divelab/Sys2Bench huggingface dataset:
Question: A man can row upstream at 10kmph and downstream at 12kmph. Find man's rate in still water ?
Options:
A)11km/hr
B)15km/hr
C)10km/hr
D)20km/hr
E)7.5km/hr
Rationale: Rate in still water = 1/2 (10+12) = 11km/hr
Answer is A
Answer: A
Question: A lump of two metals weighing 18 g is worth Rs. 87 but if their weight is interchanged, it would be worth Rs. 78.60. If the price of one metal be Rs. 6.70 per gram, find the weight of the other metal in the mixture.
Options:
A)8g
B)12g
C)15g
D)18g
E)None
Rationale: Solution: Cost of (18 g of 1st metal + 18 g of 2nd metal) = Rs. 165.60
Cost of (1 g of 1st metal + 1 g metal of 2nd metal) = Rs. 9.20
Hence cost of 1 g of 2nd metal,
= 9.20 - 6.70
= Rs. 2.5
Mean price = Rs. 87/18
quantity of 1st metal /quantity of 2nd metal = 14/6:56/30 = 5:4
Quantity of 2nd metal = (18*4)/9 = 8 g.
Answer: Option A
Answer: A
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)33
B)77
C)20
D)99
E)71
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: C
Question: In a deck of 52 cards, how many ways are there to select 13 Spade and 13 heart cards without repetition?
Options:
A)169
B)170
C)171
D)172
E)173
Rationale: 13*13=169 ways
ANSWER:A
Answer: A
Question: A completes a work in 10 days and B complete the same work in 15 days. If both of them work together, then the number of days required to complete the work will be
Options:
A)8 days
B)9 days
C)10 days
D)6 days
E)13 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 15/ 25 = 6 days.
D
Answer: D
Question: By selling 20 pencils for a rupee a man loses 60%. How many for a rupee should he sell in order to gain 60%?
Options:
A)8
B)9
C)7
D)6
E)5
Rationale: 40% --- 20
160% --- ?
40/160 * 20 = 5
Answer: E
Answer: E
Question: In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)1.9 sec
C)3.8 sec
D)6.9 sec
E)2.9 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 150/40
= 3.8 sec.
Answer: C
Answer: C
Question: If x is a whole number, then x2(x2-1) is always divisible by:
Options:
A)12
B)24
C)36
D)48
E)26
Rationale: Putting x=2, we get 22(22-1)= 12.
So, x2(x2-1) is always divisible by 12.
ANSWER:A
Answer: A
Question: If each and every term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
Options:
A)38
B)39
C)40
D)41
E)42
Rationale: For example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40).
To illustrate consider adding:
*7
*7
...
77
77
----
=350
So, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40).
Answer: C.
Answer: C
Question: 6) A marketing firm determined that , of 260 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap?
Options:
A)a) 15
B)b) 20
C)c) 30
D)d) 40
E)e) 45
Rationale: 180 = At least one of Soap A or B
Both brands = x
Brand B = 3x
=> 60 + x + 3x = 180
=> 4x = 120
=> x = 30
Answer - C
Answer: C
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate?
Options:
A)480
B)520
C)360
D)280
E)420
Rationale: Let the total no of mangoes in the crate be X.
Then the no of bruised mango = 1/30 X
Let the no of unsaleable mangoes =3/4 (1/30 X) ==> 3/120 X = 12
1/40 X =12
X=480
so the answer is Option A) 480.
Answer: A
Question: Solve the quickfire maths brain teaser âˆš4% = ?
Options:
A)30%
B)40%
C)85%
D)19%
E)20%
Rationale: âˆš4%
=> âˆš4/âˆš100
=> 2/10
=> 20/100
=> 20%
E
Answer: E
Question: A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,250 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?
Options:
A)25%
B)30%
C)35%
D)40%
E)45%
Rationale: C for me.
