divelab/Sys2Bench huggingface dataset:
Question: If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 21 women together do the work?
Options:
A)10 days
B)30 days
C)20 days
D)80 days
E)40 days
Rationale: B 30 days
Given that 12m = 20w => 3m = 5w
9 men + 21 women = 15 women + 21 women = 36 women
20 women can do the work in 54 days. So, 36 women can do it in (20 * 54) /36 = 30 days.
Answer: B
Question: If 13 = 13w/(1-w) ,then (3w)2 =
Options:
A)1/4
B)1/2
C)1
D)2
E)3
Rationale: 13-13w=13w
26w=13
w=1/2
3w=3/2
3w*2=3/2*2=3
ANSWER:E
Answer: E
Question: Find the odd man out
892, 444, 220, 112, 52, 24
Options:
A)52
B)112
C)220
D)444
E)544
Rationale: 24x2+4=52
52x2+4=108
108x2+4=220
220x2+4=444
ANSWER:B
Answer: B
Question: Find the area of a parallelogram with base 26 cm and height 12 cm?
Options:
A)281
B)284
C)288
D)255
E)312
Rationale: Area of a parallelogram = base * height
= 26 * 12
= 312 cm2
Answer: E
Answer: E
Question: January 1, 2004 was a Thursday, what day of the week lies on January 1 2005.
Options:
A)Saturday
B)Monday
C)Saturday
D)Tuesday
E)None of these
Rationale: Explanation :
Given that January 1, 2004 was Thursday.
Odd days in 2004 = 2 (because 2004 is a leap year)
(Also note that we have taken the complete year 2004 because we need to find out the odd days from 01-Jan-2004 to 31-Dec-2004, that is the whole year 2004)
Hence January 1, 2005 = (Thursday + 2 odd days) = Saturday. Answer : Option C
Answer: C
Question: A football coach must choose 4 freshers from a team of 11 players. How many different ways can the coach choose the freshers?
Options:
A)330
B)650
C)729
D)800
E)890
Rationale: Choose 4 starters from a team of 11 players. Order is not important.
\inline {\color{Black} 11C_{4}}= 330
A
Answer: A
Question: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?
Options:
A)2397
B)2401
C)2411
D)2423
E)None of the above
Rationale: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.
Answer B
Answer: B
Question: Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2100
Options:
A)30
B)70
C)210
D)300
E)700
Rationale: Since 3 is the GCF of 27 (3.3.3) and x => x has only one "3 in its prime box.
Since 10 (2.5) is the GCF of 100 (2.2.5.5) and x => x has only one 2 and one 5 in its primebox.
So x = 2.3.5.n (n=something that is not 2, 3, 5)
2100 = 2.3.5.7 =210
The GCF of x and 2100 is the product of the common factors of x and 2100 => the max possible is 2100.
ANSWER:C
Answer: C
Question: Increasing the original price of an article by 15% and then increasing the new price by 15% again is equivalent to increasing the original price by what %?
Options:
A)34
B)40
C)68
D)88
E)102
Rationale: Let the price of a commodity is increased by a% and then b% then the final increment will be
1 + a/100 + b/100 + ab/10000
Now the same logic can be applied with decrements also with just changing the signs.
Let for example price of commodity is increased by a% and then decreased by b% then the resulting increase/decrease will be
1 + a/100 - b/100 -ab/10000
For the above question the approach will be
1 + 0.15 + 0.15 + 0.0225 = 1.3225 ==> 32.25%
Closest answer is A
Answer: A
Question: Which of the following is a prime number ?
Options:
A)33
B)81
C)97
D)93
E)none
Rationale: Clearly, 97 is a prime number
Answer: C
Question: The average of first seven prime numbers which are between 30 and 70 is
Options:
A)35.4
B)42
C)44.4
D)57
E)67
Rationale: Explanation :
first seven prime numbers which are between 30 and 70 = 31, 37, 41, 43, 47, 53, 59
average = (31 + 37 +41 + 43 + 47 + 53 + 59)/7
= 44.4
Answer : C
Answer: C
Question: Mark has to visit towns B and C in any order. The roads connecting these towns with his house are shown on the diagram. How many different routes can he take starting from A and returning to A, going through both B and C and not traveling any road twice on the same trip?
