+4= 10(x-5)
<=> 9x = 54 => x = 6
Option D
Answer: D
Question: If n divided by 8 has a remainder of 1, what is the remainder when 3 times n is divided by 8?
Options:
A)1
B)3
C)7
D)5
E)6
Rationale: As per question => N=8P+1 for some integer p
hence 3N => 24Q + 3 => remainder => 3 for some integer Q
hence B
Answer: B
Question: Set J consists of 18 consecutive even numbers. If the smallest term in the set is -22, what is the range of the positive integers in set J?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Since there are only 18 integers, another approach is the just list all 18.
We get:-22, -20, -18, -16, -14,-12,-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12
Range of POSITIVE INTEGERS =12 - 2= 10
Answer: E
Answer: E
Question: Certain number of worms are placed in a container. The number of worms increases by three times every day and the container is completely filled with worms in 12 days. On what day, the worms were
1/3rd of the container ?
Options:
A)9 days
B)3 days
C)4 days
D)11 days
E)14 days
Rationale: As every day the worms increases by 3 times
1/3 × 3 = 1 [full]
Therefore on 11th day
Option D
Answer: D
Question: Which of the following is always true?
(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.
(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.
(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.
Options:
A)I and III
B)I, II and III
C)II
D)I and II
E)None
Rationale: he average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.
(-10+-9+-8+-7+-6)/5 = -40/5 = -8 same as (-10+-6)/2 = -8 True
The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.
(2+3+4+5)/4 = 14/4 same as (5+2)/2 = 7/2 always true
(1+2+3+4)/4 = 10/4 same as (4+1)/2 = 5/2
The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.
(3+4+5+6+7)/5 = 5 same as (7+3)/2 = 5 True
ANSWER:B
Answer: B
Question: A can do a work in 20 days and B can do it in 8 days. In how many days A and B can do the work?
Options:
A)5 5/7 days
B)10 days
C)6 days
D)8 days
E)7 days
Rationale: Explanation:
A's 1day's work = 1/20
B's 1day's work = 1/8
They work together = 1/20 + 1/8 = 7/40 = 40/7 = 5 5/7days
Answer: Option A
Answer: A
Question: A man counted his animals, 80 heads and 260 legs (ducks and goats). how many goats are there?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=260 and divide 2d+4g=260 by 2 we get d+2g=130 -----------> eq2
subtract eq1 from eq2
we get no of goats=50
ANSWER:C
Answer: C
Question: Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is
Options:
A)1/36
B)3/36
C)11/36
D)20/36
E)23/36
Rationale: 1. The probability of getting an even number at the first die is 1/2 (as the probability of even = the probability of odd = 1/2);
2. The probability of getting a total of 8 is 5/6^2, as there are 5 different favorable scenarios: (2,6), (6,2), (3,5), (5,3) and (4,4);
3. The probability of getting an even number at the first die AND a total of 8 is 3/6^2 (from above case);
Hence, The probability of getting an even number at the first die OR a total of 8 is 1/2+5/36-3/36=20/36.
Answer: D
Answer: D
Question: In a certain pond, 60 fish were caught, tagged, and returned to the pond. A few days later, 60 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
Options:
A)400
B)625
C)1818
D)2500
E)10 000
Rationale: The percent of tagged fish in the second catch is 2/60*100 = 3.33%.
We are told that 3.33% approximates the percent of tagged fish in the pond. Since there are 60 tagged fish, then we have 0.033x = 60 --> x = 1,818.
Answer: C.
Answer: C
Question: The distance between 2 cities A and B is 1000km. A train starts from A at 10 a.m. and travels towards B at 100 km/hr. Another starts from B at 11 a.m. and travels towards A at 150 km/hr. At what time do they meet?
Options:
A)11am.
B)12p.m.
C)3pm.
D)2p.m.
E)1p.m.
Rationale: Suppose they meet x hrs after 10 a.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000
100x + 150 (x-1) = 1000
x = 4.60 = 5 hrs
They meet at 10+5 = 3 p.m.
Answer is C
Answer: C
Question: Find the sum of first 70 odd numbers
Options:
A)4900
B)4970
C)4990
D)4980
E)4960
Rationale: Explanation:
n2 = 702 = 4900
Answer: Option A
Answer: A
Question: (39,897)(0.0096)/198.76 is approximately
Options:
A)0.02
B)0.2
C)2
D)20
E)200
Rationale: 39,897 can be written as 40,000 (approximately)
0.0096 can be written as 0.01 (approximately
198.76 can be written as 200 (approximately)
40,000*0.01/ 200= 2 (approximately)
C is the answer
Answer: C