RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: David has d books, which is 3 times as many as Jeff and 2/3 as many as Paula. How many books do the three of them have altogether, in terms of d?
A. 5/6*d
B. 7/3*d
C. 17/2*d
D. 7/2*d
Answer: C. 17/2*d
Explanation: Although we could plug in a real value for d, the problem can be just as easily solved by setting up equations. However, let’s start by defining some variables. Since we are given that David has d books, we can use variable d to represent how many books David has.
number of books David has = d
number of books Jeff has = j
number of books Paula has = p
We are given that David has 3 times as many books as Jeff. We can now express this in an equation.
d = 3j
d/3 = j
We are also given that David has ½ as many books as Paula. We can also express this in an equation.
d = (2/3)p
3d/2 = p
Notice that we immediately solved forj in terms of d and p in terms of d. Getting j and p in terms of d is useful when setting up our final expression. We need to determine, in terms of d, the sum of the number of books for David, Jeff, and Paula. Thus, we have:
d + d/3 + 3d/2
=17d/2
The answer is C.
Question: A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?
A.6
B.8
C.12
D.15
Answer: A.6
Explanation: 4/10+9/X = 1/x = 15
1/10+1/15 = 1/6 = 6 days
ANSWER A
Question: A bat is bought for Rs.400 and sold at a gain of 20% find its selling price
A.Rs.480/-
B.Rs.500/-
C.Rs.520/-
D.Rs.540/-
Answer: A.Rs.480/-
Explanation: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
A
Question: If the number is divided by 3, it reduced by 34. The number is
A.51
B.50
C.45
D.40
Answer: A.51
Explanation: Explanation:
Let the number be x. Then,
x - (x/3) = 34 => 2x/3 = 34
=> x = 51
Answer: Option A
Question: As a treat for her two crying children, a mother runs to the freezer in which she has three cherry ice pops, three orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
A.1/9
B.1/6
C.5/18
D.11/120
Answer: D.11/120
Explanation: Probability of not getting the same flavor ->
Favorable -> Cherry - orange [ 3C1 * 3C1 [or simply 3*3 ] or Cherry - lemon [ 3*4] or orange - lemon [3*4]
Prob = (3*3 + 3*4 + 3*4 ) / 9C2 = 33/360 = 11/120
Answer -> D
Question: If 2^z is a factor of 30!, which of the following could be the value of z?
I. 23
II. 26
III. 24
A.I ONLY
B.II ONLY
C.BOTH I AND II
D.III ONLY
Answer: B.II ONLY
Explanation: 2^z is a factor of 30!, what values can z take.
Powers of 2 in 30! = [30/2] + [30/4] +[30/8] + [30/16] , where [x] is the integral part of x
Powers of 2 in 30! = 15 + 7 + 3 + 1 = 26
Hence the maximum value of 2^z in 30! = 2^26
Only Statement II satisfies
Correct Option: B
Question: If 4 (P's Capital) = 6 (Q's Capital) = 10 (R's Capital), then out of the total profit of Rs 4650, how much R will receive?
A.300
B.600
C.900
D.800
Answer: C.900
Explanation: Let P's capital be p,
Q's capital be q,
and R's capital be r
Then
4p=6q=10r2p=3q=5r⋯(A)
From (A),
q=2p/3 ⋯(1)
r=2p/5 ⋯(2)
p:q:r=p:2p/3:2p/5
=15:10:6
R's share =4650×6/31=150×6=900
Answer is C.
Question: How many four letter words are formed using the letters of the word ENTERTAINMENT?
A.1716
B.1616
C.1816
D.1516
Answer: A.1716
Explanation: The number of letters in the given word is thirteen.
The number of four letter words that can be formed using these thirteen letters is 13P4
= 13 * 12 * 11 = 1716.
Answer: A
Question: What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
A.Rs.64.18
B.Rs.64.67
C.Rs.64.08
D.Rs.64.10
Answer: D.Rs.64.10
Explanation: S.I. = (1000 * 10 * 4)/100 = Rs. 400
C.I. = [1000 * (1 + 10/100)4 - 1000]
= Rs. 464.10 Difference
= (464.10 - 400)
= Rs. 64.10
Answer: D
Question: In a certain animal shelter, the ratio of the number of catsto the number of dogs is 15 to 7. If 16 additional dogs were to be taken in by the shelter, the ratio of the number of cats to the number of dogs would be 15 to 11. How many cats are in the shelter?
A.15
B.25
C.30
D.45
Answer: D.45
Explanation: This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...
