divelab/Sys2Bench huggingface dataset:
Question: An archer is shooting arrows from various distances. She shoots at a target from 50 yards, 60 yards, and 70 yards. The probability that she hits within the bullseye from 50 yards is 3/4, the probability that she hits within the bullseye from 60 yards is 2/3, and the probability that she hits within the bullseye from 70 yards is 3/5. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
Options:
A)9/10
B)14/15
C)19/20
D)29/30
E)39/40
Rationale: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses every shot = (prob that she misses from 50 yards)*(prob that she misses from 60 yards)*(prob that she misses from 70 yards)
Prob that she misses from 50 yards = 1 - 3/4 = 1/4; Prob that she misses from 60 yards = 1 - 2/3 = 1/3; Prob that she misses from 70 yards = 1 - 3/5 = 2/5
Thus the probability that she misses all shots = (1/4)*(1/3)*(2/5) = 1/30
Thus the probability that she makes at least one shot = 1 - (1/30) = 29/30
D
Answer: D
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Options:
A)2/25
B)7/14
C)9/3
D)1/45
E)18/35
Rationale: Explanation:
If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
E
Answer: E
Question: There are 10 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 10 points that contain the point A?
Options:
A)36
B)105
C)182
D)210
E)455
Rationale: Any 2 points out 9 points will create triangle with third point A, so the answer is 9C2=36.
Answer: A.
Answer: A
Question: Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?
Options:
A)11/P + 6
B)11/P + 7
C)11/P + 2
D)11/P + 1
E)11/P + 8
Rationale: Let Ben’s age now be B
Anita’s age now is A.
(A - 6) = P(B - 6)
But A is 17 and therefore 11 = P(B - 6)
11/P = B-6
(11/P) + 6 = B
Answer: A
Answer: A
Question: If I walk at 4 km/h, I miss the bus by 10 minutes. If I walk at 5 km/h, I reach 5 minutes before the arrival of the bus. How far I walk to reach the bus stand ?
Options:
A)5 km
B)4.5 km
C)5 1⁄4 km/h
D)Cannot be determined
E)None of these
Rationale: d = product of speed difference of time /difference of speed
d = 4×5/60[10−(−5)/5−4]
[Here, –ve sign indicates before the schedule time]
⇒ d = 5 km
Answer A
Answer: A
Question: If Yury has been writing programming code for 16 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?
Options:
A)126(10^2)
B)126(10^3)
C)144(10^2)
D)1.26(10^7)
E).126(10^9)
Rationale: 5 LINES IN 20 SECONDS
SO FOR 1 MINUTE ( 5 X 3 = 15 LINES )
I HOUR = 60 MINUTES
15 X 60 = 900 LINES IN AN HOUR
16 HOURS = 900 X 16 = 144(10^2)
ANSWER C
Answer: C
Question: In your classes you counted 130 hands. How many students were at the class?
Options:
A)65
B)61
C)85
D)86
E)88
Rationale: Total number of hands = 130
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 130 by 2
130 ÷ 2 = 65
Therefore, there were 65 students at the class.
ANSWER IS A
Answer: A
Question: In how many ways can you sit 7 people on a bench if 3 of them must sit together?
Options:
A)720
B)2,160
C)2,400
D)4,320
E)40,320
Rationale: In such questions, always tie the person that have to sit together. So we have effectively 4+1=5 persons to arrange.
They can be arranged in 5! ways.
Now the 3 persons can themselves be arranged in 3! ways.
Total ways: 5!*3! = 720.
A is the answer.
Answer: A
Question: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability E that the 2 apples selected will include the spoiled one?
Options:
A)a. 1/5
B)b. 3/10
C)c. 2/5
D)d. 1/2
E)e. 3/5
Rationale: there can be two ways in which one can select a spoiled apple and a good apple.
1. you pick the spoiled one first and the good one later..
Prob of picking bad one = 1/5 (one bad apple)
Prob of picking a good one from the remaining 4 good apples (4/4 =1)
therefore the total prob for case 1 = i/5 * 1 = 1/5
Total prob E= porb1 + prob2 = 1/5+1/5 = 2/5.C
Answer: C
Question: The side of a square is increased by 25% then how much % does its area increases?
