divelab/Sys2Bench huggingface dataset:
Question: The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 19 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
Options:
A)40.2
B)40.4
C)40.6
D)40.8
E)40.1
Rationale: Sum of 10 numbers = 402
Corrected sum of 10 numbers
= 402 – 13 + 31 – 19 = 401
Hence, new average = 401⁄10 = 40.1
Answer E
Answer: E
Question: A necklace is made by stringing N individual beads together in the repeating pattern white bead, green bead, red bead, yellow bead, and blue bead. If the necklace design begins with a white bead and ends with a red bead, then N could equal
Options:
A)65
B)68
C)55
D)45
E)35
Rationale: Recognize that we are going to have to look for an answer thats a multiple of 5, plus 3.
Mutliple of 5 because there are 5 beads in the pattern, and plus 3 because the bead ends on red, which is 3 into the pattern.
I just went through all the answer choices, and only E fits. 5x13 = 65, and 65+3=68
Answer : B
Answer: B
Question: Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is w, what is the difference between the probability that w is even and the probability that w is odd?
Options:
A) 1/9
B) 1/6
C) 2/9
D) 1/4
E) 1/2
Rationale: Age of Boys w:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11
Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14
9 Combinations of sum between sets(10,12,11)(13,17,14)
=23,27,24- 16,30,17- 24,28,25
Prob(Even)= 5/9
Prob(Odd) =4/9
Answer=5/9 - 4/9 = 1/9
Answer: A
Question: What is the place value of 4 in the numeral 4259
Options:
A)A)2700
B)B)4000
C)C)2900
D)D)2980
E)E)3000
Rationale: 4 * 1000 = 4000
B
Answer: B
Question: Two numbers are in the ratio of 3:4. If 12 be subtracted from each, they are in the ratio of 9:8. Find the numbers?
Options:
A)6,9
B)3,8
C)6,7
D)3,5
E)3,4
Rationale: (3x-12):(4X-12) = 9:8
x = 1 => 3,4
Answer: E
Answer: E
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)756
B)700
C)650
D)654
E)546
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.
ANSWER A 756
Answer: A
Question: A cave is going to explode. A family is trapped inside that cave. The only way to get outside is a narrow tunnel. But the tunnel is weak and thus only two people can go at one time. Also, everybody is afraid of going alone.
The father takes one minute to go through till the end, the mother takes two, the son takes four and the daughter takes five. The cave and tunnel will explode in twelve minutes. Can they make it to the other end in that time frame?
PS: Keep in mind that when two people are moving, the total time taken will be as per the slower one.
Options:
A)10 minutes.
B)12 minutes.
C)11 minutes.
D)13 minutes.
E)14 minutes.
Rationale: Solution:
12 minutes
Explanation:
Yes, surely they can all make it out of the cave.
First, father and mother will go. Time taken = 2 minutes.
Father comes back. Time taken = 2 + 1 = 3 minutes.
Both children go. Time taken = 3 + 5 = 8 minutes.
Mother comes back. Time taken = 8 + 2 = 10 minutes.
Mother and Father go. Time taken = 10 + 2 = 12 minutes.
Thus in 12 minutes, all of them will be out of the cave through the tunnel.
Answer B
Answer: B
Question: Find the value of (√1.1)/(√0.81) + (√1.44)/(√0.49) is
Options:
A)195/63
B)2.879
C)155/63
D)125/63
E)185/63
Rationale: (√1.1)/(√0.81) + (√1.44)/(√0.49)
=> 2.879
Answer is B
Answer: B
Question: Find the sum of prime numbers lying between 58 and 75?
Options:
A)198
B)331
C)252
D)272
E)None
Rationale: Solution
Required sum	=59 + 61 + 67 + 71 + 73)
= 331.
Answer B
Answer: B
Question: For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers R are there between #6 +2 and #6 +6 , inclusive?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: None is the answer. A.
Because for every k 6! + k :: k, because 6! :: k, since k is between 2 and 6.A
Answer: A
Question: A box measuring 24 inches long by 40 inches wide by 16 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
Options:
A)28
B)30
C)32
D)35
E)37
Rationale: least number of cubes will be required when the cubes that could fit in are biggest.
8 is the biggest number that could divide all three, 24, 40 and 16.
Thus side of cube must be 8, and total number of cubes = 24/8 * 40/8*16/8 = 30
Ans B
Answer: B
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 9 minutes 17 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
Options:
A)3%
B)5%
C)8%
D)10%
E)13%
Rationale: Bob's time = 640 secs.