We're told that the ratio of the number of cats to the number of dogs is 15:7. We're then told that 16 more dogs are added to this group and the ratio becomes 15:11. We're asked for the number of cats.
Algebraically, since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7, we can write this initial relationship as...
15X/7X
When we add the 16 cats and factor in the 'ending ratio', we have an equation....
15X/(7X+16) = 15/11
Here we have 1 variable and 1 equation, so we can solve for X....
(15X)(11) = (7X+16)(15)
(X)(11) = (7X+16)(1)
11X = 7X + 16
4X = 16
X = 4
With this X, we can figure out the initial number of dogs and cats...
Initial dogs = 15X = 15(4) = 60
Final Answer: D
Question: The compound interest earned on a sum for the second and the third years are $1400 and $1498 respectively. What is the rate of interest?
A.3%
B.5%
C.7%
D.9%
Answer: C.7%
Explanation: 1498 - 1400 = 98 is the rate of interest on $1400 for one year.
The rate of interest = (100 * 98) / (1400) = 7%
The answer is C.
Question: Ashok secured average of 78 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
A.66
B.74
C.78
D.98
Answer: D.98
Explanation: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 78
Therefore total marks in 6 subjects = 78 * 6 = 468
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 468 – 370 = 98
ANSWER D
Question: Six bells start ringing together and ring at intervals of 4, 8, 10, 12, 15 and 20 seconds respectively. How many times will they ring together in 60 minutes ?
A.5
B.11
C.21
D.31
Answer: D.31
Explanation: LCM of 4, 8, 10, 12, 15 and 20 = 120 seconds = 2 minutes
That means All the six bells will ring together in every 2 minutes
Number of times they will ring together in 60 minutes =1+60/2=31
Answer :D
Question: y = 248 - 390x
Which of the following values of x gives the greatest value of y in the equation above?
A. 200
B. 100
C. 0.5
D. -2
Answer: D. -2
Explanation: Clearly, the negative value of x will result in maximum value of y.
Answer is D
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
A.1/42
B.3/41
C.9/42
D.5/44
Answer: C.9/42
Explanation: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
A.6
B.4
C.8
D.2
Answer: B.4
Explanation: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9
= 4
Answer: B
Question: A, Band C are three contestants in a kmrace. If A can give B a start of 40 m and A can give C a start of 64m how many metre's start can B give C ?.
A.540 m
B.178 m
C.936 m
D.234 m
Answer: C.936 m
Explanation: While A covers 1000 m, B covers (1000 - 40) m = 960 m and
C covers (1000 - 64) m or 936 m.
When B covers 960 m, C covers 936 m
Option C
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is
A.100
B.120
C.130
D.150
Answer: D.150
Explanation: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: Option D
Question: A man, a woman and a boy can complete a job in 3,4 and 12 days respectively.
How many boys must assist 1 man and 1 woman to complete the job in ¼ of a day?
A.41
B.50
C.22
D.33
Answer: A.41
Explanation: (1 man + 1 woman)'s 1 days work = 1/3+1/4=7/12
Work done by 1 man and 1 women n 1/4 day=((7/12)*(1/4))=7/48
Remaining work= 1- 7/48= 41/48
Work done by 1 boy in ¼ day= ((1/12)*(1/4)) =1/48
Therefore, Number of boys required= ((41/48)*48)= 41 days
ANSWER A
Question: Once upon a time in ancient times there was a king who was very found of wines. He had a huge cellar, which had 1000 different varieties of wine all in different caskets (1000 caskets in all). In the adjoining kingdom there was a queen who was envious of the king’s huge wine collection. After some time when she could not bear it any more show conspired to kill her by poisoning all his wine caskets. So she sent one sentry to poison all the caskets, but no sooner had the sentry poisoned only one wine casket, he was caught and killed by the Royal guards. Now the king had a major problem in his hand so as to identify the poisonous casket, which he gave to the Minister. But the situation had two peculiarities.
I: Any one who takes even one drop from the poisonous casket will die.
II: He will die only after one month.
The king also handed over few prisoners to the Minister as “taster” of those caskets, as their lives was of little value.
If the Minister is allowed only 1 month to find out the poisonous casket, what is the minimum number of prisoners he should use as “tasters”?
A.1023
B.1024
C.1025
D.1026
Answer: B.1024
Explanation: Sol:
Study the following table carefully. Each of the prisoners drinks wine from whichever casket has a 1 in his place. If he does not drink there is a 0.
So if no one dies, Casket 1 is poisoned.
