RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability R that at least one will be orange?
A.R=7/10
B.R=3/5
C.R=2/5
D.R=3/10
Answer: A.R=7/10
Explanation: Method 1
Probability R that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10
Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10
Method 3
Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10
Answer :A
Question: Average monthly income of a family of 3 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?
A.Rs. 692.80
B.Rs. 905
C.Rs. 990
D.Rs. 1385
Answer: B.Rs. 905
Explanation: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 735 x 3 - 650 x 2 Rs.
= 905 Rs.
Correct Option: B
Question: In how many ways the word "RITUAL" can be arranged?
A.120
B.240
C.720
D.None
Answer: C.720
Explanation: Explanation :
The required number of ways = 6!
= 720
Answer : C
Question: 210 reputed college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
A.25
B.40
C.50
D.60
Answer: B.40
Explanation: We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.
So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.
Question: If |q|=−q, which of the following must be true?
A.q≥0
B.q≤0
C.q2>x
D.x3<0
Answer: B.q≤0
Explanation: |q| =-q means absolute value of q is equal to negative of q. Since absolute value cannot be negative hence negative of q should result in a non negative number. It means q is a non positive number i.e. q<0. Answer is B
Question: If a whole number n is divided by 4, we will get 3 as remainder. What will be the remainder if 2n is divided by 4 ?
A.4
B.3
C.2
D.1
Answer: C.2
Explanation: Explanation:
Let n ÷ 4 = p , remainder = 3
=> n = 4p + 3
2n = 2(4p + 3)
= 8p + 6
= 8p + 4 + 2
= 4(2p + 1) + 2
Hence, if 2n is divided by 4, we will get 2 as remainder.
Answer: C
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?
A.27 sec
B.87 sec
C.67 sec
D.47 sec
Answer: A.27 sec
Explanation: Explanation:
Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300x 18 / 40 x 5 = 27 seconds.
Answer: A
Question: How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number.
A.648
B.720
C.890
D.980
Answer: A.648
Explanation: Explanation :
Since, there is no repetition, numbers 1 to 6 will always be present in the 6 digit number.
We will go through this step by step.
Divisible by 1 and 1 at the unit place:
_ _ _ _ _ 1
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 2 and 2 at the unit place:
_ _ _ _ _ 2
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 3 and 3 at the unit place:
_ _ _ _ _ 3
Since, any number will have all the digits from 1 to 6 and the sum 1 + 2 + 3 + 4 + 5 + 6 = 21 is divisible by 3
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 4 and 4 at the unit place:
_ _ _ _ _ 4
Here, there are two cases
_ _ _ _ 2 4
This gives 4 x 3 x 2 x 1 = 24 numbers.
_ _ _ _ 6 4
This gives 4 x 3 x 2 x 1 = 24 numbers.
This gives us total of 24 + 24 = 48 numbers.
Divisible by 5 and 5 at the unit place:
_ _ _ _ _ 5
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 6 and 6 at the unit place:
_ _ _ _ _ 6
As all 6 digit numbers formed with 1 to 6 digits(without repetition) are divisible by 3 and numbers with 6 at the unit place are even.
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
None of these cases will have numbers overlapping with each other.
So, Total numbers = 120 + 120 + 120 + 48 + 120 + 120 = 648
Answer : A
Question: One year ago, Priya was four times as old as her daughter Sneha. Six years hence, Priya’s age will exeed her daughter’s age by 9 years. The ratio of the present ages of Priya and her daughter is :
A.9 : 2
B.11 : 3
C.12 : 5
D.13 : 4
Answer: D.13 : 4
Explanation: Let the ages of Priya and Sneha 1 year ago be 4x and x years respectively.
Then, [(4x + 1) + 6] - [(x + 1) + 6] = 9
3x = 9
x = 3
Required ratio = (4x + 1) : (x + 1) = 13 : 4
ANSWER:D
Question: A car averages 35 miles per hour for the first 4 hours of a trip and averages 44 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 38 miles per hour, how many hours long is the trip?
A.6
B.8
C.10
D.12
Answer: A.6
Explanation: Let T be the total time of the trip.
