divelab/Sys2Bench huggingface dataset:
Question: In a garden, trees are planted in rows. In each row there are as many trees as the number of rows in the garden. If each tree bears as many fruits as the number of trees in each row and if the total number of fruits from the trees in that garden is n, then :
Options:
A)n is a perfect square
B)n is an odd number
C)n is an even number
D)n is a perfect cube.
E)none
Rationale: say for example, there are 4 rows in d garden, then there will b 4 trees in each row and each tree wud bear 4 fruits..Then total no of fruits in d garden wud b (4*4)*4= 64...which is a cube of 4.
ANSWER:D
Answer: D
Question: There are 3 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)5
B)1
C)3
D)6
E)7
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 = 3
and for second = 2
so total methods = 3*2 = 6
ANSWER:D
Answer: D
Question: Three partners A, B, C in a business invested money such that 4(Aâ€™s capital) = 2(Bâ€™s capital) = 8(Câ€™s capital) then, The ratio of their capitals is
Options:
A)63 : 45 : 34
B)63 : 54 : 34
C)36 : 54 : 28
D)2 : 4 : 1
E)None of these
Rationale: Explanation:
Let 4(Aâ€™s capital) = 2(Bâ€™s capital) = 8(Câ€™s capital) = Rs.x
Then, Aâ€™s capital = Rs x/4, Bâ€™s capital = Rs. x/2 and Câ€™s capital = Rs. x/8.
A : B : C = x/4 : x/2 : x/8
2 : 4 : 1
Answer: Option D
Answer: D
Question: A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 199 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
Options:
A)10,000
B)11,025
C)14,400
D)12,696
E)can not be determined
Rationale: Let the side for growing cabbages this year be X ft. Thus the area is X^2.
Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2.
The area would have increased by 199 sq ft as each cabbage takes 1 sq ft space.
X^2 - Y^2 = 199
(X + Y)(X - Y) = 199
199 is a prime number and thus it will be (100 + 99)*(100-99).
Thus X = 100 and Y = 99
X^2 = 100^2 = 10,000
The answer is A.
Answer: A
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at?
Options:
A)11 min
B)12 min
C)10 min
D)15 min
E)16 min
Rationale: B
12 min
Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 6 - 1 = 5 rounds per hour.
Time taken to complete one round at this speed = 1/5 hr = 12 min.
Answer: B
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 160 of the workers of that company are men, how many of the workers are women?
Options:
A)80
B)95
C)105
D)120
E)140
Rationale: Set up equation:
x = total number of workers
160 = 0,4 * 2/3 * x + 0,8 * 1/3 * x
160 = 16/30 x
x = 300
300 - 160 = 140
Answer E
Answer: E
Question: A number is trebled and 10 is added. If the resultant is doubled, it becomes 96. What is that number?
Options:
A)4
B)6
C)8
D)None of these
E)Cannot be determined
Rationale: Solution
Let the number be x.
Then, 2(3x + 10) ‹=› 96
‹=› 3x+10 = 48
‹=› 3x= 38
x= 38/3.
Answer D
Answer: D
Question: In a certain school , 55 percent of student are females and the rest are males . In school elections , If 60 percent of males and 80 percent of females are expected to vote for a candidate (A) , what percent of students are expected to vote for candidate (A) ?
Options:
A) 58%
B) 65%
C) 69%
D) 71%
E) 73%
Rationale: say there are a total of 100 students in this school , 55 are females and 45 are males
55*0.8=44 female are expected to vote
45*0.6=27 males are expected to vote
Thus total of 44+27=71 are expected to vote , which is 71 percent of students .
answer: D
Answer: D
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 120 kilometers?
Options:
A)4.5
B)5.5
C)6.5
D)3
E)8.5
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 120 kilometers?
120 ÷ 40 = 3 × 1 gallon = 3 gallons
correct answer D
Answer: D
Question: Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 70 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach?
