divelab/Sys2Bench huggingface dataset:
Question: Let D represent a set of four distinct prime numbers. If the sum of the numbers in D is even and x is a member of D, then what is the least possible value that x can be?
Options:
A)1
B)2
C)3
D)5
E)7
Rationale: We are told that D is a set of four distinct prime numbers, and the sum of the numbers in D is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of D must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number.
Answer: C
Question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
Options:
A)41
B)43
C)31
D)84
E)81
Rationale: (1 man + 1 woman)’s 1 day work = 1/3 + 1/4 = 7/12
Work done by 1 man and 1 women in 1/4 day = ((7/12) x (1/4)) = 7/48
Remaining work = 1 - 7/48 = 41/48
Work done by 1 boy in 1/4 day = ((1/12) x (1/4)) = 1/48
Therefore, Number of boys required = ((41/48) x 48) = 41
ANSWER:A
Answer: A
Question: Find the area between two concentric circles defined by
x2 + y2 -2x + 4y + 1 = 0
x2 + y2 -2x + 4y - 11 = 0
Options:
A)11 Pi
B)12 Pi
C)13 Pi
D)14 Pi
E)15 Pi
Rationale: Rewrite equations of circles in standard form. Hence equation x2 + y2 -2x + 4y + 1 = 0 may be written as
(x - 1)2 + (y + 2) 2 = 4 = 22
and equation x2 + y2 -2x + 4y - 11 = 0 as
(x - 1)2 + (y + 2) 2 = 16 = 42
Knowing the radii, the area of the ring is Pi (4)2 - Pi (2)2 = 12 Pi
correct answer is B) 12 Pi
Answer: B
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
Options:
A)210
B)220
C)230
D)240
E)250
Rationale: 7p3 = 7 × 6 × 5 = 210
A)
Answer: A
Question: A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 2 rows or 7 rows or 9 rows, then no tree will be left. Find the least number of trees required
Options:
A)22
B)60
C)126
D)76
E)21
Rationale: Explanation:
The least number of trees that are required = LCM(2, 7, 9) = 126
Answer: C
Answer: C
Question: What will be the remainder of the following division:
(1234567....141516...20212223....404142)/43?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: first add the digits
1+2+3+.........+42
=>903
then 903 divided by 43
because it is the rule of division by 43( a prime number)
so 903%43=0
% is modulo operator it returns the remainder part
ANSWER:A
Answer: A
Question: It takes 6 tons of copper ore and 15 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 60 tons of copper ore and 90 tons of iron ore?
Options:
A) 4
B) 5
C) 6
D) 7
E) 8
Rationale: Yes, you need copper ore:iron ore in the ratio 6:15. Total 21 tons of the mix in this ratio will give 1 ton of alloy A.
If you have 60 tons of copper ore, it is enough for 60/6 = 10 tons of alloy A.
If you have 90 tons of iron ore, it is enough for 90/15 = 6 tons of alloy A.
Since iron ore is available for only 6 tons of alloy A, you can make only 6 tons of alloy A.
The leftover copper ore alone cannot make any alloy A and hence will be leftover only.
Answer must be 6.
(C)
Answer: C
Question: Two trains running opposite to each other with a speed of 60kph and 55kph having lengths of 180m and 200m respectively. How long it will take the trains to completely pass each other(in seconds)?
Options:
A)9.89
B)10.21
C)11.89
D)14.22
E)19.13
Rationale: Speed of the train relative to each other=60+55=115kph=31.94m/s
Distance need to be covered=180+200=380m
Time taken by the trains to pass each other=380/31.94=11.89s
Answer: C
Answer: C
Question: Two cars started from the same point, at 5 am, traveling in opposite directions at 40 and 50 mph respectively. At what time will they be 450 miles apart?