35*4 + 44(T-4) = 38T
6T = 176-140
T = 6
The answer is A.
Question: A store sells a certain product at a fixed price per unit. At the product's current price, v units cost a total of exactly $300. If the price were lowered by $5 from its current value, then v + 2n units would cost exactly $300; if the price were raised by $5, then v – n units would cost exactly $300. What is the value of v?
A.10
B.15
C.20
D.25
Answer: C.20
Explanation: It got too complicated when I used algebra. Using plugging in, it was quite fast.
Price Quantity total value
p v pv = 300
p-5 v+2n (p-5)(v+2n) = 300
p+5 v-n (p+5)(v-n) = 300
Solving three equations for three unknowns. Tough!!
Plugging in, I always start with C. C was the answer here, so saved calculation!
Putting values in above equations:
Price Quantity total value
15 20 300
10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5
20 15 300
So v = 20 satisfies all equations!!
Question: It would take one machine 9 hours to complete a large production order and another machine 8 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
A.72/17
B.17/72
C.14/24
D.24/56
Answer: A.72/17
Explanation: The rate of the first machine is 1/9 job per hour;
The rate of the second machine is 1/8 job per hour;
Thus, the combined rate of the machines is 1/9+1/8=17/72 job per hour, which means that it takes 1/(17/72)=72/17 hours both machines to do the job.
Answer: A.
Question: find the average of first 20 multiples of 7?
A.73.5
B.70.5
C.63.5
D.54.5
Answer: A.73.5
Explanation: Required average =7(1+2+3+…….+20)/20
(7*20*21)/(20*2)
(147/2)=73.5.
ANSWER A 73.5
Question: Out of 8 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
A.7/8
B.9/10
C.11/12
D.13/14
Answer: D.13/14
Explanation: P(no graduates) = 4C3 / 8C3 = 4/56 = 1/14
P(at least one graduate) = 1- 1/14 = 13/14
The answer is D.
Question: John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.51 more than Jane, what was the original price of the dish?
A. 24
B. 34
C. 37.8
D. 42
Answer: B. 34
Explanation: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.51--> 15p - 13.5p = 51 --> p = 34.
Answer: B.
Question: Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
A.y + 3z
B.(y +z) / 4
C.5y + 3z
D.3y + z
Answer: C.5y + 3z
Explanation: Soln:
The resulting equation is
=> (.01x + .05y + .03z)/(x+y+z) = 1.5/100
=> x + 5y + 3z = 1.5x + 1.5y + 1.5z
taking x to one side and y and z to other side we get
=> x = 5y + 3z
Ans is C
Question: If x is divisible by 3, 14, and 15, which of the following must be the least multiple of x?
A.308
B.210
C.200
D.120
Answer: B.210
Explanation: If x is divisible by 3, 14, and 15, then x must be a multiple of 3,14 and 5.
Hence,the least multiple of x will be 3*14*5=210.
ANSWER:B
Question: Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1450?
A.Rs.1000
B.Rs.1250
C.Rs.1010
D.Rs.10000
Answer: B.Rs.1250
Explanation: Explanation:
1450 = P [1 + (5*16/5)/100]
P= 1250
Answer: Option B
Question: How many different section of 4 books can be made from 10 different books if two particular books are always selected?
A.36
B.38/
C.26
D.28
Answer: D.28
Explanation: This means two books are seclected out of the remaining 8 books. Required number of ways = 8C2= 8!/6!x2!=28. Ans: D.
Question: 4 couples are seating at a round tables how many ways can the 4 women sit together
A.4!*4!
B.3!*4!
C.4!*3!
D.5!*4!
Answer: A.4!*4!
Explanation: 4 men can be arranged around a table in (4-1)!=3! ways;
Now, we can place 4 women in 4 slots between any two men and arrange these women in this slot in 4! ways.
So, total # of ways is 3!*4*4!=4!*4!
ANS:A
Question: 417 + 4.017 + 0.417 + 4.0017 = ?
