mathewhe/aqua_rat huggingface dataset:
Question: A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?
(A) 24
(B) 30
(C) 36
(D) 90
(E) 96
Rationale: 120 spend $100 on gas & electricity
60 spend $100 on gas but not on electricity
For every one that spent <$100 on both there are 4 that spent $100 on electricity not gas
Let the ones that spent on neither be x
The ones that spent on just electricity will be 4x
Total households = Those who spend >$100 on both + Those who spend >$100 on just one + Those who spend <$100 on both = 120 + 60 + 4x + x
300 = 180 + 5x implies x=24
Answer is (A)
Answer: (A) 24
Question: How many tow-digit integers exist such that all their digits are even?
(A) 20
(B) 100
(C) 120
(D) 125
(E) 135
Rationale: 0 is also an even integer
so last digit can be filled in 5 ways- 0,2,4,6,8
for both second and third digit there are 5 possibilities-
5 X 5 = 25
_______________
The first digit can be any of the four: 2, 4, 6, or 8. For both seconddigits, there are 5 possibilities. The answer is 4∗5=20.
The correct answer is A
Answer: (A) 20
Question: In Orange County, one ninth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
(A) 212
(B) 235
(C) 240
(D) 252
(E) 275
Rationale: The number must be a multiple of both 9 and 7 so the answer is 252.
The answer is D.
Answer: (D) 252
Question: Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit?
(A) 1%
(B) 2%
(C) 3%
(D) 4%
(E) 5%
Rationale: A dozen toys cost $360, so each toy cost $30.
selling price / cost price = 30.60 / 30 = 1.02
The percentage profit is 2%.
The answer is B.
Answer: (B) 2%
Question: The greatest possible length which can be used to measure exactly the length 5m, 4m 45m, 10 m 45 cm is
(A) 15 cm
(B) 25 cm
(C) 5 cm
(D) 42 cm
(E) 43 cm
Rationale: Explanation:
Required Length = H.C.F of 500 cm, 445 cm and 1045 c
= 5 cm. Answer: C
Answer: (C) 5 cm
Question: Smithtown High School is holding a lottery to raise money. The tickets are assigned numbers from 1 to 200. Tickets with numbers divisible by 2 win t-shirts, tickets with numbers divisible by 3 win gift certificates, and tickets with numbers divisible by 7 win movie passes. How many tickets win none of the prizes?
(A) 6
(B) 52
(C) 58
(D) 142
(E) 194
Rationale: Total numbers divisible by:
3->200/3=66.66; Ignore the decimal part=66
2->200/2=100;
7->200/7=28.Something; Ignore decimal part=28
3*2->200/6=33
3*7->200/21=9
2*7->200/14=14
3*2*7->200/42=4
Thus, total numbers that can win prize= 66+100+28-33-9-14+4=142 [:Note Used the same formula as we do for overlapping sets A∪B∪C=n(A)+n(B)+n(C)−n(A∩B)−n(A∩C)−n(B∩C)+n(A∩B∩C)
Non-winnable numbers=200-142=58
Ans: "C"
Answer: (C) 58
Question: Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/7 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
(A) 1/2
(B) 7/13
(C) 4/13
(D) 8/29
(E) 6/33
Rationale: Now ultimately the speed of every machine is given with respect to Mach O.
So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4
Mach O makes x units in 12 hrs
So, Mach N = 2/7 of O = 2/7*12 = 24/7 hrs to make x units
and Mach M = 3/4 of N = 3/4*24/7 = 1/6hrs to make x units
No they are running simultaneously. Lets see how much each mach makes in 1 hr
Mach O = x/12 units
Mach N = 7/24 units
Mach M = x/6 units
In 1 hr, together they make - x/12+7/24+x/6 = 13/24
So what ratio of this has Mach N made?
(7/24) / (13/24) = 7/13
Ans:B=7/13
Answer: (B) 7/13
Question: Three rugs have a combined area of 204 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?
(A) 18 square meters
(B) 20 square meters
(C) 24 square meters
(D) 28 square meters
(E) 30 square meters
Rationale: Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}
140 = 204 - 24 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 20.
Answer: B.
Answer: (B) 20 square meters
Question: 38 68 22 70 31 47 13 82
Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above?