Options:
A)8am
B)10am
C)11am
D)12am
E)14am
Rationale: After t hours the distances D1 and D2, in miles per hour, traveled by the two cars are given by
D1 = 40 t and D2 = 50 t
After t hours the distance D separating the two cars is given by
D = D1 + D2 = 40 t + 50 t = 90 t
Distance D will be equal to 450 miles when
D = 90 t = 450 miles
t = 5 hours.
5 am + 5 hours = 10 am
Answer:B
Answer: B
Question: Which of the following options is equal to 2.71 x 10(power 7)?
Options:
A)27100000
B)27500000
C)27200000
D)21100000
E)17100000
Rationale: = 2.71 x 10(power 7)
= 2.71 x 10000000
= 27100000.
Answer is A.
Answer: A
Question: IF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
Options:
A)3x^3
B)9x/3
C)9x^2
D)x(x+1)(x+2)
E)x-3
Rationale: *any number multiplied by 3, will be divided by 3
for option E if we put value x=10, 10-3=7 is not divisible by 3
Answer : E
Answer: E
Question: X, Y, W and Z are intezers and the expressing X - Y - Z is even and Y - W - Z is odd. If X is even then which of
Options:
A)W must be odd
B)J must be odd
C)Y must be odd
D)Z must be odd
E)F must be odd
Rationale: Ans. If X is even and X - Y - Z is even then Y and Z both should be odd or both should be even.
If Y - W - Z is odd, and Y and Z are also odd W should be odd
If Y - W - Z is even, and Y and Z are even then W should be odd.
W must be ODD
Answer:A
Answer: A
Question: 10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range R of the 10 numbers?
Options:
A)25
B)27
C)30
D)52
E)55
Rationale: Positions: 1 2 3 4 5 6 7 8 9 10
Given: 1st position = x; 4th position = a; 7th position = y; 10th position = b
y - x = 25
Let x be 0 and y = 25. We are asked to maximize the range and the integers are distinct.
b - a = 30 --> b = 30 + a
In order to increase the range, we have to maximize the value of 'b'.
'b' can be maximized by taking the max value of 'a'.
From the assumed values, maximum value of 'a' can be 22.
Therefore, b = 30 + 22 = 52
Range R= 52 - 0 = 52
Answer: D
Answer: D
Question: The average age of a class of 14 students is 10 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)30 Years
B)31 Years
C)32 Years
D)34 Years
E)25 Years
Rationale: Total age of students is 14X10 = 140 Years
Total age inclusive of teacher = 15X (10+1) = 165
So, Teacher's age is 165-140 = 25 Yrs
There is a shortcut for these type of problems
Teacher's age is 10+(15X1) = 25 Years
E
Answer: E
Question: A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
Options:
A)2400
B)2888
C)2766
D)91987
E)2121
Rationale: 1200 * 12: x * 9 = 2:3
x = 2400
Answer: A
Answer: A
Question: A man want to buy 2 cars. If there are 10 cars that satisfy the man's criteria,in how many different ways can the man select the 2 cars if the order of selection doesn't matter.
Options:
A)54
B)120
C)32
D)210
E)45
Rationale: The number of ways of choosing 2 cars out of 10 are counted by = 10C2 ways = 45
Answer: Option E
Answer: E
Question: In the youth summer village there are 200 people, 100 of them are not working,75 of them have families and 125 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that don't have families and that are singing in the shower?
Options:
A)125
B)150
C)100
D)130
E)140
Rationale: total =200
not working =100
having family=75
like to sing in shower = 125
working=200-100=100
not having family = 200-75=125
like to sing in shower = 125
largest possible number is the lowest possible among the above
Thus 100
C
Answer: C
Question: There are nine leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?
Options:
A)7 leopard and 3 sheep
B)8 leopard and 1 sheep
C)6 leopard and 4 sheep
D)5 leopard and 1 sheep
E)2 leopard and 5 sheep
Rationale: B
8 leopard and 1 sheep
since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer: B
Question: Two whales are moving in the same direction at 60 kmph and 42 kmph. The faster whale manages to cross the other whale in 14 seconds. Find the length of the faster whale in meters.