If P1 dies, casket 2 is poisoned.
If P1 and P3 die ⇒⇒ casket 6 is poisoned and so on.
So, if there are 3 prisoners, we can differentiate upto 2323 =8 caskets.
So for 1000 caskets [even 1024 caskets], we need only 10 prisoners as 210210 = 1024
Answer B
Question: Three numbers are in the ratio 3:5:7. The largest number is 21. What is the difference between smallest and largest number?
A.8
B.10
C.12
D.14
Answer: C.12
Explanation: The three numbers are 3x, 5x, and 7x.
The largest number is 21 = 7*3, so x = 3.
The smallest number is 3*3 = 9.
21 - 9 = 12
The answer is C.
Question: Shipment ------No. of Defective Chips/shipment---Total Chips in shipment
S2 -------------- 5 ------------------------ ----------------------12000
S3 -------------- 6 ----------------------------------------------- 18000
S4 -------------- 4 ----------------------------------------------- 16000
A computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts S1,S2,S3 and S4 comined as shown in the table above. What is the expected number T of defective chips in a shipment of 60000 chips?
A.14
B.20
C.22
D.24
Answer: B.20
Explanation: I agree with your solution = 20. But the question is:
There are different combination to get 60,000 chips. For example: 1*S3 + 2*S4 + 2*S2. In this way, we ship 60,000 chips with only 6 + 4*2 + 2*2 = 18 defective chips, better than the average of 20.
The question is to find the expected number T of defective chips, i guess it assume the minimum #, therefore it might not be 20.
Question: The number of new words that can be formed by rearranging the letters of the word 'UP' is ?
A.1
B.2
C.24
D.520
Answer: A.1
Explanation: Number of words which can be formed = 2! - 1
= 2 - 1
= 1.
Answer:A
Question: Mercy's income is 10 percent more than Timothy's income, and Timothy's income is 22 percent less than Ryan's income. What percent of Ryan's income is Mary's income?
A.81.5%
B.85.5%
C.82.5%
D.84.5%
Answer: B.85.5%
Explanation: Ryan's income = 100 (assume);
Timothy's income = 78 (22 percent less than Ryan's income);
Mercy's income = 85.5 (60 percent more than Timothy's income).
Thus, Mercy's income (85.5) is 85.5% of Ryan's income (100).
Answer: B
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in metres) is:
A.400
B.525
C.750
D.850
Answer: C.750
Explanation: Sol.
Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x metres.
Then, 2x/60 = 25 ⇔ x = 25 * 60 / 2 = 750
Answer C
Question: 16 men can do a piece of work in 16 days .4 days after they started the work, 8 more men joined them. How many days will they now take to complete the remaining work
A.7 days
B.8 days
C.9 days
D.10 days
Answer: B.8 days
Explanation: Solution:Work done by 1 man in 1 day=1/(16*16)
Work completed by 16 men in 4 days= 4[1/(16*16)]*16=1/4
Remaining work= 1- 1/4= 3/4
Total men now= 16+ 8=24
24 men do 3/4 work
=>24*number of days*Work done by 1 man in 1 day=3/4
=>24*number of days* 1/(16*16)=3/4
=>number of days=8 days
Answer B
Question: A rectangular box measures internally 1.6 m long, 1 m broad and 60 cm deep. The number of cubical blocks each of edge 20 cm that can be packed inside the box is
A.30
B.60
C.120
D.150
Answer: C.120
Explanation: Sol. Number of blocks =
160x100x60
20x20x20] = 120.
Answer C
Question: The present average age of a family of five members is 24 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)
A.27.5 years
B.17 years
C.17.5 years
D.16.5 years
Answer: C.17.5 years
Explanation: Present total age of the members = 24(5) = 120 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 120 -10 = 110 years
Their average age at the time of the birth of the youngest member = [110 - (4 * 10)] / 4 = 17.5 years
ANSWER:C
Question: In a partnership between A, B and C. A's capital is Rs.5500. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
A.23676
B.19766
C.29172
D.12925
Answer: D.12925
Explanation: Explanation:
200 + 130 = 330
800 - 330 = 470
200 ---- 5500
470 ---- ? => 12925
Answer:D
Question: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Seven years ago Jim was 13 times as old as Sam. How old is Jim now?
A.8
B.12
C.16
D.20
Answer: D.20
Explanation: We're asked how old Jim is NOW. We're given three facts to work with:
1) Today, Jim is TWICE as old as Fred
2) Today, Sam is 2 years younger than Fred
3) 7 years ago, Jim was 13 times as old as Sam.
let's TEST Answer D: 20
IF....Jim is currently 20 years old....