Options:
A)5
B)8
C)9
D)10
E)12
Rationale: Mark can travel clockwise or anticlockwise on the diagram.
Clockwise, he has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise she has four different routes.
Total routes = 8
B
Answer: B
Question: When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 26 names, the roster for her marketing class (M) had 26, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?
Options:
A)30
B)34
C)48
D)46
E)50
Rationale: Total # of students 26+26+18-(9+7+10)+4=48.
Answer: C.
Answer: C
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
Options:
A)106%
B)200%
C)100%
D)170%
E)104%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer: C
Answer: C
Question: If n and y are positive integers and 450y = n^3, which of the following must be an interger
I. y/ (3 * 2^2 * 5)
II. y/ (3^2 * 2 * 5)
III. y/ 3 * 2 * 5^2
Options:
A)None.
B)I only.
C)II only.
D)III only.
E)I, II, and III
Rationale: 450 y = n^3 -> y = n3/450 -> n3 is divisible by 450 & n is +ve integer. look for values of n^3 such that n is integer and n is divisible by 450. Clearly we have to look in the order of 1000's to find a value such that n3 is divisible by 450 and n is integer.
n3=1000 n =10 not divisible by 450
n3=8000 n =20 not divisible by 450
n3=27000 n =30 divisible by 450 y = 2700/45 = 60
Look for I, II , III which have denominators 60,90,150.
only I does and hence B
Answer: B
Question: The ratio of three numbers is 3:4:5 and the sum of their squares is 1250. The sum of the numbers is:
Options:
A)30
B)50
C)60
D)70
E)80
Rationale: Let the numbers be 3x, 4x and 5x
Then, 9x2+16x2+25x2=1250
50x2=1250
X=5
Sum of numbers= 3x+4x+5x=12x=60
ANSWER C 60
Answer: C
Question: A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 2 letters in its codes, and all letters can be repeated in any one code?
Options:
A)A.702
B)B.16226
C)C.17576
D)D.18278
E)E.28572
Rationale: The no of ways in which the company can make codes of 1 letter : 26
# for 2 letters : 26*26 = 676
The total : By adding all of them , 676+26= 702
A.
Answer: A
Question: A bike covers a certain distance at the speed of 81km/h in 7 hrs. If the bike was to cover the same distance in approximately 9 hrs, at what approximate speed should the bike travel?
Options:
A)80 km/h
B)67 km/h
C)90.14 km/h
D)63 km/h
E)92 km/h
Rationale: Ans.(D)
Sol. Total distance = 81 × 7 = 567 km
Now speed = 567/9 = 63 km/h
Answer: D
Question: There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 21 possible combinations in which Jim and Ellen are not selected, what is the value of k?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: There are k-2 members in the band, and k-4 members without Jim and Ellen.
(k-4)C2 = 21
(k-4)(k-5)/2 = 21
(k-4)(k-5) = 42 = 7*6
k = 11
The answer is D.
Answer: D
Question: A number when divided by 6 leaves a remainder 3. When the square of the same number is divided by 6, the remainder is:
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Let x=6q+3. Then, x2= (6q+3)2= 36q2+36q+9= 6(6q2+6q+1)+3.
So, when 2n is divided by 4, remainder =3.
Answer: D
Answer: D
Question: When n is divided by 20, the remainder is 6. What is the remainder when n + 16 is divided by 5?
Options:
A)1
B)3
C)4
D)5
E)6
Rationale: Assume n = 14
Remainder (n/20) = 6
n+16 = 36
Remainder (36/5) = 1
Option A
Answer: A
Question: Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 4 inches long, how wide is Jordan's rectangle, in inches?
Options:
A)25
B)23
C)32
D)30
E)18
Rationale: Area of Carol's rectangle = 24*5 = 120
Let width of Jordan's rectangle= w
Since , the areas are equal
4w = 120
=>w = 30
Answer D
Answer: D
Question: A man can row 3.6 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?
Options:
A)1.9
B)1.7
C)1.2
D)1.5
E)1.1
Rationale: Speed of boat in still water (b) = 3.6 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.2 km/hr.
Answer: C
Answer: C
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Options:
A)50
B)76
C)27
D)26
E)54
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer:A
Answer: A
Question: Ayesha's father was 58 years of age when she was born while her mother was 42 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)6
B)40
C)50
D)10
E)20
Rationale: Mother's age when Ayesha's brother was born = 42 years.