Let managers comminsion rate be M.
m*5000+ 2*0.05*5000=2250
5000*m=1750
m=35/100=35%
Answer: C
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
Options:
A)2:1
B)1:2
C)1:3
D)3:1
E)1:4
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:30000×9
=45×12:30×9
=3×12:2×9
=2:1
Correct Answer is 2:1
Answer: A
Question: In a public show 62 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
Options:
A)100
B)110
C)120
D)140
E)228
Rationale: 75 % of 600
= 62/100 × 600
= 372
Therefore, the number of vacant seats = 600 - 372 = 228.
Answer:E
Answer: E
Question: Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability Q that the new color will be one of theJaunecolors?
Options:
A)5/42
B)37/42
C)1/21
D)4/9
E)5/9
Rationale: I get B.
Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84
Probability of Jaune Q= (40 + 34)/84 = 37/42
Answer: B
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 9km apart, if they walk in the same direction?
Options:
A)15 hours
B)16 hours
C)17 hours
D)18 hours
E)19 hours
Rationale: The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 9 km
Time = Distance/Speed
Time= 9km / 0.5 kmph = 18 hrs
answer :D
Answer: D
Question: X can finish a work in 15 days. Y can finish the same work in 20 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work?
Options:
A)5
B)3
C)4
D)7
E)8
Rationale: Work done by X in 1 day = 1/15
Work done by Y in 1 day = 1/20
Work done by Y in 12 days = 12/20 = 3/5
Remaining work = 1 – 3/5 = 2/5
Number of days in which X can finish the remaining work = (1/3) / (1/15) = 5
A
Answer: A
Question: solve the given equation 9^y = 3^12, what is y?
Options:
A)1
B)3
C)4
D)5
E)6
Rationale: 3^2y = 3^12
2y=12, therefore y=6
E
Answer: E
Question: 100 identical coins each with probability "p" showing up heads & tossed. If 0 then show the number of heads?
Options:
A)33/100
B)41/101
C)51/101
D)87/101
E)98/101
Rationale: Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C
Answer: C
Question: Abby, Brandon, Cedric, and Deirdre are planning to attend a concert. If their friend Kim also goes with them, they will get a group discount on their tickets. If the total price of the tickets with the group discount is the same as the total price of the tickets without the group discount, how much is the discount?
Options:
A)5%
B)10%
C)20%
D)25%
E)33%
Rationale: Let A,B,C and D individual tickets be X and total tickets is 4X..
Now with Kelly they get a discount , total tickets here is 5x.
We are told that group discount is same as total price without discount..
When we need to solve 5X till we get 4X..
Take options..5X - 5%(5X) = 5x - (0.05)(5X) = 5x - 0.25X = 4.75X...not same as 4X..
(B) 5X - 10% of 5x => 5x - (0.1)(5x) = 4.5X, which is again not equal to 4x. So, this is not the correct option.
(C) 5X - 20% of 5x => 5x - (0.2)(5x) = 4X, this is same as 4X...no need to do other options..
Answer: option C is correct answer.
Answer: C
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 5600. What was Simran share in the profit?
Options:
A)s 9500
B)s 2400
C)s 10500
D)s 11000
E)s 1400
Rationale: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Simran's share = Rs. 5600 x	3/7	= Rs. 2,400
ANSWER :B
Answer: B
Question: What is the area of a square field whose diagonal of length 28 m?
Options:
A)288
B)289
C)200
D)112
E)392
Rationale: d2/2 = (28 * 28)/2
= 392
Answer: E
Answer: E
Question: The second of two numbers is two less than three times the first. Find the numbers if there sum is
26.
Options:
A)7-19
B)8-20
C)10-16
D)15-9
E)20-6
Rationale: We are looking for two numbers.
#1 - x
#2 - 3x – 2
The sum is 26. #1 + #2 = 26
Substituting x + 3x – 2 = 26
4x – 2 = 26
4x = 28
x = 7
The first number is 7, the second number is two less than three times 7 or 19.
correct answer A
Answer: A
Question: A money lender lent a total of $1600 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1600, how much did he lend to each of the two customers?
Options:
A)700; 1100
B)1072; 528
C)1000; 800
D)1200; 800
E)None of the above
Rationale: The method given above is the one given in the book.
However the method I used was
(1*x*5)/100 + (1600-x)*6/100 = 1600*5.67/100
Simplifying we get x= 528
B
Answer: B
Question: In a certain neighborhood, there are half as many beige houses as white houses, and six times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses?