Options:
A)80 miles
B)70 miles
C)60 miles
D)50 miles
E)40 miles
Rationale: Every hour, Nil gets ahead of Ethan 70 - 20 =
50 miles. When Nil arrived at the beach, Ethan
is only 20 × 0.5 = 10 miles behind. That tells us
they only drove 1 hour when Nil arrived at the
beach.
The distance between their home and the beach
is
Nil’s speed × Nil’s time
= 70 × 1 = 70 miles.
correct answer B
Answer: B
Question: A certain manufacturer of cake, muffin, and bread mixes has 140 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
Options:
A)a. 1/10
B)b. 3/10
C)c. 1/2
D)d. 7/10
E)e. 3/14
Rationale: C+M+B-CM-MB-CB-2CMB = 140
C - cake buyers, M - muffin an0d B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-20-2CMB = 140
B-CB-MB-2CMB = 30
hence the probability = 30/140 = 3/14.
E
Answer: E
Question: At the beginning of 2010, 60% of the population of Town X lived in the south and the rest lived in the north. During 2010, the population of Town X grew by 5.5%. If the population in the south grew by 4.5%, by how much did the population in the north grow?
Options:
A)1%
B)3.5%
C)6.5%
D)7%
E)13.75%
Rationale: Ratio of population - South:North :: 60%:40% = 3:2
Mean growth = 5.5%
South Growth: 4.5%
North Growth = ??
South-------------Average--------------North
4.5% __(2n)_____5.5%_____(3n)_____??
Since:
4.5 + 2n = 5.5
n = 1/2 (this is the multiplier of the ratio)
Therefore:
North = 5.5 + 3n
North = 5.5 + 3(0.5) = 7%
ANSWER:D
Answer: D
Question: If x/(9p) is an odd prime number, where x is a positive integer and p is a prime number, what is the least value of x?
Options:
A) 54
B) 33
C) 44
D) 66
E) 99
Rationale: x/(9p) = odd prime number
x = odd prime number * 9p
Least value of x = Lowest odd prime number * 9 * Lowest value of p
= 3 * 9* 2 = 54
Answer A
Answer: A
Question: A person traveled 3 equal distances 4km/hr, 5km/hr, 6km/hr then find its avg speed?
Options:
A)5.2km/hr
B)3.18km/hr
C)4.86km/hr
D)2.16km/hr
E)6.32km/hr
Rationale: avg speed = 3xyz/(xy+yz+zx)
required answer is = 3*4*5*6/ (20+30+24) = 4.86km/hr
Answer is C
Answer: C
Question: The ratio of 3 seconds to 30 hours
Options:
A)1:80
B)1:36000
C)1:600
D)1:400
E)1:500
Rationale: 1 hour =3600 sec
then 30 hours =30*3600=108000
so ,3:108000=1:36000
ANSWER:B
Answer: B
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
Options:
A)110 sec
B)130 sec
C)120 sec
D)140 sec
E)150 sec
Rationale: C
120 sec
Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }
= LCM (60, 40) = 120 sec.
Answer: C
Question: When 60 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
Options:
A)3 : 4
B)4 : 3
C)2 : 3
D)Data inadequate
E)None of these
Rationale: Let the first and the second numbers be x and y respect then
y + 60% of x = 140% of y
or, y + 0.6x = 1.4y
or, 0.6x = 0.4y
∴ x : y = 0.4 : 0.6 = 2 : 3
Answer C
Answer: C
Question: A salt manufacturing company produced a total of 3000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
Options:
A)5520
B)2789
C)3550
D)2889
E)2788
Rationale: Total production of salt by the company in that year = 3000 + 3100+ 3200 + .... + 4100 = 42600.
Average monthly production of salt for that year = 42600/12 = 3550.
Answer: C
Answer: C
Question: Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 56, 91
Options:
A)2
B)6
C)15
D)31
E)91
Rationale: 1(result) + (1*1) = 2.