His sis' time = 557 secs.
Percent increase needed = (640-557/640) * 100 = 83/640 * 100 = 13%. Ans (E).
Answer: E
Question: Ram, Raj started a business in partnership, which Ram invested Rs.8000/- for 1 year, Raj invested Rs.16000/- for 2 years.
At the end of the profit received by them is Rs.4000/-. What is Ram’s share?
Options:
A)Rs. 1200
B)Rs. 900
C)Rs. 1000
D)Rs. 800
E)Rs. 700
Rationale: Answer:	Solution: Ram : Raj = (8,000 * 1) : (16,000 * 2) = 1 : 4.
So Ram's share = Rs. (4000 * 1/5) = Rs. 800.
Answer: Option D
Answer: D
Question: If N = 2^0.15 and N^b = 1, b must equal
Options:
A)3/80
B)20/3
C)4
D)5/3
E)80/3
Rationale: 15/100 = 3/20
N = 2 ^ 3/20
N^b = 2^1
(2^3/20)^b = 2^1
b = 20/3
Answer: B
Answer: B
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
Options:
A)587 × 10^8 miles
B)587 × 10^10 miles
C)587 × 10^-10 miles
D)587 × 10^12 miles
E)587 × 10^-12 miles
Rationale: Solution:
The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 10^12 miles.
Answer: (D)
Answer: D
Question: What is the tens digit of 7^1033?
Options:
A)0
B)1
C)0
D)3
E)4
Rationale: 7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649
We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )
0 , 4 , 4 , 0 .
1033= 4*258 + 1
The ten's digit will be 0 .
Answer C
Answer: C
Question: A bag contains 10 red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability Q that all 3 jellybeans removed from the bag are blue?
Options:
A)9/100
B)2/19
C)1/8
D)3/20
E)3/10
Rationale: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability Q= 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 2/19
Answer: option B
Answer: B
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)4567
B)3435
C)5667
D)4567
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: If (x + 1) times (2x + 3) is an odd integer, then x must be:
Options:
A)an odd integer
B)an even integer
C)a prime number
D)a composite number
E)a negative integer
Rationale: Solution:
(x + 1) times (2x + 3) means (x + 1)(2x + 3)
(x + 1)(2x + 3) = 2x^2+5x+3
For 2x^2+5x+3 to be odd, 5x+3 must be odd since 2x^2 is always even.
So 5x must be even, hence x must be even.
Therefore x is an even integer.
Answer: B
Answer: B
Question: Water boils at 212°F or 100°C and ice melts at 32°F or 0°C . If the temperature of a pot of water is 55°C, what is the temperature of the pot of water in °F?
Options:
A)116°F
B)125°F
C)131°F
D)138°F
E)145°F
Rationale: Let F and C denote the temperature in Fahrenheit and Celsius respectively.
(F - 32) /(212 - 32) = (C - 0)/(100 - 0)
F = 9C/5 + 32
F = 9(55)/5 + 32 = 131°F
The answer is C.
Answer: C
Question: A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?
Options:
A)35
B)45
C)25
D)15
E)55
Rationale: A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=175×9/35=5×9=45
Answer is B.
Answer: B
Question: The sum of five numbers is 200. The average of the first two numbers is 20 and the third number is 50. Find the average of the two numbers?
Options:
A)50
B)55
C)60
D)65
E)70
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 200
(P + Q)/2 = 20 and R = 50
P + Q = 40 and R = 50
P + Q + R = 90
S + T = 200 - (P + Q + R) = 110
Average of the last two numbers
= (S + T)/2 = 55
Answer:B
Answer: B
Question: What approximate value should come in place of the question mark (?) in the following equation?
159% of 6531.8 + 5.5 × 1015.2 = ? + 5964.9
Options:
A)10,000
B)10,900
C)11,000
D)10,600
E)12,000
Rationale: ? ≈ 160% of 6530 + 5.5 × 1010 – 5965
≈ 10448 + 5555 – 5965 ≈ 10,000
Answer A
Answer: A
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)120 m
B)240 m
C)300 m
D)400 m
E)None of these
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
ANSWER:B
Answer: B
Question: One boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
Options:
A)A)4^30
B)B)2^30
C)C)1^30
D)D)3^30
E)E)6^30
Rationale: Each Mango can be given to any one of the four people or in other words..1 mango can be divided into 1 ways...so all 30 can be divided in 1^30 ways
ANS:C
Answer: C
Question: 1370 , 1320 , 1070 , -180, -6430, X
Options:
A)-37680
B)6530
C)6630
D)6730
E)6830
Rationale: 1370-50*(5^0)=1320
1320-50*(5^1)=1070
1070-50*(5^2)=-180
-180-50*(5^3)=-6430
-6430-50*(5^4)=-37680
ANSWER:A.