A.425.4357
B.423.7563
C.629.6357
D.425.5637
Answer: A.425.4357
Explanation: 417
4.017
0.417
+ 4.0017
--------
425.4357
---------
Answer is A
Question: If the radius of a circle is increased by 60% then the area is increased by:
A.44%
B.120%
C.156%
D.40%
Answer: C.156%
Explanation: initially A=pi*r2
now R2=160/100r
then area=Pi*(160R/100)2
area=256R/100
that is area increases from 100 to 256=increase in area=156%
ANSWER:C
Question: A daughter lent $750 to her mother to help pay her rent. At the end of the month, the daughter received y dollars more than than the amount that was lent due to interest. The mother also gave her daughter an additional $5 for goodwill. In terms of y, what fraction of the total amount that the daughter received was the goodwill amount?
A.(5y-1)/(755-y)
B.5/(755+y)
C.5y/(755+y)-1
D.5y/(755+y)
Answer: B.5/(755+y)
Explanation: The amount of money the daughter received was (750 + 5+ y) dollars. The $5 goodwill gift as a fraction of the amount received was, therefore, 5/(755+y).
Answer: B.
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the
probability that it is neither blue nor green?
A.2/3
B.8/21
C.3/7
D.9/22
Answer: B.8/21
Explanation: Explanation:
Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: B
Question: From a pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king ?
A.1/212
B.1/223
C.1/221
D.2/213
Answer: C.1/221
Explanation: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
C
Question: When p is divided by 9, the remainder is 8. All of the following are possible values of p, except for which of the following?
A.17
B.35
C.53
D.61
Answer: D.61
Explanation: Four of these numbers can be expressed in the form of 9x+8, where x can be 0,1,2,3,4....
However, 61 = 9(6) + 7
The answer is D.
Question: A shop owner sells 30mtr of cloth and gains SP of 10 metres. Find the gain %?
A.30%
B.40%
C.50%
D.65%
Answer: C.50%
Explanation: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)
Selling price of 20 m cloth = Selling Price of 30 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000
Profit% = 10 × 100 = 50%
20
Profit of 50 % was made by the merchant.
C
Question: The difference between the circumference and the radius of a circle is 37 cm. The area of the circle is:
A.111 cm2
B.148cm2
C.154cm2
D.259cm2
Answer: C.154cm2
Explanation: 2πr-r=37 or (2π-1)r=37.
Or (2* 22/7 -1)r=37 or 37r/7=37 or r=7.
Therefore, Area= πr2= (22/7 *7*7)= 154 cm2
ANSWER:C
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
A.Rs.3919
B.Rs.3910
C.Rs.3997
D.Rs.3900
Answer: D.Rs.3900
Explanation: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer:D
Question: There are three prizes to be distributed among nine students. If no students gets more than one prize, then this can be done in?
A.10
B.45
C.5
D.84
Answer: D.84
Explanation: Explanation :
3 prize among 9 students can be distributed in 9C3 ways = 84 ways.
Answer : D
Question: What percentage of numbers from 1 to 70 have squares that end in the digit 1?
A.90%
B.28%
C.20%
D.23%
Answer: C.20%
Explanation: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such numbers = 14.
Required percentage = (14/70 * 100) =20%
Answer:C
Question: An ant walks an average of 1000 meters in 30 minutes. A beetle walks 10% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?
A.1.8
B.1.6
C.2.775.
D.1.9
Answer: A.1.8
Explanation: the ant walks an average of 1000 meters in 30 minutes
1000 meters in 1/2 hours
the beetle walks 10% less distance = 1000-10=900 meters in 30 minutes
0.900 km in 30/60 = 1/2 hours
speed = 0.900*2= 1.8 km/h
I guess option A should be 1.8
Question: A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days.If they get Rs 1500 for the whole work, the daily wages of B and C are?
A.225
B.276
C.126
D.187
Answer: A.225
Explanation: Explanation:
Let the total work = 30 units.
Then capacity of A = 3 units, B = 2 units. Now they worked for 5 days. So they must have completed 25 units. Rest of the work 5 units done by C in 2 days. So C capacity = 5/2 = 2.5 units.