2(result) + (2*2) = 6.
6(result) + (3*3) = 15.
15(result) + (4*4) = 31.
31(result) + (5*5) = 56.
56(result) + (6*6) = 92.
Now we are getting 92 not 91.. So 91 is the wrong number of the given.
answer : E
Answer: E
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
Options:
A)1928
B)1900
C)1927
D)1919
E)1917
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer: B
Answer: B
Question: A boy was asked to multiply a number by 25. He instead multiplied the next number by 52 and got the answers 324 more than the correct answer. The number to be multiplied was
Options:
A)10
B)12
C)15
D)25
E)35
Rationale: Let the number be a
52xa=25xa+324
52a=25a+324
52a-25a=324
27a=324
a=12.
ANSWER:B
Answer: B
Question: In an examination it is required to get 30% of minimum marks to pass. A student got 170 marks and was declared failed by 10 marks difference. Then what is total marks:?
Options:
A)550
B)500
C)600
D)700
E)None of these
Rationale: Explanation:
30 % -------> 180 ( 30 * 6 = 180)
100% -------> 600 (100 * 6 = 600)
Answer: Option C
Answer: C
Question: The ratio of 2 numbers is 3:7 and their H.C.F. is 10. Their L.C.M. is ?
Options:
A)220
B)210
C)252
D)236
E)260
Rationale: Let the numbers be 3x and 7x
Their H.C.F. = 10
so the numbers are 3*10 , 7*10 = 30,70
L.C.M. = 210
Answer is B
Answer: B
Question: At a summer camp with 900 participants, 1/2 of the campers are aged 8 to 12. Next year, the number of campers aged 8 to 12 will increase by 1/3. After this change, what percentage of the total 900 campers will the 8- to 12-year-olds represent?
Options:
A)64%
B)66 2/3%
C)62%
D)60%
E)56%
Rationale: Total - 900 participants
campers are aged 8 to 12 = (1/2)*900 = 450
Next year, campers are aged 8 to 12 = (4/3)*450 = 600
Percentage = (600/900)*100 = 66 2/3%
Answer: Option B
Answer: B
Question: A man spends 1810 for buying bed sheets at 200 each and pillows at 70 each. What will be the ratio of bed sheets to pillows when maximum number of bed sheets are bought?
Options:
A)3 : 8
B)8 : 3
C)9 : 1
D)1 : 9
E)None of these
Rationale: The man can’t purchase more than 8 bedsheets
∴ cost of 8 bedsheets = 8 × 200 = 1600
Remaining amount = 1810 – 1600 = 210
And in 210, the man can purchase
210⁄70 = 3 pillows
Reqd ratio = 8 : 3
Answer B
Answer: B
Question: Look at this series: 8, 22, 8, 28, 8, ... What number should come next?
Options:
A)9
B)29
C)32
D)34
E)36
Rationale: Explanation: This is a simple addition series with a random number, 8, interpolated as every other number. In the series, 6 is added to each number except 8, to arrive at the next number.
Answer: Option D
Answer: D
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
Options:
A)120
B)240
C)360
D)480
E)520
Rationale: Let x be the number he chose, then
2⋅x−138=102
2x=240
x=120
correct answer A
Answer: A
Question: A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $121 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?
Options:
A)4
B)6
C)8
D)10
E)12
Rationale: $121 = 23*$5 + 2*$3
We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).
The number of $5 chocolates can be 23, 20, 17, 14,...,2 for a total of 8 combinations.
The answer is C.
Answer: C
Question: 2 trains starting at the same time from 2 stations 200km
apart and going in opposite direction cross each other ata
distance of 110km from one of the stations.what is the ratio of
their speeds.
Options:
A)10:9
B)11:9
C)9:9
D)9:10
E)5:6
Rationale: In same time ,they cover 110km & 90 km respectively
so ratio of their speed =110:90 = 11:9
Answer is B.