(A) 56
(B) 68
(C) 69
(D) 71
(E) 73
Rationale: Arrange the numbers in ascending order:
13, 22, 31, 38, 47, 68, 70, 82 (Just cross check the count to ensure that you didn't miss anything)
How many numbers do we see?
8, alright.
What's (1/4)8?
2.
What's (3/4)8?
6.
We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two.
13, 22, 31, 38, 47, 68,70, 82
13, 22, 31, 38, 47, 68: Find a number greater than any of these numbers.
70, 82: Find a number smaller than any of these numbers.
Only 69 fits the description.
Ans:C
Answer: (C) 69
Question: A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?
(A) Rs.662.22
(B) Rs.662.20
(C) Rs.662.02
(D) Rs.662.12
(E) Rs.662.09
Rationale: Amount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)]
= [200 * 21/20(21/20 * 21/20 + 21/20 + 1)]
= Rs.662.02
Answer: C
Answer: (C) Rs.662.02
Question: Teacher took exam for English, average for the entire class was 80 marks. If we say that 10% of the students scored 95 marks and 20% scored 90 marks then calcualte average marks of the remaining students of the class.
(A) 60
(B) 70
(C) 65
(D) 75
(E) 80
Rationale: Lets assume that total number of students in class is 100 and required average be x.
Then from the given statement we can calculate :
(10 * 95) + (20 * 90) + (70 * x) = (100 * 80)
70x = 8000 - (950 + 1800) = 5250 ANSWER : D
x = 75.
Answer: (D) 75
Question: Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
(A) 10
(B) 12
(C) 14
(D) 15
(E) 20
Rationale: Speed of the first train =(120/10) m/sec = 12 m/sec
Speed of the second train =(120/15) m/sec = 8 m/sec
Relative speed = (12 + 8) = 20 m/sec.
Required time = (120+120)/20 sec = 12 sec
answer :B
Answer: (B) 12
Question: The sum of the digits of a two-digit number is 9 less than the number. Which of the following digits is at unit’s place of the number?
(A) 1
(B) 2
(C) 4
(D) Data inadequate
(E) None of these
Rationale: Solution
Let the ten's digit be x and unit's digit be y. Then, (10x + y) - (x + y) = 9 or x = 1.
From this data, we cannot find y, the unit's digit. So the data is inadequate.
Answer D
Answer: (D) Data inadequate
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
(A) 10%
(B) 12%
(C) 100%
(D) 18%
(E) 80%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C
Answer: (C) 100%
Question: what is next no. 11 23 47 83 131 191 263 347???
(A) 171
(B) 181
(C) 443
(D) 201
(E) 211
Rationale: 11+12*1=23
23+12*2=47
47+12*3=83
83+12*4=131
131+12*5=191
191+ 12*6=263
263+12*7=347
347+12*8=443
ANSWER:C
Answer: (C) 443
Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
(A) 76
(B) 79
(C) 85
(D) 87
(E) 89
Rationale: Explanation:
Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 x 10 = 320.
Now increase in avg = 4runs. So, new avg = 32+4 = 36runs
Total runs = new avg x new no. of innings = 36 x 11 = 396
Runs made in the 11th inning = 396 - 320 = 76 Answer: A
Answer: (A) 76
Question: if A and B can do a piece of work in 10 days and A alone can do it in 15 days, how long will B take to do it?
(A) 20
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: 1/10-1/15=1/30
30 days
ANSWER:B
Answer: (B) 30
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) 59002
(B) 59028
(C) 59128
(D) 59000
(E) 59122
Rationale: Explanation:
Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000
Answer:D
Answer: (D) 59000
Question: If −2≤f≤0 and n > 19, which of the following CANNOT be the value of fn?
(A) -48
(B) -38
(C) -20
(D) 0
(E) 19
Rationale: value of fn not equal to -19=E -19....Rest all are achievable
Answer: (E) 19
Question: Arun went for a movie nine days ago. He goes to watch movies only on Thursdays. What day of the week is today?