Options:
A)110 m
B)45 m
C)70 m
D)120 m
E)113 m
Rationale: Relative speed = ( 60 - 42 ) * 5 / 18 = 5 mps.
Distance covered in 14 seconds = 14 * 5 = 70 m.
The length of the faster whale = 70m.
Answer: C
Answer: C
Question: There are 12 cans in the refrigerator. 8 of them are red and 4 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.
Options:
A)460
B)490
C)493
D)455
E)424
Rationale: Ways to pick 4 cans so that at least one red and at least one blue cans to remain the refrigerator =
total ways to pick 4 can out of 12 - ways to pick 4 red out of 8 red - ways to pick 4 blue out of 4 blue
12C4âˆ’8C4âˆ’4C4=495âˆ’70âˆ’1=424
ANSWER:E
Answer: E
Question: Two numbers are respectively 20% and 25% more than a third number. So find the percentage that is first of the second is?
Options:
A)96
B)20
C)35
D)78
E)89
Rationale: First - 120
second - 125
third - 100
125----120
100-----96
ANSWER A
Answer: A
Question: A, B and C invested Rs.6000, Rs.7200 and Rs.10800 respectively, in a partnership business. Find the share of C in profit of Rs.19000 after a year?
Options:
A)3630
B)5580
C)19000
D)8550
E)6000
Rationale: Explanation:
6000 :7200 : 10800
5:6:9
9/20 * 19000 = 8550
Answer: D
Answer: D
Question: There are 22 girls in hostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl.
Options:
A)1 year
B)1 years 2 months
C)3 years 8 months
D)4 years
E)None
Rationale: Total decrease = 22 * 2 = 44 months
= 3 years 8 months
C
Answer: C
Question: One-third of 1206 is what percent of 162?
Options:
A)324.11
B)300.12
C)248.14
D)None of these
E)cannot be determined
Rationale: Answer
Let one-third of 1206 is N% of 162.
∵ 1206/3 = (N x 162)/100
∴ N = (402 x 100) / 162= 248.14
Correct Option: C
Answer: C
Question: 7th number in the series....
99,18,36,9,18
Options:
A)17
B)18
C)19
D)20
E)21
Rationale: its 7 th number in the series 99,18,36,9,18,_,?
99 18.....9+9=18*2=36
36 9.......3+6=9*2=18
18 ?........1+8=9*2=18
ANSWER:B
Answer: B
Question: Given 5^x, for any real integer of x, which of the following is a possible resultant?
Options:
A)15,620
B)15,652
C)15,623
D)15,653
E)15,625
Rationale: Given that the answers have different last digits, there are several ways to solve this, but the most straight forward way is to check the algorithm. 5^x has a cycle of 0.
5^1 = 5
5^2 = 25
5^3 = 125
Observe that the last digit of all the resultants of 5^x is 5. If we continue 5^x, the last digit follows the pattern 5, 5, 5, 5, 5, 5, .... So, all we need look for is the last digit in the pattern, 5.
Answer: E
Answer: E
Question: If x = 1/8 and y = -1/2, what is the value of the expression -2x – y^2?
Options:
A)-3/2
B)-1/2
C)1
D)3/2
E)7/4
Rationale: -2X- y^2
-2x1/8 - (1/2)^2
-1/4-1/4
-1/2
B correct
Answer: B
Question: On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done?
Options:
A)2880
B)2778
C)2682
D)8222
E)6282
Rationale: Explanation:
There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways.
Further, in each category (subject), books are to be arranged in different order, we get,
Required number of ways: 3! * [2! * 2! * 5!] = 2880
ANSWER: A
Answer: A
Question: What is the value of m and n ?
if log3m/log3n=log 52
Options:
A)1,5
B)2,5
C)3,5
D)4,5
E)2,3
Rationale: log (base a) b=log(base n)b/log(base n)a
here base are same in reverse way of formula
so
log(base n)m=log(base 5) 2
hence
n=5,m=2
ANSWER:B
Answer: B
Question: In what ratio should a variety of oil costing Rs. 9 per ltr be mixed with another variety of oil costing Rs. 17.25 per ltr to obtain a mixture costing Rs. 11.75 per ltr?