Answer: A
Question: A square is drawn inside a right-angled triangle with the two perpendicular sides as 12 cm and 8 cm. what is the side of the largest possible square that can be drawn?
Options:
A)4.8 cm
B)4.4 cm
C)4.9 cm
D)5.0 cm
E)6.0 cm
Rationale: Explanation :
Area of triangle is 1/2 * 12 * 8 = 48
Side of square = x
The entire triangle split into two right angled triangle and one square with dimensions as follows
i) square with side x
ii) Right angled triangle with perpendicular sides x and 12-x
iii) Right angled triangle with perpendicular sides 8-x and x
Sum of area of all three = 48
=> x2 + 1/2*x*(12-x) + 1/2*x*(8-x) = 48
=> x = 4.8 cm
Hence (A) is the correct answer.
Answer : A
Answer: A
Question: 7, 10.5, 15.75, 23.63, 35.43, (...)
Options:
A)52.112
B)53.156
C)54
D)89
E)88
Rationale: 7
(7Ã—3)Ã· 2 = 10.5
(10.5Ã—3)Ã· 2 = 15.75
(15.75Ã—3)Ã· 2 = 23.63
(23.63Ã—3)Ã· 2 = 35.43
(35.43Ã—3)Ã· 2 = 53.156
Answer is B
Answer: B
Question: If E is the product of all positive integers less than 31, than what is the greatest integer k for which E/18^k is an integer?
Options:
A)3
B)6
C)7
D)14
E)26
Rationale: 30!E must be divisible by (3*3*2)^k.
As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).
Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.
3 6 9*
12 15 18*
21 24 27**
30
The stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively.
3=3 (occurs 10 times) +10
3*3=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3)
3*3*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted)
Total: 14.
For every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result.
Answer: 7 -> Answer choice: C.
Answer: C
Question: A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 2 and 3 are not together ?
Options:
A) 48
B) 72
C) 36
D) 60
E) 120
Rationale: Reqd ways = (Total No. of ways - cases when both 2 and 3 are together)
5 numbers can be arranged in 5 places in 5! ways. Now tie 2 and 3 together so effectively there are 4 nos. they can be arranged in 4! ways. 1 and 2 can be arranged within themselves in 2!ways.
Reqd. Answer = 5! - 4!2! = 120 - (24*2) = 72
Answer: B
Answer: B
Question: A water tank is two-fifth full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely?
Options:
A)6 min.to empty
B)9 min.to empty
C)5 min.to empty
D)4 min.to empty
E)7 min.to empty
Rationale: Explanation:
Clearly,pipe B is faster than pipe A and so,the tank will be emptied.
part to be emptied = 2/5
part emptied by (A+B) in 1 minute=
so, the tank will be emptied in 6 min
Answer: A
Answer: A
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 4 men and 2 women will do that task.
Options:
A)5/7
B)3/10
C)5/18
D)5/16
E)5/11
Rationale: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
4 m + 2 w =10 w
Answer is 10/14 =5/7
Answer: A
Answer: A
Question: Jessica can text 85 words per minute, while Maurice can text 55 words per minute. An abridged English translation of Tolstoy’s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace?
Options:
A)0.3
B)1.9
C)3
D)9
E)11.3
Rationale: Since the answer choices are reasonably spaced out, we can approximate and save time
Combined words per day = 150*60*24 which should be 216000
410400/216000 will be 1.9,
So, Answer should be B
Answer: B
Question: A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1.What is the percent W of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?
Options:
A)9%
B)11%
C)15%
D)25%
E)90%
Rationale: Cost of 12 paper towels individually = 1*12=12
Cost of a set of 12 paper towels = 9
Cost of one roll = 9/12 = 3/4 = 0.75
Savings per roll = 1-.75 = 0.25
% of savings is W= .25/ 1 *100 = 25% D is the answer.