(A) Wednesday
(B) Saturday
(C) Friday
(D) Sunday
(E) None of these
Rationale: Explanation :
Clearly it can be understood from the question that 9 days ago was a Thursday
Number of odd days in 9 days = 2 (As 9-7 = 2, reduced perfect multiple of 7 from total days)
Hence today = (Thursday + 2 odd days) = Saturday. Answer : Option B
Answer: (B) Saturday
Question: After offering a discount of 37.5%, Pankaj sold the rice at a profit of 25%. Had he offered a discount of 41.67%, his profit or loss percent would have been:-
(A) 16.66% profit
(B) 12% loss
(C) 29.17% loss
(D) 8.33% profit
(E) None of these
Rationale: Explanation :
Let the Marked Price of the rice = 8p,
And the discount is 37.5% i.e 37.5%=(3/8)MP.
Thus, the Selling Price is:-
=>8p-(3/8)8p=5p.
=>5p=CP(25/100)x25.
=>CP=4p.
If he had offered a discount of 41.67%=5/12.
S.P=8p-(5/12)X8p.
=>14p/3.
The profit is:-
=>(14p/3)-4p.
=>2p/3.
Hence, the required profit percentage is :-
=>(2p/3)x100/4p.
=>(100/6)%.
=>16.66%.
Answer : A
Answer: (A) 16.66% profit
Question: A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?
(A) 19
(B) 21
(C) 23
(D) 25
(E) 27
Rationale: Explanation:
20 15 5
25 20 8
500 + 300 + 40 = 840/40 = 21
B
Answer: (B) 21
Question: At a loading dock, each worker on the night crew loaded 1/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/6
Rationale: Method: X = No. of boxes loaded by day crew.
Boxes by night crew = 1/4 * 4/5 X = 1/5 X
% loaded by day crew = X/(X + 1/5X) = 5/6
Answer E
Answer: (E) 5/6
Question: The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then their difference is
(A) 19
(B) 10
(C) 28
(D) 27
(E) 29
Rationale: Let the numbers be x and (100-x).
Then,
\inline \fn_jvn \Rightarrow \inline \fn_jvn x^{2}-100x+2475=0
\inline \fn_jvn \Rightarrow (x-55) (x-45) = 0
\inline \fn_jvn \Rightarrow x = 55 or x = 45
\inline \fn_jvn \therefore The numbers are 45 and 55
Required difference = (55-45) = 10
Answer:B
Answer: (B) 10
Question: Alex takes a loan of $9,000 to buy a used truck at the rate of 9 % simple Interest.Calculate the annual interest to be paid for the loan amount.
(A) 680
(B) 810
(C) 800
(D) 730
(E) 750
Rationale: From the details given in the problem Principle = P = $9,000 and R = 9% or 0.09 expressed as a decimal.
As the annual Interest is to be calculated, the time period T =1.
Plugging these values in the simple Interest formula,
I = P x T x R
= 9,000 x 1 x 0.09
= 810.00
Annual Interest to be paid = $810
answer :B
Answer: (B) 810
Question: According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 272 6 ounces servings of orange juice?
(A) a) 25
(B) b) 34
(C) c) 50
(D) d) 67
(E) e) 100
Rationale: Its B.
Total juice rquired = 272*6 = 1632 ounce
12 ounce concentate makes = 12 * 4 = 48 ounce juice
Total cans required = 1632/48 = 34.
Answer B
Answer: (B) b) 34
Question: The value of (256)5/4 is:
(A) 11 hrs 562 min
(B) 3 hrs 860 min
(C) 7 hrs 1020 min
(D) 7 hrs 1024 min
(E) NOne
Rationale: Sol.
(256)5/4 = (44)5/4 = 4(4*5/4) = 45 = 1024.
Answer D
Answer: (D) 7 hrs 1024 min
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 2 m wide at the bottom and the area of cross-section is 4200 sq m, the depth of cannel is?
(A) 500
(B) 600
(C) 700
(D) 800
(E) 900
Rationale: 1/2 * d (12 + 2)
= 4200
d = 600
Answer: B
Answer: (B) 600
Question: If the LCM of 7, 10, 3, and x is 210, which of the following could be x?
(A) 13
(B) 6
(C) 21
(D) 2
(E) 14
Rationale: Using elimination method, eliminate the option to arrive at 21
if x is replaced by 21 and the LCM is calculated you arrive at 210
C
Answer: (C) 21
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51
kmph, find the speed of the stream?