Fred is 10 years old
Sam is 8 years old
7 years ago, Jim was 13 and Sam was 1, so Jim WAS 13 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.
D
Question: In how many different ways can the letters B, E, N, E, F, I, C, I, A, L be arranged?
A.10×9×8×7×6×5×3×2
B.10×9×8×7×6×5×4×3
C.8!
D.9!
Answer: A.10×9×8×7×6×5×3×2
Explanation: Number of ways of arranging BENEFICIAL = 10! / 2! * 2! = 10×9×8×7×6×5×3×2. Hence A
Question: A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 12 on Wednesday, what would be the value of D calculated on the following Saturday?
A.2140
B.2520
C.2960
D.3360
Answer: B.2520
Explanation: On Saturday, the value would be 7*6*5*12 = 2520
The answer is B.
Question: 4 is what percent of 50?
A.0.2%
B.8%
C.10%
D.20%
Answer: B.8%
Explanation: 4= x*50/100
x = 8%
Ans; B
Question: John purchased a house for Rs.45000 and a site for Rs.25000 respectively, if he sold the house for Rs.55000 and the site for Rs.16000, then find the resultant percentage of gain?
A.1.39%
B.1.40%
C.1.41%
D.1.42%
Answer: D.1.42%
Explanation: Sol.
Total CP = 70000 & total SP = 71000 ⇒ gain = SP/CP = 71000/70000 = 1.0142 = 1.42%.
Answer D
Question: The monthly rent of a shop of dimension 20feet × 18feet is Rs.1440. What is the annual rent per square foot of the shop?
A.48
B.56
C.68
D.87
Answer: A.48
Explanation: Sol. Monthly rent per square feet = 1440/(20*18) = 4
& Annual rent per square feet
=12*4=48
Answer : A
Question: 1 2 1 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 .........,sum of first 1230 terms of series
A.2311
B.2411
C.2511
D.2611
Answer: B.2411
Explanation: Start with making two series
1+1*2=3 terms 2
1+2*2=5. 3
1+3*2=7. 4
....
....
....
1+47*2=95. 48
1+48*2=97. 49
And last term
1+5*2=11. 6
Total sum= 48(3+97)/2+11=2411
ANSWER:B
Question: A rectangular box of volume Y has width, depth and height in the ratio of 3:2:4 (in that order). What is the height as a function of Y?
A.(4Y/6)^(1/2)
B.(Y/6)^(1/2)
C.(Y/4)^(1/2)
D.(2Y/3)^(1/2)
Answer: A.(4Y/6)^(1/2)
Explanation: We are given width = 3, depth = 2, height = 4.
Then Volume = Width x Depth x Height = 3*2*4 = 24
i.e. Y = 24
The correct option should result in 4 (the height) on substituting the value of Y=24.
Checking options with Y=24:
A) (4Y/6)^(1/2) = (96/6)^(1/2) = 4 CORRECT ANSWER
B) (Y/6)^(1/2) = (24/6)^(1/2) = 2 INCORRECT ANSWER
C) (6Y/4)^(1/2) = (144/4)^(1/2) = 6 INCORRECT ANSWER
D) (Y/3)^(1/2) = (24/3)^(1/2) = 8^(1/2) INCORRECT ANSWER
E) (Y)^(1/2) = (24)^(1/2) INCORRECT ANSWER
Answer: Option A
Question: Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 21 in two years, at the same percent rate per annum?
A.Rs. 200
B.Rs. 209
C.Rs. 202
D.Rs. 238
Answer: A.Rs. 200
Explanation: Explanation:
SI in 2 years = Rs. 20, SI in 1 year = Rs. 10
CI in 2 years = Rs. 21
% rate per annum = [(CI – SI) / (SI in 1 year)] *100
= [(21 – 20) / 20] * 100
= 5 % p.a.
Let the principal be Rs. X
Time = T = 2 years
% rate = 5% p.a.
SI = (PRT/100)
20 = (X*5*2) / 100
X = Rs. 200
ANSWER: A
Question: If n = 8^9 – 8, what is the units digit of n?
A.4
B.0
C.1
D.2
Answer: B.0
Explanation: 8 ^ 9 - 8 = 8 (8 ^ 8 - 1)
==> 8 (2 ^ 24 - 1)
Last digit of 2 ^ 24 is 6 based on what explanation LiveStronger is saying. 2 ^ 24 - 1 yields 6 - 1 = 5 as the unit digit. Now on multiply this with 8, we get unit digit as 0
Answer : B
Question: How often between 11 O'clock and 12 O'clock are the hands of the clock together at an integral number value?