Answer: B
Question: Find the average of all the numbers between 26 and 54 which are divisible by seven
Options:
A)18
B)38.5
C)44
D)50.8
E)None of these
Rationale: Explanation :
Average = (28 + 35 + 42 + 49)/4 = 154/4 = 38.5.
Answer : B
Answer: B
Question: The side of a square has the length of 6. What is the area of the region shaded?
Options:
A)48-8π
B)48-6 π
C)24+6π
D)16+8π
E)64-8π
Rationale: The area of a square whose side is 6 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded
The correct answer is B.
Answer: B
Question: A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 2 red and 4 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)
Options:
A)1/5
B)1/2
C)2/3
D)4/5
E)6/5
Rationale: Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B
FOR THE FIRST BUCKET ...
Red color - 2
Blue color - 2
FOR THE SECOND BUCKET
Red color - 3
Blue color -2
In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :
Scenario I - He picks Red color from List A and Blue color from List B
Scenario II - He picks Blue color from List A and Red color from List B
Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5
Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...
Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...
We get 1/5 + 3/10 = 4/5 (D)
Answer: D
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is?
Options:
A)128
B)276
C)100
D)277
E)110
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 ⇒ x - y = 20 .... (i)
and x + 20 = 2(y - 20) ⇒ x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
∴ The required answer A = 100.
Answer: C
Answer: C
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
Options:
A)85 %
B)26 %
C)10 %
D)20 %
E)15 %
Rationale: Explanation:
SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer:D
Answer: D
Question: Of the families in City X in 1998, 30 percent owned a personal computer. The number of families in City X owning a computer in 2002 was 20 percent greater than it was in 1998, and the total number of families in City X was 8 percent greater in 2002 than it was in 1998. what percent of the families in City X owned a personal computer in 2002?
Options:
A)50.12%
B)52.66%
C)56.33%
D)33.33%
E)74.12%
Rationale: Say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 30
Number of families owning computer in 2002 = 30 * 120/100 = 36
Number of families in 2002 = 108
The percentage = 36/108 * 100 = 33.33%.
Option: D
Answer: D
Question: A three-person committee must be chosen from a group of 7 professors and 15 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?
Options:
A)A)70
B)B)1085
C)C)630
D)D)1,260
E)E)1,980
Rationale: Total number of ways to select at least one professor = Number of ways to select 3 people from 15 students and 7 professors - Number of ways to select 3 people from 15 student (i.e. without including any professor)
= 22C3 - 15C3 = 1540 - 455 = 1085
ANSWER:B
Answer: B
Question: A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?
Options:
A)111
B)105
C)888
D)266
E)882
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer: B
Answer: B
Question: Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 8 such machines produce in 4 minutes ?
Options:
A)648
B)1800
C)2700
D)1440
E)None of these
Rationale: Solution
Let the required number of bottles be x.
More machines,More bottles (Direct Proportion)
More minutes,More bottles (Direct Proportion)
âˆ´ 6 Ã— 1 Ã— x = 8 Ã— 4 Ã— 270 â‡” x = 8x4x270/6= 1440 . Answer D
Answer: D
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Options:
A)833 1/7
B)833 1/3
C)833 2/9
D)833 1/1
E)833 1/4
Rationale: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3
= 833 1/3 grams.
Answer: B
Answer: B
Question: The price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?
Options:
A)8789
B)8721
C)2189
D)2789
E)2791
Rationale: Actual price = 95% of 90% of 85% of Rs. 12000
= 95/100 * 90/100 * 85/100 * 12000
= Rs.8721.
Answer:B
Answer: B
Question: The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 13 consecutive integers that start with (m + 2)?
Options:
A)m + 6
B)n + 6
C)n + 3
D)m + 5
E)n + 4
Rationale: The average of consecutive numbers is the middle number.
Then n = m+2.
The average of 13 consecutive numbers starting from n is n+6.