Options:
A)56.28
B)56.25
C)56.2
D)56.24
E)56.21
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 % Answer:B
Answer: B
Question: Find the total no. of distinct bike no.'s that can beformed using 2 letters followed by 2 no.'s. How many letters need to be distinct?
Options:
A)59
B)89
C)94
D)100
E)110
Rationale: Out of 26 alphabets two distinct letters can be chosen in \inline {\color{Black}26P_2{}} ways. Coming to numbers part, there are 10 ways.(any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10ways to choose the second digit. Hence there are totally 10X10 = 100 ways.
Combined with letters there are \inline {\color{Black}6P_2{}} X 100 ways = 65000 ways to choose vehicle numbers.
D
Answer: D
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Options:
A)2/28
B)2/25
C)2/21
D)2/08
E)2/18
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = 3C2/15C2 = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = 2C2/15C2 = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (3C1 * 2C1)/15C2 = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Answer: C
Question: Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?
Options:
A)3
B)5
C)6
D)8
E)9
Rationale: Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
1/x + 1/(x + 6) = 1/4
x2 - 2x - 24 = 0
(x - 6)(x + 4) = 0 => x = 6.
Answer: C
Answer: C
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
Options:
A)1
B)3
C)5
D)6
E)8
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Answer: A
Question: power windows: 60%
anti-lock brakes: 25%
CD player: 60%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes?
Options:
A)23
B)18
C)11
D)3
E)0
Rationale: Answer:A
Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.
If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 60%, we can set up the following equation:
60=15+22+x
x=23, choiceA.
Answer: A
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 6 km in stationary water
Options:
A)40 min
B)1hr
C)1hr 15 min
D)1hr 30 min
E)4 hr
Rationale: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(6/4)=1 1/4=1hr 30 min
Answer(D)
Answer: D
Question: The average age of 15 students of a class is 16 years. Out of these, the average age of 6 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?
Options:
A)10years
B)11years
C)12years
D)13years
E)14years
Rationale: Age of the 15th student
=[15 * 16 - (14 * 6 + 16 * 9)]
= (240 - 228) = 12 years.
Answer:C
Answer: C
Question: If p is the product of the integers from 1 to 35, inclusive, what is the greatest integer k for which 3^k is a factor of p?
Options:
A)11
B)13
C)15
D)17
E)19
Rationale: 35! has 3, 6, 9,....30, 33 as factors, which are 11 multiples of 3.
We need to add 4 more to these 11 because of 9, 18, and 27.
The greatest integer of k is 15.
The answer is C.
Answer: C
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
Options:
A)22 1/8 kmph
B)24 3/2 kmph
C)22 1/2 kmph
D)22 1/5 kmph
E)22 9/2 kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 1/2 kmph
Answer:C
Answer: C
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Options:
A)2 kmph
B)2 kmph
C)8 kmph
D)9 kmph
E)1 kmph
Rationale: Explanation:
S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: Option C
Answer: C
Question: A pipe can fill a cistern in 55 minutes. Find the time in which 1/11 part of the cistern will be filled?
Options:
A)5min
B)2min
C)3min
D)1min
E)10min
Rationale: Full cistern filled in = 55 minutes
1/11 part filled in = 55*1/11 = 5minutes
Answer is A
Answer: A
Question: Ravi, Ramu and Raja are three partners in business. If Ravi’s capital is equal to twice Ramu’s capital and Ramu’s capital is three times Raja’s capital, the ratio of the capitals of Ravi, Ramu, Raja is
Options:
A)2:1:3
B)1:2:6
C)6:3:1
D)1:3:6
E)None of these
Rationale: Explanation:
Let Raja’s capital be Rs. X. Then,
Ramu’s capital = Rs 3x and A’s capital = Rs. 6x
Ravi : Ramu : Raja = 6x : 3x : x = 6 : 3 : 1
Answer: Option C
Answer: C
Question: A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 3 games?
