divelab/Sys2Bench huggingface dataset:
Question: Among 250 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 60 watch exactly two channels. How many watch exactly one channel?
Options:
A)185
B)180
C)170
D)190
E)195
Rationale: 250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
250 = n(Exactly 1 channel) + 60 + n(Exactly 3 channels)
Let's find the value of n(Exactly 3 channels) = x
250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
250 = 116 + 127 + 107 - 60 - 2x
x = 25
250 = n(Exactly 1 channel) + 60 + 25
n(Exactly 1 channel) = 170
Answer (C)
Answer: C
Question: In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
Options:
A)32
B)36
C)38
D)40
E)50
Rationale: Assume that in x days, one cow will eat one bag of husk.
More cows, less days (Indirect proportion)
More bags, more days (direct proportion)
Hence we can write as
(cows)40:1
(bags)1:40
x:40
=40×1×40=1×40×x
=x=40
ANSWER : D
Answer: D
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Options:
A)Rs. 4991
B)Rs. 5991
C)Rs. 6001
D)Rs. 6991
E)Rs. 7991
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
ANSWER:A
Answer: A
Question: If the wages of 6 men for 15 days be Rs.2100, then find the wages of
for 12 days.
Options:
A)Rs. 2530
B)Rs. 2520
C)Rs. 2500
D)Rs. 1520
E)Rs. 3520
Rationale: Let the required wages be Rs. x.
More men, More wages	(Direct Proportion)
Less days, Less wages	(Direct Proportion)
Men 6: 9 : :2100:x
Days 15:12
Therefore (6x15 x x)=(9x12x2100) <=> x=(9x12x2100)/(6x15) =2520
Hence the required wages are Rs. 2520.
Answer is B.
Answer: B
Question: what is the smallest integer that is multiple of 5,7,11
Options:
A)A)70
B)B)35
C)C)385
D)D)280
E)E)140
Rationale: It is the lcm of 5, 7 and 11 which is 385.
The answer is C.
Answer: C
Question: A and B together can complete one-ninth of a job in a day. What is the difference between the maximum and minimum number of days A could take to complete the job alone, if A and B take whole number of days to complete the job alone?
Options:
A)45
B)B.60
C)C.80
D)D.90
E)be determined
Rationale: A and B together can complete one-ninth of a job in a day means that AB together does one whole work in 9 days.
1/A +1/B = 1/9
The minimum value A can take is 10 days (Anything less than 10 days is not possible because in other case, no of days taken by B will become negative, which is not possible practically)
When A takes least time (10Days) then B would take the Max time (90 days) to complete the work alone.
In order to find the Max time taken by A, find out the min time taken by B as we did earlier.
The minimum value B can take is 10 days (Anything less than 10days is not possible because in other case, no of days taken by A will become negative, which is not possible practically)
When B takes least time (10Days) then A would take the Max time (90 days) to complete the work alone.
So the required difference = Max Time taken-Min Time taken
= 90 - 10
=80 Days
Option C
Answer: C
Question: What is the rate percent when the simple interest on Rs.910 amount to Rs.260 in 4 Years?
Options:
A)7.14
B)6.14
C)5.14
D)3.14
E)2.14
Rationale: 260 = (910*4*R)/100
R = 7.14%
Answer: A
Answer: A
Question: Evaluate permutation
8P8
Options:
A)40290
B)40300
C)40310
D)40320
E)40330
Rationale: Explanation:
nPn=n!
8P8=8*7*6*5∗4∗3∗2∗1=40320
Option D
Answer: D
Question: 1. If the product of 6 integers is negative, at most how many of the integers can be negative?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: We're told that the product of 6 numbers is negative (the fact that they're integers is actually irrelevant). We're asked for the MAXIMUM number of those 6 that COULD be negative. We'll start with the largest and work our way down..
6 are negative: (-1)(-1)(-1)(-1)(-1)(-1) = + 1...which is NOT a negative product
5 are negative: (-1)(-1)(-1)(-1)(-1)(+1) = -1...which IS a negative product
D
Answer: D
Question: The ratio of the incomes of Rajan and Balan is 7:6 and the ratio of their expenditure is 6:5. If at the end of the year, each saves $1000 then the income of Rajan is?