Options:
A)4 : 1
B)1 : 3
C)3 : 1
D)1 : 2
E)2 : 1
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (17.25 - 11.75) / (11.75 - 9) = 22/11=2/1
ANSWER:E
Answer: E
Question: A small beaker is 1/2 filled with salt water. Another beaker, which has five times the capacity of the small beaker, is 1/2 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)2/5
B)3/5
C)3/10
D)7/20
E)11/20
Rationale: 1/2 of the small beaker is 1/10 of the large beaker.
1/10 + 1/2 = 3/5
The answer is B.
Answer: B
Question: A train 120 m long running at 60 kmph crosses a platform in 35 sec. What is the length of the platform?
Options:
A)338
B)277
C)463
D)456
E)271
Rationale: D = 60 * 5/18 = 35 = 583 – 120 = 463
Answer: C
Answer: C
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 25 seconds, what is the ratio of their speeds?
Options:
A)1:3
B)4:1
C)2:3
D)3:2
E)3:4
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 25 s
= (27x + 17 y)/(x+y) = 25
= (27x + 17 y)/ = 25(x+y)
= 2x = 8y
=x/y = 8/2 = 4/1 i.e 4:1
Answer :B
Answer: B
Question: If Jake loses 12 pounds, he will weigh twice as much as his sister. Together they now weigh 156 pounds. What is Jake’s present weight, in pounds?
Options:
A)108
B)135
C)139
D)147
E)188
Rationale: Lets say J is the weight of Jack and S is the wt of his sister.
If he loses 8 pounds, he s twice as heavy as his sister.
J-12=2*S
Also, together they weight 156 pounds
J+S=156
solvong the 2 equation ,we get J=108 pounds !
A
Answer: A
Question: If the speed of X meters per second is equivalent to the speed of Y meters per minute, what is Y in terms of X? (1 kilometer=1000 meters)
Options:
A)15x/18
B)6x/5
C)18x/5
D)600x
E)60x
Rationale: x=y/60
y = 60x
Answer : E
Answer: E
Question: What is the greatest number of three digits which is divisible by 4, 8, 12 ?
Options:
A)989
B)999
C)978
D)972
E)984
Rationale: Greatest number of 3 digits = 999
LCM of 4, 8, 12 = 24
999 ÷ 24= 41, remainder = 15
Hence, greatest number of four digits which is divisible by 4,8,12
= 999 - 15 = 984
answer : E
Answer: E
Question: Three-twentieths of the members of a social club are retirees who are also bridge players, eight-twentieths of the members are retirees, and one-half of the members are bridge players. If 120 of the members are neither retirees nor bridge players, what is the total number of members in the social club?
Options:
A)240
B)160
C)360
D)400
E)480
Rationale: {Total} = {Retirees} + {Bridge players} - {Both} + {Neither}
x = 8/20*x + x/2 - 3/20*x + 120
20x = 8x + 10x - 3x + 120*20 (multiply by 20)
15x = 120*20
x = 160
Answer: B
Answer: B
Question: In how many ways can the letters D, I, G, I, T, K be arranged so that the two I's are not next to each other?
Options:
A)36
B)48
C)72
D)96
E)240
Rationale: 1 D
2 I
1 G
1 T
1 K
Number of ways these letters can be arranged = 6!/2! (2! to account 2 same Is) = 360
Consider 2 Is as 1 entity and thus the number of arrangements for (II)DGT = 5! = 120
Total allowed cases = 360-120 =240
E is the correct answer.
Answer: E
Question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
Options:
A)21
B)25
C)40
D)47
E)58
Rationale: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
C
Answer: C
Question: The contents of a certain box consist of 24 carrots and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be carrrots?