Options:
A)x + 3y/(n + 3)
B)x + y/(n + 3)
C)(x + 3y)/(n + 3)
D)(nx + 3y)/(n + 3)
E)(3x + ny)/(n + 3)
Rationale: Total points in first n games = nx
Total marks in next 3 games is 3y
So, Average marks in n + 3 games = (nx+3y)/(n+3)
Hence, correct answer will be (D)
Answer: D
Question: How should a profit of Rs.500 be divided into two partners, if one of them invested Rs.6000 for 5 months and other invested Rs.5000 for 4 months? (in Rs.)
Options:
A)1000,5000
B)3000,2000
C)500,400
D)2000,3000
E)300,200
Rationale: ratio come as 3:2, pofit become as 300,200.
ANSWER:E
Answer: E
Question: In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit 7?
Options:
A)180
B)196
C)286
D)324
E)288
Rationale: We have to find the total number of 3-digit odd numbers not having 7 as a digit.
Units digits will be among 1,3,5,9
Tenth digits will be among 0,1,2,3,4,6,5,8,9
Hundredth digits will be among 1,2,3,4,6,5,8,9
So total numbers = 4*9*8 =288
Answer : E
Answer: E
Question: There are two decks of 11 cards each. The cards in each deck are labeled with integers from 11 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?
Options:
A)0.23
B)0.36
C)0.4
D)0.42
E)0.46
Rationale: If 6 is a multiple, we need 2 and 3 as a factor of the number. If we factor the numbers 11 through 20 we have:
11 = 11
12 = 2*2*3
13 = 13
14 = 7*2
15 = 5*3
16 = 2*2*2
17 = 17
18 = 3*2*3
19 = 19
20 = 5*2*2
Combos that have a 2 and a 3 as factors (first + second card):
12 + anything - 19 of these possibilities (we count 12 + 12 only once)
14 + 15 - 2 of these possibilities
15 + 16 - 2 of these possibilities
15 + 20 - 2 of these possibilities
18 + anything (except 12, since that is counted in our first option) - 17 of these possibilities
Total possibilities that will be a multiple of 6: 42
Total possibilites: 10*10=100
Probability = 42/100 = 0.46
Answer:E
Answer: E
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
Options:
A)729
B)362
C)154
D)653
E)234
Rationale: The first ring can be worn in any of the 3 fingers (3 ways).
Similarly each of the remaining 5 rings also can be worn in 3 ways.
Hence total number of ways
=3×3×3×3×3×3=36=729
Ans: A
Answer: A
Question: Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 22,the first number is :
Options:
A)22
B)21
C)77
D)99
E)25
Rationale: Explanation:
Let the numbers be a,b,c,d
Given, a + b + c = 48, b + c + d = 45
Now, d = 22
thus, b + c + 22 = 45 ⇒ b + c = 23
Putting the value of b + c in a + b + c = 48
a + 23 = 48 ⇒ a = 25
Answer: E
Answer: E
Question: 25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
Options:
A)625
B)600
C)576
D)676
E)700
Rationale: we can go in any bus out of the 25 buses.
Hence He can go in 25 ways.
Since we can not come back in the same bus that he used for travelling,
we can return in 24 ways.
Total number of ways = 25 x 24 = 600
ANSWER:B
Answer: B
Question: if m^3 has 16 factors then m^4 will have how many factors ????? and m is not a prime no.
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: 25 m^3 = (3+1)(3+1) = 16
then m^4 = (4+1)(4+1)=25
ANSWER:B
Answer: B
Question: The area of a triangle is with base 3m and height 6m?
Options:
A)88 m2
B)9 m2
C)66 m2
D)77 m2
E)31 m2
Rationale: 1/2 * 3 * 6 = 9 m2
Answer: B
Answer: B
Question: Find the number of zero's in the expression 1^1 * 2^2 * 3^3 * 4^4 * 5^5 * ……..10^10.
Options:
A)28
B)15
C)16
D)17
E)81
Rationale: To find the number of zero's we have to find the powers of 2's and 5's.
Powers of 2's = 2 + 4 + 6 + 8 + 10 = 26
But 4, 8 contains more 2's which are equal to 4 + 8 = 12
8 contains another eight 2's.
So total 2's = 46
Number of 5's = 5 + 10 = 15
So trailing zeroes = 15.
Answer:B
Answer: B
Question: If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?