Options:
A)$7600
B)$7000
C)$8000
D)$9000
E)$5000
Rationale: Let the income of Rajan and Balan be $7x and $6x
Let their expenditures be $6y and $5y
7x-6y = 1000-------1)
6x-5y = 1000-------2)
From 1) and 2)
x = 1000
Rajan's income = 7x = 7*1000 = $7000
Answer is B
Answer: B
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
Options:
A)1/3
B)2/3
C)2/5
D)2/9
E)3/7
Rationale: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C
Answer: C
Question: If a and b are integers and (a*b)^5 = 128y, y could be:
Options:
A)1
B)2
C)4
D)8
E)16
Rationale: Distribute the exponent.
a^5 * b^5 = 128 y
Find the prime factorization of 96. This is 2^5 *2^2.
We need 2^3 (or some other power of 2 that will give us a multiple of 2^5 as our second term).
2^3 = 8
The answer is D.
Answer: D
Question: A car rental company charges for mileage as follows: 10 dollars per mile for the first n miles and 11 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?
Options:
A)7d-n
B)5d-n
C)3*11d-n
D)11d-n
E)4d-n
Rationale: Total Distance in miles = d
Millage Charge = 10n + (d-n) 11
10n --> For the first n Miles
(d-n)11--> Total no of miles after traveling the first n miles is d-n and the rate after n miles is 11 .
If we solve the equation , We will get 11d-n
Answer : D
Answer: D
Question: On dividing a number by 357, we get 39 as remainder.On dividing the same number by 17, what will be the remainder ?
Options:
A)4
B)5
C)8
D)7
E)2
Rationale: Let x be the number and y be the quotient.Then,
x=357*y+39
=(17*21*y)+(17*2)+5
=17*(21y+2)+5.
Required number =5.
Answer is B
Answer: B
Question: The variables m and n are positive integers. When m is divided by 4, there is a remainder of 5, and when n is divided by 3, there is a remainder of 4. Which of the following are possible values of m + n?
I. 50
II. 70
III. 92
Options:
A)I only
B)III only
C)I and II
D)I​ and III
E)II and III
Rationale: m = 4k + 5 --> Values are 5, 9, 13, 17
n = 3k + 4 --> Values are 4, 7, 10, 13
I. 16 --> 9 + 7 --> Possible
II. 24 --> Not possible
III. 29 --> Not possible
Answer: A
Answer: A
Question: If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day?
Options:
A)100
B)102
C)104
D)106
E)108
Rationale: Using the chain rule,
M1 x T1 = M2 x T2
Thus, (34 x 8 x 9) / 2/5 = (M2 x 6 x 9) / 3/5
M2 = 68.
Therefore, required number of men = (68 + 34) = 102
ANSWER:B
Answer: B
Question: March 11, 2003 is a Tuesday. What will be the day on which march 11 2004 comes??
Options:
A)Thursday
B)Friday
C)Saturday
D)Sunday
E)Monday
Rationale: 2004 is a leap year that means 29 days in feb.
so march 11,2003 to march 11, 2004 will be 366 days.
366/7=52 weeks + 2 days. Hence Thursday
ANSWER:A
Answer: A
Question: Two electronic musical instruments were purchased for 8000. The first was sold at a profit of 40% and the second at loss of 40%. If the sale price was the same in both the cases, what was the cost price of two electronic musical instruments?
Options:
A)2000, 5000
B)2200, 5500
C)2400, 5000
D)2400, 5600
E)None of these
Rationale: Here, SP1 = SP2
⇒ 140 CP1 = 60CP2 ⇒ CP1/CP2=6/14=3/7
∴ CP1 = 3(3+7)×8000=24003(3+7)×8000=2400
and CP2 = 8000 – 2400 = 5600
Answer D
Answer: D
Question: What is the average of first 21 multiples of 7 ?
Options:
A)49
B)77
C)66
D)57
E)50
Rationale: Required average = 7(1+2+....+21) / 21
(7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 77
ANSWER IS B
Answer: B
Question: A recipe for a large batch of fruit juice at a factory calls for 10% oranges, 20% lemons, and 70% limes. if 200 lemons are used, how many limes are needed?
Options:
A)100
B)200
C)300
D)700
E)1400
Rationale: 20%= 200 fruit
100%=1000 fruit
70% of 1000 fruit=700 fruit
700 limes
ANSWER:D
Answer: D
Question: What is the compound interest paid on a sum of Rs.4500 for the period of 2 years at 10% per annum.
Options:
A)945
B)620
C)610
D)600
E)None of these
Rationale: Solution= Interest % for 1st year= 10
Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100=11
Total % of interest= 10 + 11=21
Total interest = 21 % 4500 = 4500* (21/100)= 945
Answer A
Answer: A
Question: Combine terms: 8a + 26b -4b – 16a.
Options:
A)4a + 22b
B)-28a + 30b
C)-8a + 22b
D)28a + 30b
E)5a + 30b
Rationale: Solution:
8a + 26b -4b – 16a.