Options:
A)1:3
B)1:9
C)2:5
D)5:3
E)6:1
Rationale: The ratio of beige:white:brown = 3:6:1
The answer is A.
Answer: A
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 260 m long?
Options:
A)34 Seconds
B)22 Seconds
C)41 Seconds
D)24 Seconds
E)29 Seconds
Rationale: D
24 Seconds
Distance travelled = 140 + 260m = 400m
Speed = 60 * 5/8 = 50/3m
Time = 400 * 3/50 = 24 Seconds
Answer: D
Question: Machine P and Machine Q are each used to manufacture 440 sprockets. It takes Machine P 10 hours longer to produce 440 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
440/x = 440/1.1x + 10
1.1(440) = 440 + 11x
11x = 44
x = 4
The answer is B.
Answer: B
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
Options:
A)17
B)15
C)11
D)16
E)12
Rationale: CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs. 15.
Answer: B
Answer: B
Question: Lake A has a duck population of 30 females and 36 males. Lake B’s duck population consists of the same ratio of females to males. If 4 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following?
Options:
A)144
B)105
C)78
D)75
E)36
Rationale: Lake A has a duck population of 30 females and 36 males --> the ratio is F:M = 30:36 = 5:6.
Lake B’s duck population consists of the same ratio of females to males --> F:M = 5:6.
D
Answer: D
Question: In how many ways Chief Minister and Minister be elected froma team of 12 members?
Options:
A)120
B)124
C)132
D)135
E)139
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 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 12*11 = 132 ways.
C
Answer: C
Question: When positive integer x is divided by positive integer y, the result is 59.32. What is the sum R of all possible 2-digit remainders for x/y?
Options:
A)560
B)616
C)672
D)728
E)784
Rationale: ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
R=8(2+3+4....+12)=616.B
Answer: B
Question: An amount of money was lent for 3 years. What will be the difference between the simple and the compound interest earned on it at the same rate?
I.	The rate of interest was 8 p.c.p.a.
II.	The total amount of simple interest was Rs. 1200.
Options:
A)I alone sufficient while II alone not sufficient to answer
B)II alone sufficient while I alone not sufficient to answer
C)Either I or II alone sufficient to answer
D)Both I and II are not sufficient to answer
E)Both I and II are necessary to answer
Rationale: EXPLANATION
Given: T = 3 years.
I. gives: R = 8% p.a.
II. gives: S.I. = Rs. 1200.
Thus, P = Rs. 5000, R = 8% p.a. and T = 3 years.
Difference between C.I. and S.I. may be obtained.
answer is (E).
Answer: E
Question: When positive integer v is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?
I. 8
II. 15
III. 30
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)None of the above
Rationale: ans E..
we can tell the ans w/o using examples..
the units digit of product v*n is 3..
this means v and n are odd positive integers..
therefore n cannot have an even factor so 8 and 30 are out..
n cannot have a factor ending in 5 because in that case the units digit has to be 5 or 0... so 15 is also out
Answer: E
Question: A certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $1.60, what total number of pens and pencils did the customer purchase?
Options:
A)6
B)9
C)10
D)11
E)12
Rationale: Answer: Algebraically, the question looks like this: 2.5 = 0.35x + 0.25y. There are six possible numbers of pencils that fit that requirement:
1 pen: $0.35 and 5 pencils for $0.25 each. That's 1 pens and 5 pencils for a total of 6 pens and pencils. Choice (A) is correct.
Answer: A
Question: In the formula A = 22/7*b^2, if b is halved, then A is multiplied by
Options:
A)4
B)1/8
C)1/4
D)8
E)1/2
Rationale: Say b=2 => A1 = 88/7
when r=1; A2 = 22/7
A2 = 1/4*A1.
Answer : C
Answer: C
Question: From a pack of 52 cards, one card is drawn at random. Find the probability that the drawn card is a club or a jack?