Given that toatal wages are Rs.1500 for 30 units. So for 1 unit of work they get Rs.50. Now B and C per day work = (2 + 2.5) = 4.5 units. So their daily wages = 4.5 × 50 = Rs.225
Answer:A
Question: Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend?
A.$6.80
B.$8.40
C.$7.70
D.$4.70
Answer: A.$6.80
Explanation: Linda spent
1.20 ? 3 = $3.60 on notebooks
The total amount of money that Linda spent is equal to
3.60 + 1.50 + 1.70 = $6.80
correct answer A
Question: The present ages of three persons are in proportions 4:7:9.Thirteen years ago, the sum of their ages was 81. Find their present ages.
A.24, 42
B.28, 36
C.35, 45
D.35, 55
Answer: A.24, 42
Explanation: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 13) + (7x - 13) + (9x - 13) = 81
20x = 120 => x = 6
Their present ages are 24, 42 and 54 years respectively.
ANSWER:A
Question: 57+58=115. How many such 2 consecutive numbers are there less than 1500 when added gives a sum which is divisible by 5?
A.100
B.200
C.300
D.400
Answer: C.300
Explanation: since 2+3=5 & 7+8=15
any combination with these no be will give u desirable result...
so total no in 100 will be 20 & that's why in 1000,it will be 20X15=300.
ANSWER:C
Question: The average (arithmetic mean) monthly income of four workers is $1,000. After one worker’s income increases by 50 percent the new average income is $1,200. What was the original income of the worker whose monthly income increased?
A.$1,800
B.$1,500
C.$1,300
D.$1,600
Answer: D.$1,600
Explanation: Increase in total income was 200*4=$800, we know that this increase was 50% (1/2) of the workers original income, thus his/her original income was 800*2=$1,600.
Answer: D
Question: What is the largest 4 digit number exactly divisible by 35?
A.4676
B.4678
C.9975
D.9504
Answer: C.9975
Explanation: Largest 4 digit number = 9999
9999 ÷ 35 = 285, remainder = 24
Hence largest 4 digit number exactly divisible by 88
= 9999 - 24 = 9975
answer :C
Question: The sum of 3 consecutive numbers is definitely
A.Positive.
B.Divisible by 2.
C.Divisible by 4.
D.Divisible by 3.
Answer: D.Divisible by 3.
Explanation: If 1st term is x:
x+(x+1)+(x+2)=3x+3--->Always divisible by 3
If 2nd term is x:
(x-1)+x+(x+1)=3x--->Always divisible by 3
If 3rd term is x:
(x-2)+(x-1)+x=3x-3--->Always divisible by 3
Answer: D
Question: A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then
leaves. A alone can finish the remaining work in
A.5 days
B.6 days
C.7.5 days
D.8.5 days
Answer: C.7.5 days
Explanation: Explanation:
B's 5 days work =
110
∗
5=12Remaining work =1−12=12A can finish work =15
∗
12=7.5days
Answer: C
Question: The average of marks obtained by 120 boys was 39. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?
A.100
B.110
C.120
D.130
Answer: C.120
Explanation: Let the number of boys who passed = X.
Then, 39 x X + 15 x (120 - X) = 120 x 39
24X = 4680 - 1800
=> X = 2880/24
X = 120.
Hence, the number of boys passed = 120.
ANSWER:C
Question: If the numerator of a fraction T is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?
A.16 1⁄6%
B.25%
C.33 1⁄3%
D.50%
Answer: D.50%
Explanation: This question can be dealt with conceptually or by TESTing VALUES.
We're told that the numerator of a fraction T is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.
Let's TEST 2/1
If we triple the numerator and double the denominator, we end up with....
(2x3)/(1x2) = 6/2 = 3
Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50%
D
Question: At what rate percent on simple interest will Rs.750 amount to Rs.1125 in 5 years?
A.2
B.10
C.4
D.5
Answer: B.10
Explanation: 375 = (750*5*R)/100
R = 10%.Answer: B
Question: If 45% of a class averages 95% on a test, 50% of the class averages 78% on the test, and the remainder of the class averages 60% on the test, what is the overall class average? (Round final answer to the nearest percent).