A.55
B.56
C.4
D.5
Answer: D.5
Explanation: Solution:
At 11 O'clock, the hour hand is 5 spaces apart from the minute hand.
During the next 60 minutes, i.e. between 11' O clock and 12' O clock the hour hand will move five spaces [integral values as denoted by the 56 minute, 57 minute, 58 minute, 59 minute and 60 minute positions].
For each of these 5 positions, the minute hand will be at the 12th minute, 24th minute, 36th minute, 48th minute and 60th minute positions.
Hence the difference between the positions of the hour hand and the minute hand will have an integral number of minutes between them.
i.e. 5 positions.
Answer D
Question: A bag contains 4 red, 3 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
A.1/13
B.2/23
C.1/6
D.4/27
Answer: C.1/6
Explanation: P(Both are red),
=4C29C2=4C29C2
=6/36=1/6
C
Question: 20 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.
A.19
B.20
C.21
D.22
Answer: B.20
Explanation: in case of cycle no of handshakes = no of persons
hence ans = 20
ANSWER:B
Question: In an election between two candidates, the first candidate got 60% of the votes and the second candidate got 240 votes. What was the total number of votes?
A.400
B.600
C.800
D.1000
Answer: B.600
Explanation: Let V be the total number of votes.
0.4V = 240
V = 600
The answer is B.
Question: In the manufacture of a certain product, 5 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
A.0.125%
B.0.2%
C.0.8%
D.1.25%
Answer: B.0.2%
Explanation: Percent of defective produced = 5%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(5/100)*100%
= (20/10000)*100%
= (20/100)%
= .2 %
Answer B
Question: A number is increased by 50 % and then decreased by 50 %. Find the net increase or decrease per cent.
A.25%
B.18%
C.17%
D.13%
Answer: A.25%
Explanation: Let the number be 100.
Increase in the number = 50 % = 50 % of 100
= (50/100 Ã— 100)
= 50
Therefore, increased number = 100 + 50 = 150
This number is decreased by 50 %
Therefore, decrease in number = 50 % of 150
= (50/100 Ã— 150)
= 7500/100
= 75
Therefore, new number = 150 - 75 = 75
Thus, net decreases = 100 - 75 = 25
Hence, net percentage decrease = (25/100 Ã— 100) %
= (2500/100) %
= 25 %
Answer:A
Question: A certain fraction is equivalent to 3/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the sum of the numerator and denominator of the original fraction?
A. 49
B. 35
C. 28
D. 56
Answer: D. 56
Explanation: x/y = 3/5 -> 1
(x+4)/2y = 1/3 -> 2
Divide 1 by 2 :
=> 2x/(x+4) = 9/5
=> 10x = 9x + 36
=> x = 36
=> y = 5/3 * 12 = 20
so x + y = 56
The answer is D.
Question: Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much?
A.9680
B.8130
C.8134
D.8556
Answer: B.8130
Explanation: (6200*5*3)/100 = 930
7200
--------
8130
Answer: B
Question: From the given choices select the odd man out
A.37, 14, 19, 8
B.37, 14, 19, 0
C.37, 14, 19, 2
D.37, 14, 19, 7
Answer: D.37, 14, 19, 7
Explanation: Explanation:
All the numbers in those options are prime numbers except 14 in option 4.
Answer:D
Question: If x is a positive integer, which of the following must be odd?
A.x+1
B.x^2+x
C.x^2+x+1
D.x^2−1
Answer: C.x^2+x+1
Explanation: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 1 = ODD
Hence C.
Question: If |x – 9/2| = 5/2, and if y is the median of a set of s consecutive integers, where s is odd, which of the following must be true?
I. xys is odd
II. xy(s^2 + s) is even
III. x^2y^2s^2 is even
A.II only is true
B.III only is true
C.I and III
D.II and III
Answer: A.II only is true
Explanation: given:
s is Odd
y is the median of odd numbers, hence y is Odd
x = solving the modulus you get 7 and 2. Hence x is Even or Odd
Therefore: s = O, y = O and x = O or E
Statement I = x*y*s = y*s*x = O x O x O/E = O x O/E = Odd or even. So False
Statement II = xy(s^2 + s) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true
Statement III. x^2y^2s^2 is even. E/O x O x O = Odd or even. Hence False.
Answer = A.