Father's age when Ayesha's brother was born = (58 + 4) years = 62 years.
Required difference = (62 - 42) years = 20 years.
Answer:E
Answer: E
Question: The average score of 35 students in a class is 37. If every student is given 3 grace marks, the new average of the class is:
Options:
A)33
B)21
C)38
D)40
E)92
Rationale: Explanation:
Average score = 37
Grace mark 3 is given to 35 student then its average will be 3.
Hence new average = 37 + 3 = 40
Answer: D
Answer: D
Question: The sector of a circle has radius of 21 cm and central angle 120o. Find its perimeter?
Options:
A)91.5 cm
B)11.5 cm
C)91.8 cm
D)86 cm
E)99.5 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (120/360 * 2 * 22/7 * 21) + 2(21)
=44 + 42
= 86 cm
Answer:D
Answer: D
Question: Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 60 envelopes
Options:
A)1 minute
B)5 minutes
C)7 minutes
D)3 minutes
E)4 minutes
Rationale: earl takes 1 min. for 36 envelopes.
ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envlpes a min.
so both of them when work together can stuff 36+24=60 envelopes in 1 min.
for 60 envelopes they will take 60/60 mins. i.e., 1 mins.
ANSWER:A
Answer: A
Question: How many times the keys of a writer have to be pressed in order to write first 200 counting no's?
Options:
A)452
B)462
C)472
D)482
E)492
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 200 = 101 * 3 = 303
-----------
492
E
Answer: E
Question: If x is a prime number, which of the following cannot be an integer?
Options:
A)x/2
B)5x/3
C)3x/7
D)15x/6
E)x/6
Rationale: x/2 can be an integer when x=2
5x/3 can be an integer when x=3
3x/7 can be an integer when x=7
15x/6==> 5x/2 can be an integer when x=2
x/6 can't be an integer==> when x=2, x/6=1/3 when x=3, x/6=1/2
ANSWER:E
Answer: E
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.
Options:
A)306.05
B)306.00
C)306.04
D)306.05
E)306.01
Rationale: A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
Answer: A
Answer: A
Question: The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ?
Options:
A)170
B)185
C)190
D)198
E)200
Rationale: 185
Answer is B
Answer: B
Question: A container contains 20 liters of milk, From this container 2 liters of milk was taken out and replaced by water. This process was repeated further 2 times. How much milk is now contained by the container?
Options:
A)14.58 liters
B)20.16 liters
C)22.45 liters
D)26.95 liters
E)31.45 liters
Rationale: Amount of milk left after 3 operations = 20 (1 - 2/20)^3 = 20 * 9/10 * 9/10 * 9/10 = 14.58 liters
Answer is A
Answer: A
Question: Calculate the percentage increase in the area of a rectangle, if each of its sides is increased by 10%?
Options:
A)20%
B)29%
C)27%
D)24%
E)21%
Rationale: Assume original length = 100m by 50m
original area = 100*50= 5000
10% increase on each side
l = 100 + 10 = 110
w = 50 + 5 = 55
new area = 110*55= 6050
increase in area = 6050 - 5000 = 1050
%increase =21%
Answer E
Answer: E
Question: Tough and Tricky questions: Arithmetic.
(8^2 + 8^2)/4^2 =
Options:
A)4
B)29
C)8
D)58
E)116
Rationale: Ans is 8
my approach was:
(8^2 + 8^2)/4^2 =8(8+8)/4*4
=8*16/4*4=2*4=8
C
Answer: C
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.6
B)10.9
C)10.4
D)10.8
E)10.1
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
Answer: D
Answer: D
Question: If -y^2= 2xy, then (x+y)^2 =
Options:
A)x^2
B)3x^2
C)4xy
D)2y^2
E)-y^2
Rationale: Its B
-y^2 = 2xy
0 = 2xy + y^2
Add x^2 on both sides we get
x^2 +0 = x^2 +y^2 +2xy
x^2 = (x+y)^2
Correct Option : A
Answer: A
Question: Lion, rat stay in jungle happily. Lion lies on: Mon, Tue, Wed. Rat lies on: Wed, Thurs , Sat. If lion says: I didn't lie yesterday. Rat says: I didn’t lie yesterday. So what day is today?