Answer: D
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)5/7
B)2/7
C)3/7
D)7/9
E)1/7
Rationale: =10/10+25
=10/35=2/7
ANSWER B
Answer: B
Question: The speed of a train is 70 kmph. What is the distance covered by it in 10 minutes?
Options:
A)10.66 kmph
B)11.66 kmph
C)21.66 kmph
D)12.66 kmph
E)11.96 kmph
Rationale: 70 * 10/60 = 11.66 kmph
ANSWER:B
Answer: B
Question: pipes P and Q would fill a cistern 18 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in 12 minutes?
Options:
A)after 12 mins
B)after 9 mins
C)after 8 1/2 mins
D)after 10 mins
E)after 15 mins
Rationale: Explanation:
x/18 + 12/24 = 1
x = 9
ANSWER IS B
Answer: B
Question: It takes 6 beavers 10 hours to build a certain dam, working at a uniform rate. If three beavers start to build the same dam at 8:00 AM, and one beaver per hour is added beginning at 6:00 PM, at what time will the dam be complete?
Options:
A)7:30 PM
B)8:00 PM
C)9:00 PM
D)10:00 PM
E)11:00 PM
Rationale: The rate of 1 beaver is 1/60.
The amount of work done by 3 beavers in 10 hours is 3/60 *10 = 30/60
In the next hour, 4 beavers do 4/60 for a total of 34/60.
In the next hour, 5 beavers do 5/60 for a total of 39/60.
In the next hour, 6 beavers do 6/60 for a total of 45/60.
In the next hour, 7 beavers do 7/60 for a total of 52/60.
In the next hour, 8 beavers do 8/60 for a total of 60/60.
The dam will be completed at 11:00 pm.
The answer is E.
Answer: E
Question: For a performance, a few dancers are arranged in a row. Nancy is standing in the middle of the row at the 6th position.
Can you find out the total number of girls in that row?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Since Nancy is the middle at 6th position, there should be 5 girls on both her sides.
5 + 5 = 10
Counting Nancy as well, the total number of girls in that row = 10 + 1 = 11
correct answer is D)11
Answer: D
Question: A train 250 m long passed a pole in 25 sec. How long will it take to pass a platform 700 m long?
Options:
A)28 sec
B)89 sec
C)95 sec
D)16 sec
E)15 sec
Rationale: Speed = 250/25 = 10 m/sec.
Required time = (250 + 700)/10
= 95 sec.
Answer:C
Answer: C
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)17%
B)62%
C)12%
D)8%
E)22%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:C
Answer: C
Question: In a classroom teacher has 20 boxes, they issues 8 boxes gifted to their students. Then how many boxes they had?
Options:
A)9
B)28
C)12
D)15
E)9
Rationale: 20-8=12. Answer is C
Answer: C
Question: Two quarts containing 5⁄6 water and 1/6 formula are mixed with three quarts containing 7⁄10 water and 2⁄10 formula. Approximately what percent of the combined five-quart mixture is water?
Options:
A)70.4%
B)72.4%
C)75%
D)73.4%
E)65.4%
Rationale: 5/6 of 2 quarts = 10/6 quarts of water
7/10of 3 quarts = 21/10 quarts of water
10/6 = 1.67
21/10 = 2.1
Total water = 1.67 + 2.1= 3.77
Total quarts = 5
3.77/5 = 75.4% approx. 75%
Answer : C
Answer: C
Question: The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 16 positive perfect squares?
Options:
A)1,010
B)1,164
C)1,240
D)1,316
E)1,496
Rationale: First we need to find the constant 'c'. The easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively.
Hence LHS = 1+4 and plug n=2 for RHS and simplify to get c = 1/2.
Plug values of n = 16 and c = 1/2 into the equation and simplify to get the answer 1496
Option E.
Answer: E
Question: What is the least value of x. So that 23x57 is divisible by 3.
Options:
A)2
B)0
C)1
D)3
E)4
Rationale: Explanation:
The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 7 = 17 + x
Least value of x may be 1
Therefore 17 + 1 = 18 is divisible by 3.
Answer: Option C
Answer: C
Question: Ana climbs up stairs 20 floors building and back. She takes the exact same route both ways. On the trip up she climbs an average speed of 2 steps per second. On the trip back she climbs down at an average speed of 4 steps per second. What is her approximate average speed for the round trip in miles per hour?
Options:
A)1
B)1.25
C)1.33
D)1.5
E)1.75
Rationale: Average speed = total distance/total time
Here number of steps to 20th floor and back is same as she takes the same route.