Options:
A) 24
B) 26
C) 30
D) 46
E) 50
Rationale: carrrots = (carrrots + kiwi + x)*0.3
24 = (30 + 24 + x)*0.3
x = 26.
Answer: B.
Answer: B
Question: Convert the 12/43 m/s into kilometers per hour?
Options:
A)3.5 kmph.
B)2.5 kmph.
C)1 kmph.
D)1.5 kmph.
E)1.9 kmph.
Rationale: 12/43 m/s = 12/43 * 18/5 = 1 (1/250) = 1 kmph.
ANSWER:C
Answer: C
Question: How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2?
Options:
A)6
B)7
C)5
D)4
E)18
Rationale: So, the numbers should be from 1,000 to 10,000
The following two cases are possible for the sum of the digits to be 2:
1. Two 1's and the rest are 0's:
1,001
1,010
1,100
3 numbers.
2. One 2 and the rest are 0's:
2,000
1 number.
Total = 4 numbers.
Answer:D
Answer: D
Question: The average (arithmetic mean) of four distinct positive integers is 20. If the average of the smaller two of these four integers is 24, which of the following represents the maximum possible value of the largest integer?
Options:
A)8
B)16
C)36
D)20
E)1
Rationale: Let the distinct number be A,B,C, and D
Its given A > B > C > D
also A + B + C + D =80 and A + B = 24 means C + D = 56
Since the question ask for the largest possible number we should choose the least value for A and B,C. So D should be 36. If D=36 then C = 20 > A,B <20
Answer : C
Answer: C
Question: If 10 bulls can plough 20 identical fields in 3 days working 10 hours a day, then in how many days can 30 bulls plough 32 same identical fields working 8 hours a day?
Options:
A)8
B)7
C)5
D)2.0
E)1
Rationale: Explanation:
M1*D1*W2 = M2*D2*W1
10*3*10*32 = 30*d*8*20
d = 2 days
ANSWER: D
Answer: D
Question: There are 4 sections with 6 questions each. If two questions are selected from each section, the chance of getting different questions is________
Options:
A)225
B)245
C)300
D)240
E)289
Rationale: we have to select two questions from each section so the chances are 6C4.6C4=225
ANSWER:A
Answer: A
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
Options:
A)231
B)756
C)125
D)451
E)123
Rationale: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways	= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
= (525 + 210 + 21)
= 756.
Ans: B
Answer: B
Question: Which of the following is between 23/30 and 17/21?
Options:
A)1/3
B)3/8
C)1/2
D)5/8
E)7/9
Rationale: I see this as a POE (Process of Elimination) and Ballparking (Estimation) question. Not sure if this is the most efficient, but it worked:
1) I estimate 23/30 to be ~3/4+ (approximately slightly greater than 3/4)
2) I estimate 17/21 to be ~4/5+ (approximately slightly greater than 4/5)
3) So now I'm looking for an answer choice that is .75 < x < .80
It should be pretty easy to identify which answer choices are less than .75 (or 3/4) if you have had practice with fractions.
A) clearly wrong - it's less than 3/4
B) also clearly wrong - it's less than 3/4
C) also clearly wrong - it's less than 3/4
D) also clearly wrong - it's less than 3/4
I would just stop here and select E. But to verify:
E) 7/9 ~ .77 which is greater than .75 and less than .80
Answer: E
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 40%?
Options:
A)600
B)887
C)256
D)654
E)700
Rationale: Cost price = Rs.500
profit = 40% of 500 = Rs.200
Selling price = Cost price + Profit
= 500 + 200 = 700
Answer: E
Answer: E
Question: The average of first six prime numbers which are between 50 and 90 is
Options:
A)35.4
B)42
C)45.7
D)64
E)67
Rationale: Explanation :
first six prime numbers which are between 50 and 90 = 53, 59, 61, 67, 71, 73
average = (53 + 59 + 61 + 67 + 71 + 73)/6
= 64
Answer : D
Answer: D
Question: A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 7 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?