Options:
A)Tuesday
B)wednesday
C)Thursday
D)Friday
E)Sunday
Rationale: Tuesday -- lion ll tell lie on tuesday
lion is saying lie that he didn't lie sday [ again a lie... bcozzz lion ll say lie on monday also]
Tuesday -- Rat ll not say lie on tuesday
ANSWER:A
Answer: A
Question: 64 Ã— 64 Ã— 64 Ã— 64 x 64 =8 ^?
Options:
A)4
B)7
C)8
D)10
E)None of these
Rationale: 64 Ã— 64 Ã— 64 Ã— 64 x 64 = 8^?
or, 8(2) Ã— 8(2) Ã— 8(2) Ã— 8(2) x 8(2) = 8?
or 7(10) = 8? or, ? = 10
Answer D
Answer: D
Question: 337.62+5.628+33.4=?
Options:
A)376.648
B)112.6
C)258.69
D)5874.3
E)269.88
Rationale: 337.62
5.628
33.4
----------
376.648
Answer is A
Answer: A
Question: What is the least common multiple of 12,27 and 40
Options:
A)8521
B)1080
C)368
D)8979
E)6584
Rationale: factors of 12 =2*2*3
factors of 27= 3*3*3
factors of 40 =2*2*2*5
thus the l.c.m is 2^3*3^3*5=1080
the answer is B
Answer: B
Question: A right triangle STU has an area=30. If the longest side of the triangle is SU and value of ST=5. What are the lengths of sides TU and SU?
Options:
A)12, 13
B)5, 13
C)24, 26
D)12, 24
E)None of the above
Rationale: Area=30 and ST=5. By applying Area=STxTU, we get that TU=12, which is the first part of our answer.
By Pythagorean Theorem, we can now find the value of SU since we have value of ST and we found value of TU. So the correct answer is A.
Answer: A
Question: If one-third of one-fourth of a number is 20, then three-tenth of that number is:
A. 35
Options:
A)23
B)87
C)26
D)54
E)72
Rationale: Explanation:
The number is 1/3 of 1/4 is =15 then 1/3 Ã— 1/4 = 20
Number is 240 then 240 Ã— 3/10 = 72
Answer: E
Answer: E
Question: If two trains are 120 miles apart and are traveling toward each other at constant rate of 30 miles per hour and 40 miles per hour, respectively, how far apart will they be 1 hour before they meet?
Options:
A)10
B)30
C)40
D)50
E)70
Rationale: They would meet in 120/70 = 12/7 hours
1 hour earlier 5/7 hours
distance between trains = total distance -(distance covered by train A + distance covered by train B)
= 120-(5/7(40+30)) [ distance of A = 5/7* 40; like wise distance by B]
= 70 Km
ANSWER:E
Answer: E
Question: The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
Options:
A)2.54%
B)4.56%
C)6.125%
D)7.134%
E)8.341%
Rationale: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W
Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%
C
Answer: C
Question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
A)32
B)27
C)88
D)26
E)12
Rationale: S = (100 + 300)/45 = 400/45 * 18/5
= 32
Answer:A
Answer: A
Question: the difference between a positive fraction and its reciprocal is 9/20 find the sum of that fraction and its reciprocal.
Options:
A)41/20
B)17/20
C)11/20
D)9/20
E)None of these
Rationale: Explanation :
Let the fraction = x
Then x − (1/x) = 9/20
⇒ (x2 − 1)/x = 9/20
⇒ x2 − 1 = 9x/20
⇒ 20x2 − 20 = 9x
⇒ 20x2 − 9x − 20 = 0
x=−b±b2−4ac√2ax=−b±b2−4ac2a =9±(−9)2−4×20×(−20)√2×20=9±(−9)2−4×20×(−20)2×20 =9±81+1600√40=9±4140=5040Or−3240=9±81+160040=9±4140=5040Or−3240
Given that the fraction is positive. Hence
x = 50/40 = 5/4
1/x = 4/5
x + (1/x) = (5/4) + (4/5) = (5 × 5 + 4 × 4)/20 = 41/20. Answer : Option A
Answer: A
Question: Find the least number must be subtracted from 5264 so that remaining number is divisible by 17.
Options:
A)11
B)14
C)18
D)20
E)29
Rationale: When dividing 5264 by 17, we get the remainder 11, so 11 should be subtracted. The answer is A.