A.83%
B.84%
C.85%
D.86%
Answer: C.85%
Explanation: This question is a Weighted Average question with a series of dependent variables.
The remaining portion of the class represents 100% - 45% - 50% = 5% of the class
Converting the portions of the class population to decimal weights, we find:
Class Average = 0.45x95 + 0.50x78 + 0.05x60 = 84.75
The class average (rounded) is 85%
Final Answer
C) 85%
Question: An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 2 ?
A.1/9
B.1/3
C.1/2
D.2/3
Answer: C.1/2
Explanation: n(n+2) to be divisible by 2 either n or n+2 must be a multiples of 2.
In each following group of numbers: {1, 2, 3, 4}, {5, 6, 7, 8}, ..., {97, 98, 99, 100} there are EXACTLY 2 numbers out of 4 satisfying the above condition. For example in {1, 2, 3, 4} n can be: 2, or 4. Thus, the overall probability is 2/4 =1/2.
Answer: C.
Question: The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides.
A.12, 9
B.18, 3
C.15.16, 6
D.12, 12.37
Answer: D.12, 12.37
Explanation: CM=3
AREA=PM*CM/2, thus PM=12
By Pythagorean Theorem, we can now find the value of PC.
D is the correct option.
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 34 cm?
A.680 sq.cm
B.268 sq.cm
C.618 sq.cm
D.297 sq.cm
Answer: A.680 sq.cm
Explanation: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225)
= √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus
= 1/2 * d1d2
= 1/2 * 40 * 34
= 680 sq.cm.
Answer:A
Question: In a dairy farm, 46 cows eat 46 bags of husk in 46 days. In how many days one cow will eat one bag of husk?
A.1
B.46
C.20
D.26
Answer: B.46
Explanation: Explanation :
One bag of husk = 46 cows per day
⇒ 46 × 1 × 46 = 1 × 46 × x
For one cow = 46 days
Answer : B
Question: A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 488. What is the sum of the last 8 of the even integers?
A.598
B.604
C.610
D.616
Answer: D.616
Explanation: The sum of the first 8 numbers is: x + (x+2) +...+ (x+14) = 488
The sum of the next 8 numbers is: (x+16) + (x+2+16) +...+ (x+14+16) =
488 + 8(16) = 488 + 128 = 616
The answer is D.
Question: During a given week A programer spends 1/4 of his time
preparing flow chart, 3/8 of his time coding and the rest of
the time in debugging the programs. If he works 48 hours
during the week , how many hours did he spend debugging the
program.
A.15 hours
B.16 hours
C.17 hours
D.18 hours
Answer: D.18 hours
Explanation: 1/4 of time for flow charts =48/4=12 hours
3/8 time for coding =48*3/8=18
so remaining time for debugging =48-12-18=18 hours
ANSWER:D
Question: Q. How many 6-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5?
A.180
B.240
C.210
D.270
Answer: A.180
Explanation: the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2
i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _
case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6
when the units digit is 2 i.e 1 _ _ _ _ _ 2
number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60
when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30
case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6)
number of ways this can be done would be 5! / (2!) for 2 =60
and 5! / 2! for 6 ... = 60
adding all of these ... gives the answer 180 ...
the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat
A
Question: In year Y imported machine tools accounted for 60 percent of total machine-tools sales in the United States, and Japanese imports accounted for 30 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
A.55x/9
B.50x/9
C.60x/9
D.65x/9
Answer: B.50x/9
Explanation: Sales of imported tools = 60% of the total sales = 0.60*{total} = 3{total}/5;
Sales of Japanese tools = 30% of the sales of imported tools = 3/10*3{total}/5 = 9{total}/50.
Since the sales of of Japanese tools was x, then 9{total}/50 = x -->9 {total} = 50x
{total} = 50x/9
Answer: B
Question: 5,9,17,29,49,__
A.79
B.80
C.81
D.82
Answer: D.82
Explanation: (9+5) +3 = 17
(16+9) +4 = 29
(28+16)+5 = 49
(48+28)+6 = 82
ANSWER:D