Options:
A)1/12
B)1/15
C)1/19
D)1/13
E)1/11
Rationale: X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
Answer: A
Answer: A
Question: How many words can be formed by using all the letters of the word “DAUGHTER” so that vowels always come together & vowels are never together?
Options:
A)5120
B)1240
C)4320
D)6512
E)1204
Rationale: Given word contains 8 different letters
When the vowels AUE are always together we may suppose
them to form an entity ,treated as one letter
then the letter to be arranged are DAHTR(AUE)
these 6 letters can be arranged in 6p6 = 6!
= 720 ways
The vowels in the group (AUE) may be arranged in 3! = 6 ways
Required number of words = 760 * 6 =4320
Ans: C
Answer: C
Question: 5 men or 8 women do equal amount of work in a day. a job requires 3 men and 5 women to finish the job in 10 days how many woman are required to finish the job in 14 days.
Options:
A)10
B)7
C)6
D)12
E)13
Rationale: 1 man can do the work of 8/5 = 1.6 women
equivalent of 3*1.6 + 5 = 9.8 women take 10 days
so women needed to do the work in 14 days
= [10/14]*9.8
= 7
ANSWER:B
Answer: B
Question: A meeting has to be conducted with 6 managers. Find the number of ways in which the managers be selected from among 10 managers, if 2 managers will not attend the meeting together?
Options:
A)120
B)110
C)105
D)140
E)135
Rationale: we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together
so 8C6 + (8C5 * 2C1)
this is 28 + 112=140
Answer : D
Answer: D
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
Options:
A)22
B)28
C)27
D)36
E)88
Rationale: (9*12)/3 = 36
Answer:D
Answer: D
Question: 5000 voted in an election between two candidates.14% of the votes were invalid.The winner won by a margin approximately closer to 15%.Find the number of votes secured by the person
Options:
A)2128
B)2472
C)2689
D)26707
E)17191
Rationale: nvalid Votes = 14 % (5000) = 700
Valid Votes = 5000 - 700 = 4300 = R (say)
Assume the looser got 'L" votes and winner got "W" votes.
W - L = 15% (R)
W + L = R
Solving we get W = 57.5% and L = 42.5%
So Winner got 57.5%(4300) = 2472
Answer:B
Answer: B
Question: A store reduced the price of all items in the store by 10% on the first day and by another 14% on the second day. The price of items on the second day was what percent of the price before the first reduction took place?
Options:
A)80.0
B)80.9
C)77.4
D)81.1
E)81.9
Rationale: consider price of the all items as $100
after a initial reduction of 10% price becomes = 0.9 *100 = $ 90
after the final reduction of 14% price becomes = 0.86* 90 = $ 77.4
price of all items on second day is 77.4% of price on first day
correct answer option C
Answer: C
Question: A contractor undertook to do a certain piece of work in 6 days. He employed certain number of men, but 5 of them being absent from the very first day, the rest could finish the work in 10 days. The number of men originally employed were :
Options:
A)12
B)10
C)13
D)11
E)None of these
Rationale: Explanation :
Let there be x men at the beginning. Less men, More days (Indirect Proportion)
12 : 6 :: x : (x - 5) 12 (x - 5) = 6x <=> 6x = 60 x = 10
Answer : B
Answer: B
Question: Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 3 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?
Options:
A)4 minutes
B)32/7 minutes
C)192/7 minutes
D)224/7 minutes
E)32/5 minutes
Rationale: Pipe A can fill a tank in 32 minutes --> the rate of A = 1/32 tank/minute;
Pipe B can fill the same tank3 times fasterthan pipe A --> the rate of B = 1/32 + 3/32 = 4/32 tank/minute.
Their combined rate = 1/32 + 4/32 = 5/32tank/minute;
Therefore, A and B can fill the tank in 32/5minutes.
Answer: E
Answer: E
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 70%?
Options:
A)6
B)5
C)8
D)9
E)10
Rationale: We need on-time departure rate to be higher than 7/10, so it should be at least 8/11, which means that 8 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 8-3=5 subsequent flights need to depart on-time.
Answer: B
Answer: B
Question: If 2x+y = 10, 2y+z = 20 and 2x+z = 30. Where x, y,and z are real number. What is the value of 2x ?