Options:
A)17/52
B)8/13
C)4/13
D)1/13
E)2/13
Rationale: Solution:
n(S) = 52
n(E) = 16
P(E) = n(E) / n(S) = 16/ 52
= 4/13
ANSWER IS C
Answer: C
Question: If the price of an article went up by 40%, then by what percent should it be brought down to bring it back to its original price?
Options:
A)16 2/3%
B)16 4/3%
C)16 7/3%
D)16 6/3%
E)28 4/7%
Rationale: Let the price of the article be Rs. 100.
40% of 100 = 40.
New price
= 100 + 40 = Rs. 140
Required percentage
= (140 - 100)/140 * 100
= 40/140 * 100
= 200/7
= 28 4/7%.
Answer:E
Answer: E
Question: Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 10 such machines produce in 4 minutes ?
Options:
A)648
B)1800
C)2700
D)10800
E)None of these
Rationale: Solution
Let the required number of bottles be x.
More machines,More bottles (Direct Proportion)
More minutes,More bottles (Direct Proportion)
∴ 6 × 1 × x = 10 × 4 × 270 ⇔ x = 10x4x270/6= 1800 . Answer B
Answer: B
Question: The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 12 terms of the arithmetic progression?
Options:
A)300
B)120
C)150
D)170
E)270
Rationale: n th term of A.P. is given by a+(n-1)d
4 th term = a+3d
12 th term = a+11d
Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10
Sum of n term of A.P = n/2[2a+(n-1)d]
subsitiuing n = 12 ...we get 12/2[ 2a + 14d] = 15 [a+7d] = 12*10 = 120...
Answer is B...
Answer: B
Question: In a practice paper at 2iim.com, questions were given from 5 topics. Out of the appearing students, 10% passed in all topics while 10% did not pass in any. Of the remaining, 20% passed in one topic only and 25% in two topics only. If 24% of the total students passed 4 topics only and 500 students passed in 3 topics only, find the total number of students who appeared in the examination?
Options:
A)2500
B)2000
C)1600
D)4545
E)6565
Rationale: DETAILED SOLUTION
Let the number of appearing students be 100.
Pass only in 0 topic – 10
1 – 16 (20% of 80)
2 – 20 (25% of 80)
3 – 20% (100 – (16+20+24+20))
4 – 24%
5 – 20%
Therefore, 20% of x = 500 = ) x = 2500
Correct Answer: A
Answer: A
Question: In the junior basketball league there are 18 teams, 2/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad?
Options:
A)4.
B)6.
C)7.
D)8.
E)10
Rationale: otal teams =18
bad teams=(2/3)*18=12
rich teams=9
so maximum value that the both rich and bad can take will be 9. so E= 10 can not be that value.
ANSWER:E
Answer: E
Question: A money lender lends Rs.2500 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
Options:
A)2205
B)1978
C)2834
D)2827
E)2756.25
Rationale: A = 2500(21/20)2
= 2756.25
Answer: E
Answer: E
Question: If a, b, c and g are non-zero integers, 3 ≥ c ≥ – 9 , 5 ≥ a ≥ –2 , 10 ≥b ≥ –1 , 4 ≥ g ≥ 1, then which of the following expresses the smallest possible value of ag/(bc)?
Options:
A)–90
B)–20
C)–10
D)1/90
E)15/4
Rationale: ag have to be greatest from its range && bc to be smallest with -ve sign to became ag/bc smallest
A)-90 never possible case.(all nos. are integers and ag has max. 20 value)
B)-20 a=5,b=4 and b=1,c=-1 then it is possible
Option C,D,E are > -20....
Ans B
Answer: B
Question: The value of (4x10^7)(7x10^8) is closest to which of the following?
Options:
A)10^15
B)10^12
C)10^13
D)10^14
E)10^17
Rationale: multiplying these we get,
28 x 10^7 x 10^8
= 2.8x 10^16
which is closer to 10^17
Answer: E
Answer: E
Question: The area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?
Options:
A)450 m3
B)100 m2
C)60 m3
D)400 m3
E)500 m3
Rationale: lb = 20 ; lh = 15 ; fh = 12
(lbh)2 = 20 * 15 * 12 => lbh = 60 m3
ANSWER:C
Answer: C
Question: Two men Amar and Bhuvan have the ratio of their monthly incomes as 6 : 5. The ratio of their monthly expenditures is 3 : 2. If Bhuvan saves one-fourth of his income, find the ratio of their monthly savings?