= 8a – 16a + 26b – 4b.
= -8a + 22b.
Answer: (C)
Answer: C
Question: 8 cups of milk are to be poured into a 4-cup bottle and a 8-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 8-cup bottle?
Options:
A) 16/3
B) 7/3
C) 5/2
D) 4/3
E) 3
Rationale: Let x be the # of cups going into the 8 cup bottle.
so.... x/8 = ((8-x)/4)
64 - 8x = 4x
64 = 12x
x = 16/3.
Answer : A
Answer: A
Question: Which number should replace both the asterisks in (* /20) x (*/80) = 1 ?
Options:
A)20
B)40
C)60
D)80
E)120
Rationale: Let (y/20) x (y/80) = 1
y^2 = 20 x 80 = 20 x 20 x 4
y = (20 x 2) = 40
The answer is B.
Answer: B
Question: Mrs. Rodger got a weekly raise of $148. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Options:
A)$140
B)$141
C)$142
D)$148
E)$145
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 148.
So after completing the 1st week she will get $ (x+148).
Similarly after completing the 2nd week she will get $ (x + 148) + $ 148.
= $ (x + 148 + 148)
= $ (x + 296)
So in this way end of every week her salary will increase by $ 148.
correct answer D)$148
Answer: D
Question: In a class there are 20 boys and 24 girls. In how many ways can a boy and a girl be selected?
Options:
A)508
B)480
C)800
D)570
E)503
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 24 girls in 24 ways
We select a boy and girl in 20 * 24 ways i.e., = 480 ways.
Answer:B
Answer: B
Question: The average temperature in Lincoln in July is 85 degrees. Last
Wednesday, it was 90 degrees. Today it was 15 degrees cooler than
last Wednesday. What was the temperature today?
Options:
A)15 degrees
B)25 degrees
C)75 degrees
D)45 degrees
E)55 degrees
Rationale: The July temperature is extra information. 90 – 15 = 75
It was 75 degrees today.
correct answer C
Answer: C
Question: Boys and girls in a class are writing letters. There are twice as many girls as boys in the class, and each girl writes 3 more letters than each boy. If boys write 24 of the 90 total letters written by the class, how many letters does each boy write?
Options:
A)3
B)4
C)6
D)8
E)12
Rationale: There are twice as many girls as boys in the class --> g = 2b.
Each girl writes 3 more letters than each boy --> boys write x letters, girls write x+3 letters.
Boys write 24 letters --> bx = 24.
Girls write 90-24=66 letters --> (2b)(x+3) = 66 --> 2bx + 6b = 66 --> 2*24 + 6b = 66 --> b = 3.
bx = 24 --> 3x = 24 --> x = 8.
Answer: D.
Answer: D
Question: In how many different orders can the people Alice, benjamin Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, David, Charlene must be on the line before each of Frederick, Gale, and Harold?
Options:
A)2016
B)1,296
C)1,512
D)2,018
E)2,268
Rationale: Place B and E first: 8 options for B, 7 options for E.
We are left with 6 empty places. A, D and C must take first 3 places and F, G, H must take the remaining three. A, D and C can be arranged in their places in 3! ways. The same for F, G, and H.
Total = 8*7*3!*3! = 2,016.
Answer: A
Answer: A
Question: Deby normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Deby averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?
Options:
A)135
B)105
C)95
D)75
E)45
Rationale: Deby normally drives to work in 45 minutes at an average speed of 40 miles per hour.Use formula D = RT
Car:
T1: 45 min
R1: 40 mph
D1: [(40*45)/60] = 30 miles
Bike:
T1:?
R2: 12 - 16 mph
D2: 08*D1 = 24 miles
T1: [(24*60)/12] = 120 min (Only 12 mph speed yields an answer given in the choices)
Therefore, Deb has to leave 120 min - 45 min = 75 min early
ANSWER: D
Answer: D
Question: In a 100 m race, A runs at 8km per hour. If A gives B a start of 4 m and still him by 15 seconds, what is the speed of B ?
Options:
A)5.56 km/hr.
B)5.06 km/hr.
C)5.76 km/hr.
D)6.76 km/hr.
E)5.72 km/hr.
Rationale: Time taken by A to cover 100 m =(60 X 60 / 8000)	x 100 sec = 45 sec.
B covers (100 - 4) m = 96 m in (45 + 15) sec = 60 sec.
B's speed = (96 x 60 x 60)/(60 x 1000)km/hr = 5.76 km/hr.
Answer is C
Answer: C
Question: A boat running up stram takes 4 hours to cover a certain distance, while it takes 8 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?