(A) 16 kmph
(B) 19 kmph
(C) 14 kmph
(D) 17 kmph
(E) 13 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1) = 3/1
= 3:1
Speed of the stream
= 51/3 = 17 kmph.
Answer: D
Answer: (D) 17 kmph
Question: (w^2+x^2)x(y^2+z^2) is always divisible by which of the max no. Where w;x;y;z are odd integers?
(A) 20
(B) 8
(C) 4
(D) 2
(E) 6
Rationale: ((odd)^2+(odd)^2)*((odd)^2+(odd)^2)
(even)*(even)
2*2
4
ANSWER:C
Answer: (C) 4
Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full?
(A) 17 minutes
(B) 87 minutes
(C) 40 minutes
(D) 27 minutes
(E) 11 minutes
Rationale: 1/20 - 1/40 = 1/40
40 minutes
Answer:C
Answer: (C) 40 minutes
Question: A 150 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 220 meter
(B) 225 meter
(C) 230 meter
(D) 350 meter
(E) None of these
Rationale: Explanation:
As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec
Let the length of other train is x meter then
x+150 /9=500 /9
=>x+150=500
=>x=350
So the length of the train is 350 meters
Option D
Answer: (D) 350 meter
Question: Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?
(A) Rs.6400
(B) 2878
(C) 2899
(D) 2660
(E) 2701
Rationale: Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,
(x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508
28x - 22x = 350800 - (13900 * 22)
6x = 45000 => x = 7500
So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.Answer:A
Answer: (A) Rs.6400
Question: In how many ways Chief Minister and Minister be elected from a team of 6 members?
(A) 124
(B) 29
(C) 30
(D) 154
(E) 165
Rationale: To do this, if captain is elected first, then we have 6 ways of doing this.
For election of vice-captain, we have only 5 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 6*5 = 30 ways.
C
Answer: (C) 30
Question: In shop contains some articles each of a cost of $5. He sold them at a price of $10. If the shop keeper has a order of 150 articles, how much profit he will get?
(A) 200
(B) 250
(C) 750
(D) 1000
(E) 500
Rationale: Total money after selling articles = 150*10 = 1500
cost price = 150*5 = 750
profit = 750
correct option is C
Answer: (C) 750
Question: With # andeach representing different digits in the problem below, the difference between #and ## is 623. What is the value of?
#
-##
___
623
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 100x
-(10x +x)
-----------
89 x= 667
x = 7
A
Answer: (A) 7
Question: 40 + 5 * 12 / (180/3) = ?
(A) 23
(B) 78
(C) 27
(D) 61
(E) 41
Rationale: Explanation:
40 + 5 * 12 / (180/3) = 40 + 5 * 12 / (60)
= 40 + (5 * 12)/60 = 40 + 1 = 41.
Answer:E
Answer: (E) 41
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly, equal. Which of the parts is not equal to the other four? The number of that part is the answer.
(A) 375.789 + 41.28 – 115.249
(B) 6.45 × 120.8 – 477.34
(C) 1015.71 – 738.416 + 24.526
(D) 853.12 + 109.73 – 661.03
(E) 132.8 × 3.5 – 152.98
Rationale: Others are equal to 301.82.
Answer E
Answer: (E) 132.8 × 3.5 – 152.98
Question: A Certain item costs to Harris $50. At what price must the merchant sell this item in order to make a profit of 10% ?
(A) $50
(B) $55
(C) $65
(D) $60
(E) $50
Rationale: Cost Price = $50
Profit % = 10
Selling Price = ?
Selling Price = (100 + profit %) * Cost Price /100
= (100 + 10) * 50 / 100
= 55
Answer is B
Answer: (B) $55
Question: How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?
(A) 72
(B) 24
(C) 48
(D) 120
(E) 30
Rationale: The given word contains 5 different letters.
Taking the vowels EA together, we treat them as one letter.
Then, the letters to be arranged are XTR (EA).
These letters can be arranged in 4! = 24 ways.
The vowels EA may be arranged amongst themselves in 2! = 2 ways.
Number of words, each having vowels together = (24x2) = 48 ways.
Total number of words formed by using all the letters of the given words
= 5! = (5x4x3x2x1) = 120.