Answer: A
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is
Options:
A)0.5928
B)0.5904
C)0.5297
D)0.5297
E)0.5101
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36)
= 0.5904
Answer:B
Answer: B
Question: Find the greatest number which on dividing 6215 and 7373, leaves a reminder of 23 and 29 respectively
Options:
A)125
B)127
C)129
D)131
E)144
Rationale: Explanation:
In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (6215 - 23) and (7373 -29)
= HCF (6192, 7344) = 144
Option E
Answer: E
Question: The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son
Options:
A)6
B)7
C)9
D)2
E)5
Rationale: Let sons age = x years. Then fathers age = (45 - x)years.
(x—5)(45—x—5) = 4(45- x - 5) hence (x—5) = 4 so x = 9
Their ages are 36 years and 9 years.
Answer: C
Answer: C
Question: There are 20,6 and 9 rupees notes. you have to form 99 rupees with minimum number of notes.At what minimum number of notes you can achieve this?
Options:
A)9
B)8
C)7
D)6
E)5
Rationale: 20*3 = 60
6*2 = 12
9*2 = 18
9*1 = 9
9 notes
ANSWER:A
Answer: A
Question: It is known that no more than 6 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?
Options:
A)35
B)105
C)60
D)210
E)420
Rationale: The question states that there are no more than 6 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4, 5 or 6 children.
If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally.
similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally.
or if there were 210 cookies, and 4 children, cookies cannot be distributed equally.
Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 6).
And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5, 6), i.e., 60.
Answer (C)
Answer: C
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 18 more than n. What is y in terms of x ?
Options:
A)x+2
B)x-2
C)x+5
D)x+6
E)x+3
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 18 more than 10x+y
10x+y+18=10y+x
10x-x+18=10y-y
9x+18=9y
x+2=y
OR
y=x+2
Answer : A
Answer: A
Question: As a treat for her two crying children, a mother runs to the freezer in which she has two cherry ice pops, three orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
Options:
A)1/9
B)1/6
C)5/18
D)13/18
E)5/6
Rationale: Probability of not getting the same flavor ->
Favorable -> Cherry - orange [ 2C1 * 3C1 [or simply 2*3 ] or Cherry - lemon [ 2*4] or orange - lemon [3*4]
Prob = (2*3 + 2*4 + 3*4 ) / 9C2 = 26/36 = 13/18
Answer -> D
Answer: D
Question: In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the probability that he has offered English and Hindi?
Options:
A)2/10
B)1/10
C)3/10
D)2/5
E)3/5
Rationale: P(E)=30/100,
P(H)=20/100
P(E and H)=10/100
P(E or H)=3/10+2/10-1/10
=2/5
ANSWER D 2/5
Answer: D
Question: The length of a rectangular field is 7/5 its width. If the perimeter of the field is 336 meters, what is the width of the field?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: Let L be the length and W be the width. L = (7/5)W
Perimeter: 2L + 2W = 336, 2(7/5)W + 2W = 336
Solve the above equation to find: W = 70 m and L = 98 m.
correct answer C)70
Answer: C
Question: The average of 11 numbers is 10.8. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
Options:
A)71.5
B)11.5
C)81.5
D)11.5
E)12.6
Rationale: Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11] = 12.6.
Answer E
Answer: E
Question: f, b, c, and d are positive integers. If the remainder is 9 when f is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?
Options:
A) 20
B) 19
C) 18
D) 16
E) 15
Rationale: When f is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.
b + d cannot be 15, hence E is the answer.
Answer: E
Question: Of the teams competing in the world archery championships, sixty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
Options:
A)1/20
B)15/20
C)13/15
D)17/20
E)13/17
Rationale: Assume 100 total people.
60% of 100 = 60 --->Europeans
1/2 of 60 ---> 30 Americans
1/20 of 100 ---> 5 Africans
Now you would add them all up, and minus it by the total (100). 100 - 95= 5. So, 65 people out of 100 are not EU, US or Africans. 5/100 is also equal to 1/20.
So therefore, the answer is A.
Answer: A
Question: The population of a town is 8000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years?
Options:
A)5100
B)5120
C)5200
D)5400
E)6480
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
8000 Ã— 90/100 Ã— 90/100= 6480
Answer : E
Answer: E