Options:
A)3 : 5
B)3 : 10
C)3 : 8
D)1 : 2
E)2:1
Rationale: Let the monthly incomes of Amar and Bhuvan be 6x and 5x respectively.
Let the monthly expenditure of Amar and Bhuvan be 3y and 2y respectively.
Savings of Bhuvan every month = 1/4(5x)
= (His income) - (His expenditure) = 5x - 2y.
=> 5x = 20x - 8y => y = 15x/8.
Ratio of savings of Amar and Bhuvan
= 6x - 3y : 1/4(5x) = 6x - 3(15x/8) : 5x/4 = 3x/8 : 5x/4
= 3 : 10.
ANSWER:B
Answer: B
Question: Griffin has a bag of marbles that contains 6 black marbles and 6 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be red?
Options:
A)1/11
B)2/33
C)3/44
D)4/55
E)5/66
Rationale: P(3 red marbles) = 6/12*5/11*4/10 = 1/11
The answer is A.
Answer: A
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
Options:
A)5 : 6
B)3 : 4
C)7 : 8
D)8 : 9
E)None of these
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
ANSWER:C
Answer: C
Question: In the class of 40 students, 30 speak Tamil and 20 speak Telugu. What is the lowest possible number of students who
speak both the languages?
Options:
A)8
B)10
C)20
D)30
E)32
Rationale: let the student who speaks hindi-x
let the student who speaks english-y
as (xuy)-(xny)=total
30+20-(xny)=40
=10
B)
Answer: B
Question: 24 oz of juice P and 25 oz of juice W are mixed to make smothies X and Y . The ratio of p to W in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: Easy way to solve this question is start from the answer and then conform the information provided in the question.
we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to W ratio is 4:1
this gives us that quantity of juice P in X = 20 therefore quantity of Juice W will be 5 ... hence ratio = 4:1
This will lead to quantity of juice P in X = 4 and quantity of Juice W = 20 ... hence ratio 1:5
if we calculate total Juice P = 24 and total of juice W = 25
it fits because totals are same as what mentioned in the question ...
thus ans is D
Answer: D
Question: The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in eight colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?
Options:
A)24
B)32
C)48
D)60
E)321
Rationale: I have no idea how you got 8C8, 7C6 and 4C1.
I could have understood 8C1*6C1*4C1 (I have explained why this doesn't work in the post above)
The best way to solve it is by first selecting 3 colors out of the given 4 in 4C3 ways. (say, you got black, red and green)
Now for each color, you have 2 choices - model A or B
So you select a model in 2 ways.
No of ways of selecting the 3 cars = 6C3 * 2 * 2 * 2 = 321
Well, my logic was
The number of ways of selecting r objects from n different objects is nCr.
We have 8 options and can select either of the 8 as the first - 8C8
One car is gone and one becomes a forbidden choice so we have 7 options and need to select either of the 6 as the first - 7C6
Two cars are gone and two becomes a forbidden choice so we have 6 options and need to select either of the 4 as the first - 6C4
E
Answer: E
Question: A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 35, how many coins of each type are there?
Options:
A)20 coins
B)30 coins
C)28 coins
D)25 coins
E)None of these
Rationale: Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 35
⇒ 1.75x = 35 ⇒ x = 20 coins
Answer A
Answer: A
Question: In the youth summer village there are 125 people, 50 of them are not working, 25 of them have families and 75 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that don't have families and that are singing in the shower?
Options:
A)75
B)80
C)85
D)100
E)90
Rationale: total =125
not working =50
having family=25
like to sing in shower = 75
working=125-50=75
not having family = 125-25=100
like to sing in shower = 100
largest possible number is the lowest possible among the above
Thus 75
A
Answer: A
Question: Average of five consecutive even numbers is 35. Find the greatest number in these five numbers?
Options:
A)37
B)38
C)39
D)41
E)42
Rationale: 39
Option 'C'
Answer: C