Options:
A)2 : 3
B)5 : 6
C)4 : 5
D)3 : 1
E)8 : 1
Rationale: Explanation:
Let speed of boat is x km/h and speed stream is y km/hr
4(x+y) = 8(x-y)
4x+4y = 8x-8y
12y = 4x
3y = x
x/y = 3/1
3 : 1
Answer: Option D
Answer: D
Question: Jane received an assorted bouquet of 25 flowers which included 8 white flowers,7 lavender flowers and 9 purple flowers.
She closed her eyes a pulled one flower from the bouquet. She opened her eyes, noticed that it was white and placed it aside. She closed her eyes and pulled a 2nd flower from the bouquet. What is the probability that the 2nd flower will also be white?
Options:
A)8/25
B)7/24
C)7/25
D)8/25
E)9/15
Rationale: Solution: Initially, there are 25 flowers total. After the first white flower is removed, 7 white flowers remain and a total of 24 flowers overall are left in the bouquet.
Probability = Favorable outcomes / Total out comes
Therefore, probability = 7/24
Answer Option: B
Answer: B
Question: A man travelled from the village to the post-office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village
Options:
A)20
B)87
C)276
D)198
E)171
Rationale: Explanation:
Average speed = (2 ×a × b)/(a + b) here a = 25 b = 4
Average speed = 2 × 25 × 4/(25 + 4) = 200/29 kmph.
Distance covered in 5 hours 48 minutes = Speed × time
Distance = (200/29) × (29/5) = 40 kms
Distance covered in 5 hours 48 minutes = 40 kms
Distance of the post office from the village = (40/2) =20 km.
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)165
B)185
C)198
D)221
E)240
Rationale: 185
Answer is B
Answer: B
Question: Let R1 and R2 respectively denote the maximum and minimum possible remainders when (276)n is divided by 91 for any natural number n,n>= 144. Find R1+R2.
Options:
A)89
B)90
C)91
D)92
E)93
Rationale: But the least value for n can be= 144 (as given in question, n>=144)
So, 3n/91= 3*144/91= 68
now, the highest remainder can be when it reaches 68+3+3+3+3+3+3+3= 89
(as each time we increment n by 1 the remainder increases by 3,
3*145/91= 71- remiander
3*146/91= 74
3*147/91=77
... so on and so far upto 89 after which it becomes 89+3= 92 which means it crosses 91)
Hence least remainder would be 92 -91=1
and highest remainder = 89
R1+ R2= 89+1 = 90
ANSWER:B
Answer: B
Question: Set A contains all the even numbers between 12 and 60 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
Options:
A)850
B)1250
C)1650
D)2050
E)2450
Rationale: Each term in set B is 50 more than the corresponding term in set A.
The difference of the sums = 25 * 50 = 1250.
The answer is B.
Answer: B
Question: The average (arithmetic mean) of four different positive integers is 10. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?
Options:
A)5
B)4
C)3
D)2
E)0
Rationale: Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 = 10
=> 5x + 2 + a = 40
=> 5x + a = 40
=> a = 40 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=8
This gives us a= 40 - 40 = 0
Therefore the minimum value that the fourth integer can have is 0. Option E.
Answer: E
Question: 38, 85, 22,75, 31,47, 13, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above?
Options:
A)a- 56
B)b- 68
C)c- 69
D)d- 71
E)e- 78.5
Rationale: Important:- Arrange the numbers in ascending order first.
13, 22, 31, 38, 47, 75, 82, 85
3/4th of the number list represents- 75 (6th number)
remaining 1/4th list represents 82 (7 th number)
78.5 fits in between above 2
Answer:- E
Answer: E
Question: Here is a simple arithmetical puzzle in his own flowery, poetical language.
If one-fifth of a hive of bees flew to the badamba flower, one-third flew to the slandbara, three times the difference of these two numbers flew to an arbour, and one bee continued to fly about, attracted on each side by the fragrant Ketaki and Malati, what was the total number of bees?
Options:
A)11
B)15
C)18
D)17
E)19
Rationale: B
15
The number of bees was 15
Answer: B
Question: Machine A and machine R are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine R. Machine R produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
Options:
A)6
B)6.6
C)60
D)100
E)110
Rationale: [Reveal]Spoiler:
TimeR: 660/x
TimeA: [660/x+10]
660/x = [660/x+10] *110/100
660/x =66*11/x+10
660x+10= 66*11*x
660x +6600 = 66*11*x
x= 100
plug in back to timeA
660/100+10 => 660/110 = 6
Answer: A
Question: How many positive even integers less than 100 contain digits 3 or 9?