Number of words, each having vowels never together = (120-48) = 72
ANSWER A 72
Answer: (A) 72
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
(A) 7
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%
Answer: B
Answer: (B) 5
Question: Sum of the squares of 3 no.'s is 99 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 24
(C) 19
(D) 28
(E) 30
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 99 + 2* 131
a + b + c = √361 = 19
C
Answer: (C) 19
Question: Two numbers are in the ratio of 1 : 2. If 8 be added to both, their ratio changes to 3 : 5. The greater number is
(A) 20
(B) 24
(C) 28
(D) 32
(E) 36
Rationale: Let the ratio be X : Y,
Given X/Y = 1/2 ,
(X + 8)/(Y + 8) = 3/5
=> X = 16
And Y = 32
ANSWER:D
Answer: (D) 32
Question: If 0 < a < b and k = (5a + 5b)/b , which of the following must be true?
(A) k < 2
(B) k < 7
(C) k < 9
(D) k > 9
(E) k > 11
Rationale: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 as a < b, you get k = (5+10)/2 = 7.5. This eliminates all but option C , making it the correct answer.
Answer: (C) k < 9
Question: In My, Xiang sold 15 used cars. For these 15 used cars the range of selling prices was 15,000 and the lowest selling price was 3,000. In June, Xiang sold 10 cars. For these 10 cars the range of selling was 16,000 and the lowest selling price was 6,100. What was the range of selling prices for the 25 used car sold by xiang in May and June?
(A) 15,600
(B) 15,750
(C) 16,820
(D) 18,100
(E) 19,200
Rationale: for 10 cars - 16000+ 6100 = 22,100
for 15 cars - 15000+ 3000 = 18,000
max = 22,100 min 4500
answer is approx 19100.
Option E is closest.
Answer: (E) 19,200
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
(A) 27
(B) 24
(C) 62
(D) 78
(E) 25
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer:B
Answer: (B) 24
Question: Which of the following must be divisible by 4, given that y is a positive integer?
(A) (y−1)*y*(y+3)
(B) y^2*(y−3)
(C) y(y^2−2)
(D) y(y+2)^3
(E) (y−2)·(y+1)·(y+3)
Rationale: option A) (y−1)*y*(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be A
Answer: (A) (y−1)*y*(y+3)
Question: In a class of 40 students, 10 did not opt for math. 15 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science?
(A) 13
(B) 15
(C) 7
(D) 17
(E) 18
Rationale: 40 students total
10 did not opt for math
15 did not opt for science
2 did not opt for either
Total of 30 students in math and 13 did not opt for sci but did for math
30-13=7
7 students of the class opted for both math and science
Answer:
C. 7
Answer: (C) 7
Question: In how many ways can a cricket eleven be chosen out of a batch of 15 players?
(A) 1365
(B) 1523
(C) 2165
(D) 1012
(E) 2135
Rationale: Required number of ways = 15C11 = 15C (15-11) = 15C4
15C4 = (15*14*13*12)/(4*3*2*1) = 1365
Answer is A
Answer: (A) 1365
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability W that the team will have exactly 2 women?
(A) 1/14
(B) 1/7
(C) 2/7
(D) 3/7
(E) 1/2
Rationale: 5C2 * 3C2 -> it gives combination of exactly 2 women and 2 men.
8C4 -> gives total possibilities of 4 people from 5 women and 3 men.
Probability = 5C2*3C2 / 8C4 = 3/7
SECOND METHOD:
Probability of two women -> 5/8 * 4/7.
probability of two men -> 3/6 * 2/5.
Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.
Answer: (D) 3/7
Question: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many four letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
(A) 2,145
(B) 6,435
(C) 326,040
(D) 12,870
(E) 25,740
Rationale: Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All four
2. One symmetry and other three non
3. Two symmetry and other two non
4. Three symmetry and one non
4. All the three letters can be arranged in 24 ways
( 11c4 + 11c1 * 15c3 + 11c2 * 15c2 + 11c3 *15c1 ) * 6
(330 +5005 + 5775+2475 ) * 24
326,040
IMO option C is the correct answer..
OA please...will correct if I missed anything.. C
Answer: (C) 326,040