D = 2T1 and D=4T2
Therefore, T1 = D/2 and T2 = D/4
T1+T2 = 3D/4
Therefore, average speed = 2d/3d/4 =2d * 4/3d
Answer is 1.3 Since, the options are far away we need not solve till the decimal points
So correct answer is option C
Answer: C
Question: A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 6 hats randomly out of the drawer and returning each hat before taking out the next one?
Options:
A)3/8
B)1/4
C)5/8
D)5/16
E)7/16
Rationale: Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue-blue-blue.
The probability of this is 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64
There are 6C3 = 20 such cases so we need to multiply this by 20.
P(exactly 3 red hats) = 20*1/64 = 5/16
Note that when we get exactly 3 red hats, then we also get exactly 3 blue hats.
So we don't need to consider the case of exactly 3 blue hats separately.
The answer is D.
Answer: D
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 1 year ago?
Options:
A)152460
B)214560
C)168000
D)210000
E)200000
Rationale: population 2 years ago = 176400/(1 + 5/100)
Answer is C
Answer: C
Question: For any non-zero a and b that satisfy |ab| = -ab and |a| = -a, |b-4| + |ab-b| =
Options:
A)ab-4
B)2b-ab-4
C)ab+4
D)ab-2b+4
E)4-ab
Rationale: Given: |ab| = -ab and |a| = -a
Question: |b-4| + |ab-b| = ?
**** Looking at |ab| = -ab tells us that either one of a or b is negative.
**** Looking at |a| = -a tells us that a must be negative
**** Combine two observations: b is positive
Let a=-1 and b=1
|b-4| + |ab-b| = |1-4| + |-1-1| = 5
Test a) |ab-4| = |(1)(-1)-4| = |-5|=5
Test b) 2b-ab-4 = (2)(1) - (-1) - 4 = -1
Test c) ab+4 = -1 + 4 = 3
Test d) ab-2b+4 = -1-2(1)+4=1
test e) 4-1=3
ANSWER=A
Answer: A
Question: A train passes a 50 metres long platform in 14 seconds and a man standing on the platform in 10 seconds. The speed of the train is:
Options:
A)24 km/hr
B)36 km/hr
C)40 km/hr
D)45 km/hr
E)None of these
Rationale: Explanation:
Let the length of train be L m.
L/10 = (L+50)/14
14L= 10L+500
L= 125 m .
Speed = (25/2) m/s = (25/2) x 18/5= 45 Km/hr
Answer D
Answer: D
Question: A multiple choice test consists of 4 questions, and each question has 5 answer choices. In how many F ways can the test be completed if every question is unanswered?
Options:
A)24
B)120
C)625
D)720
E)1024
Rationale: 5 choices for each of the 4 questions, thus total F of 5*5*5*5 = 5^4 = 625 ways to answer all of them.
Answer: C.
Answer: C
Question: A grocer has a sale of Rs. 6400, Rs. 7000, Rs. 6800, Rs. 7200 and Rs. 6500 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. 4500
B)Rs. 4700
C)Rs. 4800
D)Rs. 5000
E)Rs. 5100
Rationale: Total sale for 5 months = Rs. (6400+ 7000 + 6800 + 7200 + 6500) = Rs. 33900
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 33900)
= Rs. 5100
ANSWER :E
Answer: E
Question: In a room there are 11 people. Each person shook hands with every other person. How many hand shakes were there?
Options:
A)52
B)53
C)54
D)55
E)56
Rationale: 11C2 = 55
The answer is D.
Answer: D
Question: What is the dividend. divisor 16, the quotient is 8 and the remainder is 4
Options:
A)127
B)128
C)130
D)131
E)132
Rationale: E = d * Q + R
E = 16 * 8 + 4
E = 128 + 4
E = 132
Answer: E
Question: How many total number of ways in which y distinct objects can be put into two different boxes is
Options:
A)n2
B)2y
C)2n
D)3n
E)None of these
Rationale: Let the two boxes be B1 and B2. There are two choices for each of the y objects. So, the total number of ways is
2 × 2 ×.....× 2 (y times ) = 2y
Answer B
Answer: B
Question: Find the number of ways in which 7 different beads can be arranged to form a necklace.
Options:
A)30
B)20
C)420
D)60
E)80
Rationale: Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,7 beads can be arranged to form a necklace in(7-1)! /2ways
= 6*5*4*3*2/2 = 420 ways
Answer is C
Answer: C