The answer is B.
Answer: B
Question: The ratio of two quantities is 5 : 4. If each of the quantities is increased by 10, what is the ratio of the new quantities?
Options:
A)It cannot be determined from the information given
B)5:4
C)2:3
D)1:5
E)4:1
Rationale: Since the ratio is 5:4 we can put the quantities as 5K and 4K.
Moreover increasing quantities implies that the quantities become 5K+10 and 4K+10. So the ratio is (5K+10):(4K+10). The ratio value depend on the value of K. So It cannot be determined from the information given.
The answer is A
Answer: A
Question: If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 8, respectively, what is the probability that b/a will not be an integer?
Options:
A)2/12
B)3/12
C)4/12
D)1/2
E)2/3
Rationale: a is from the following set {1,2,3,4}
b is from the following set {8,10,12}
The total number of ways of choosing 2 integers, one from each set is 4*3 = 12 ways.
The possibilities where b/a is not an integer is for the following outcomes:
{b,a} = {8,3},{10,3},{10,4} = 3 ways
Thus the probability is 3/12 = 1/4
The answer is B.
Answer: B
Question: If x is a positive number and a=√x∗x−x, which of the following must be true?
I. a is even
II. a is positive
III. a is an integer
Options:
A)I only
B)II only
C)III only
D)I and II
E)None of the above
Rationale: If x=14 then a=√x∗x−x=1/2∗1/4−1/4=−1/8. Now, −1/8 is not an integer at all (hence not even) and also not positive, so none of the options MUST be true.
Answer: E.
Answer: E
Question: Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
Options:
A)8 hrs 19 min
B)8 hrs 18 min
C)8 hrs 15 min
D)8 hrs 65 min
E)8 hrs 18 min
Rationale: Number of pages typed by Ronald in 1 hour
= 32/6 = 16/3
Number of pages typed by Elan in 1 hour
= 40/5 = 8
Number of pages typed by both in 1 hour
= (16/3 + 8) = 40/3
Time taken by both to type 110 pages
= (110 * 3/40) = 8 1/4 = 8 hrs 15 min
Answer:C
Answer: C
Question: If the sum of 7 consecutive integers is x, which of the must be true?
I. x is even
II. x is odd
III. x is a multiple of 7
Options:
A)I only
B)II only
C)III only
D)I and III
E)II and III
Rationale: sum of 3 consecutive integers
= (n) + (n+1) + (n+2) ++ (n+3) + (n+4) + (n+5)+(n+6)
=7n+21
= odd + odd = even
= 7(n+3) = divisible by 7
Hence, x is even and divisible by 7.
Answer: D
Answer: D
Question: Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 6 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If two minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?
Options:
A)12
B)24
C)36
D)60
E)72
Rationale: the difference of the speed is 1m per second so in two minute Sacha will be 120 m ahead of Bruno..
Bruno will cover this in 120/5=24 secs..
B
Answer: B
Question: A team of six entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
Options:
A)288
B)497
C)168
D)127
E)664
Rationale: Explanation:
6 * 84 = 504 - 7 = 497
Answer:B
Answer: B
Question: A group of people,dogs, and birds has seventy legs, thirty heads, and twenty
tails. How many cats are among this group? (Assume all birds have two legs and a tail.)
Options:
A)0
B)5
C)13
D)15
E)20
Rationale: Write P, C, and B for the number of people, dogs, and birds respectively, so that
we have
2P + 4C + 2B = 70, P + C + B = 30,C + B = 20:
Comparing the last two equations we obtain P = 10, and the first equation simplifies to
4C + 2B = 50, or 2C + B = 25. Therefore,
C = (2C + B) -(C + B) = 25- 5 = 5
correct answer B
Answer: B
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.15 less, he could have gained 25%. What is the cost price?
Options:
A)197
B)375
C)279
D)278
E)75
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
15 ----- ? => 75
Answer:E
Answer: E