Options:
A)3/2
B)sqrt(15)
C)sqrt(6)/2
D)15
E)18
Rationale: Explanation :
Let, 2x = a, 2y = b and 2z = c
Then from the question:
2x+y = 2x * 2y = ab = 10
Similarly, bc = 20 , ac = 30
ab/bc = 1/2
=> a/c = 1/2
and ac = 30
(a/c)*ac = 1/2*30 = 15
a = sqrt(15)
Answer : B
Answer: B
Question: The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 4. If p is any prime number then f(p)=
Options:
A)p-1
B)p-2
C)(p+1)/2
D)(p-1)/2
E)2
Rationale: The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.
Answer: C.
Answer: C
Question: A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $3 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
Options:
A)$28
B)$82
C)$110
D)$138
E)$193
Rationale: by the question, the equation would be 150 p - 83*150 - 16500 = 0
p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.
solving the equation, we get p = $ 193. Answer E for me.
Answer: E
Question: At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 42 liters of forest green to change it to Verdant green?
Options:
A)14
B)12
C)15
D)11
E)10
Rationale: 42 liter of Forset green have 24 liter of blue and 18 liter of yellow
Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is
Blue/yellow =24/(18+x) = ¾
54+3x=96 => x =14
Answer : A
Answer: A
Question: Insert the missing number
1, 2, 4, 8, 16, 32, 64, ..., 256
Options:
A)128
B)148
C)154
D)164
E)174
Rationale: The sequence is just like multiples of 2..
i.e., 1 = 1
1 * 2 = 2
2 * 2 = 4
4 * 2 = 8
8 * 2 = 16
8 * 2 = 32
32 * 2 = 64
64 * 2 = 128
128*2 = 256
ANSWER:A
Answer: A
Question: The slant height of a conical mountian is 2.5 km and the area of its base is 1.54 km². The height of the mountain is:
Options:
A)2.4 km
B)2.6 km
C)4.5 km
D)5.4 km
E)None
Rationale: Sol.
Let the radius of the base be r km. Then,
∏r² = 1.54 ⇒ r² = [1.54 * 7 / 22] = 0.49 ⇒ r = 0.7 km.
Now, l = 2.5 km, r = 0.7 km.
∴ h = √(2.5)² = (0.7)² km = √6.25 - 0.49 km
= √5.76 km = 2.4 km
Answer A
Answer: A
Question: Which one of the given numbers is completely divisible by 45?
Options:
A)202860
B)165642
C)112330
D)112333
E)None of these
Rationale: We know that 45 = 9 × 5 where 9 and 5 are co-prime numbers. Also 9 and 5 are
factors of 45. Hence
if a number is divisible by 5 and 9, the number will be divisible by their product 45 also.
If a number is not divisible by 5 or 9, it is not divisible by 45
You must learn Divisibility Rules to say whether a given number is divisible by another number
Answer is A
without actually performing the division. Please go through divisibility rules before proceeding
further.
112330 is divisible by 5 but not divisible by 9 => 112330 is not divisible by 45
202860 is divisible by 5 and 9 => 202860 is divisible by 45
165642 is not divisible by 5 and 9 => 165642 is not divisible by 45
Answer: A
Question: In a dairy farm, 16 cows eat 16 bags of husk in 16 days. In how many days one cow will eat one bag of husk?
Options:
A)16
B)40
C)20
D)26
E)30
Rationale: Explanation :
One bag of husk = 16 cows per day
⇒ 16 × 1 × 16 = 1 × 16 × x
For one cow = 16 days
Answer : A
Answer: A
Question: Which of the following must be equal to zero for all real numbers x ?
I. −1x−1x
II. x + (-x)
III. x^0
Options:
A)I only
B)II only
C)I and III only
D)II and III only
E)I, II , and III
Rationale: I. -1/x will not be 0 for any real number; The value will be undefined if x is 0;
II. The value will be 0 for any real number. (ex.,) 2 + (-2) = 2-2 = 0;
III. x^0 = 1 for real numbers;
II only.
Ans is (B)
Answer: B
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 5 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
Options:
A)45
B)65
C)77
D)89
E)90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 5 = 73
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 73 + 4 = 77
C
Answer: C