Options:
A)(a) 24/5
B)(b) 5
C)(c) 26/5
D)(d) 84/13
E)(e) 28/5
Rationale: from the uphill we can find out the distance = 7*2 = 14
average speed = total distance/total time
= 28/ (2+ (14/6)) = 84/13
Answer is D.
Answer: D
Question: Two trains are moving at 85 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
A)5 25/31 sec
B)7 1/17 sec
C)7 2/2 sec
D)8 1/2 sec
E)7 1/9 sec
Rationale: 70 + 85 = 155 * 5/18 = 775/18 mps
D = 150 + 100 = 250 m
T = 250 * 18/775 = 180/31 = 5 25/31 sec
Answer: A
Answer: A
Question: In how many ways a group of 5 male and 2 female be made out of a total of 7 male and 3 female?
Options:
A)55
B)78
C)63
D)89
E)98
Rationale: req no of ways = 7c5*3c2 = 7*6/2*1 * 3 = 63
ANSWER C
Answer: C
Question: The least number which when subtracted from both the terms of the ratio 4 : 5 to give a ratio less than 14 : 23, is
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Explanation :
Let x is subtracted. Then, ((4 - x)/(5 - x)) < 14 / 23
23(4 - x) < 14(5 - x) => 9x > 22 = x > 2.4.
Least such number is 3.
Answer : B
Answer: B
Question: AMS employs 8 professors on their staff. Their respective probability of remaining in employment for 10 years are 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years at least 8 of them still work in AMS is ?
Options:
A)0.19
B)1.22
C)0.00363.
D)0.16
E)none of these
Rationale: Asking atleast 6 of them continue ,
it has 3 cases.
1 all 8 professors continue.
1st case all 8 continue is = 2/10*3/10*4/10*5/10*6/10*7/10*/8/10*9/10=
=>0.00363.
C
Answer: C
Question: A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.33 per litre so as to make a profit of 30% on cost when he sells the resulting milk and water mixture for Rs.36 In what ratio should he mix the water and milk?
Options:
A)1:20
B)23:120
C)1:8
D)1:4
E)6:11
Rationale: water = w (liter)
Milk = m (liter)
==> Cost = Price x Quantity = 0.33m
==> Revenue = Price x Quantity = 0.36(m + w)
==> Profit =0.36(m+w) - 0.33m = 0.3*(0.33m)[30% of cost]
==> 0.36m + 0.36w - 0.33m = 0.099m
==> 0.069m = 0.36w
==> m/w = 0.36/0.069 = 120/23
--OR--
w/m = 23/120
B is correct.
Answer: B
Question: What is the largest 4 digit number exactly divisible by 88?
Options:
A)8844
B)9944
C)7744
D)6644
E)5544
Rationale: Largest 4 digit number = 9999
9999 ÷ 88 = 113, remainder = 55
Hence largest 4 digit number exactly divisible by 88
= 9999 - 55 = 9944
Answer is B.
Answer: B
Question: During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?
Options:
A)32
B)40
C)55
D)64
E)80
Rationale: Total smelt = x.
Then, 0.5*80+0.3(x-80)=0.4*x --> x=160 --> 0.4*x=64.
Answer: D.
Answer: D
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. The area of the lawn is 2109 sq. m. what is the width of the road?
Options:
A)5 M
B)4 M
C)2 M
D)3 M
E)6 M
Rationale: AREA OF THE PARK = 60 * 40 = 2400 M^2
GIVEN AREA OF THE LAWN = 2109 M^2
TOTAL AREA OF THE CROSS ROADS = 2400 - 2109 = 291 M^2
ASSUME THAT THE WIDTH OF THE CROSS ROAD = X
= AREA OF ROAD 1 + ROAD 2- COMMON AREA CROSS ROAD
= 60X + 40 X - X^2
TOTAL AREA OF CROSS ROAD = 60X+40X-X^2 = 291 M^2
(X-97)(X-3) = 0
X =3
ANSWER D
Answer: D