Options:
A)16
B)17
C)18
D)19
E)10
Rationale: Two digit numbers:
3 at tens place: 30,32,34,36,38
9 at tens place: 90,92,94,96,98
If 3 and 7 is at units place, the number cant be even
Total:5+5= 10
Answer E
Answer: E
Question: For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 2| + |-b| + |b – a| + |ab| =
Options:
A)-ab + 3
B)ab + 2b + 2
C)ab + 2b – 2a – 3
D)-ab + 2b + 3
E)ab + 3
Rationale: Observation-1: |a – b| = b – a
which is possible only when signs of a and b are Same
Since Given a > 0
so we figure out that a and b are both positive
Observation-2: |a – b| must be Non-Negative and so should be the value of b-a which is possible only when absolute value of b is greater than or equal to absolute value of a
Now you may choose the values of a and b based on above observations
e.g. b = 2 and a=1 and check the value of given functions and options
|a + 2| + |-b| + |b – a| + |ab| = |1 + 2| + |-2| + |2 – 1| + |1*2| = 8
-ab + 3 = -1*2+3=1
ab + 2b + 2= 1*2+4+2=8
ab + 2b – 2a – 3=1*2+2*2-2*1-3=1
-ab + 2b + 3=5
ab + 3=5
Answer : B
Answer: B
Question: Rathi took a loan for 6 years at the rate of 5% per annum on Simple Interest, If the total interest paid was Rs. 1230, Find the principal amount?
Options:
A)4000
B)3500
C)3100
D)4100
E)5000
Rationale: P = SI * 100/R*T
P = 1230*100/6*5==>4100
ANSWER D
Answer: D
Question: Winson will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
Options:
A)5
B)6
C)9
D)24
E)26
Rationale: Winson will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A
Answer: A
Question: Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?
Options:
A)130
B)140
C)150
D)220
E)280
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 550
But x = 150% of y = 150y/100 = 15y/10
∴15y/10 + y = 550
⇒ y[15/10 + 1] = 550
⇒ 25y/10 = 550
⇒ 25y = 5500
⇒ y = 5500/25 =Rs.220
D)
Answer: D
Question: A military garrison in a wild frontier has 600 men who have provisions to last 22 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?
Options:
A)13 1/3
B)12 1/3
C)10 2/3
D)12 1/2
E)12 3/4
Rationale: Total provisions=600*22*7=92400
Provisions used for in 6 weeks=6*7*600=25200
remaining provisions=67200
remaining provisions need to be split between 900(600+300) people.
Number of provisions per person= 67200/900
we need to find the answer in terms of weeks=(67200/900)/7=10 2/3
Answer:C
Answer: C
Question: I sold a book at a profit of 10%. Had I sold it for $110 more, 15% would have been gained. Find the cost price?
Options:
A)$2000
B)$2200
C)$3000
D)$3120
E)$1540
Rationale: 115% of cost - 110% of cost = $110
5% of cost = $110
cost = 110*100/5 = $2200
Answer is B
Answer: B
Question: eleven books,consisting of 5 engineering books , 4 maths books,2 physics books are arranged in a shelf at random .what is the probability that books of each kind are all together?
Options:
A)0.001443
B)0.002443
C)0.003443
D)0.004443
E)0.005443
Rationale: 3 lots can be arranged in 5!x3!x4!x2!
total arrangements possible= 11!
hence probability of the same=(5!x3!x4!x2!)/11!=0.001443
ANSWER:A
Answer: A
Question: If x > 6 and y < -6, then which of the following must be true ?
Options:
A)x/y > 1
B)x/y < -1
C)x/y < 0
D)x + y > 0
E)xy > 0
Rationale: Pick x=3, y = -3
A) x/y > 1 - Incorrect as x/y = -1
B) x/y < -1 - Incorrect as x/y = -1
C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0
D) x + y > 0 - Incorrect. x + y = 0
E) xy > 0 - Incorrect. XY = -9 which is less than zero.
D should be the answer.
Answer: D
Question: If the probability of rain on any given day in City X is 50%, what is probability that it rains on exactly 3 days in a 4 day period?
Options:
A)1/2
B)1/4
C)1/8
D)1/16
E)3/16
Rationale: One possible way is rain-rain-rain-no rain.
The probability of this is 1/2*1/2*1/2*1/2 = 1/16
The number of possible ways is 4C3 = 4, so we multiply this by 4.
P(rain on exactly 3 days) = 4*1/16 = 4/16 = 1/4
The answer is B.
Answer: B