mathewhe/aqua_rat huggingface dataset:
Question: A completes a work in 6 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be
(A) 8 days
(B) 9 days
(C) 10 days
(D) 4.8 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 = 6 × 24/ 30 = 4.8 days.
D
Answer: (D) 4.8 days
Question: A man swims downstream 40 km and upstream 30 km taking 5 hours each time, what is the speed of the man in still water?
(A) 12
(B) 8
(C) 36
(D) 5
(E) 7
Rationale: 40 --- 5 DS = 8
? ---- 1
30 ---- 5 US = 6
? ---- 1 M = ?
M = (8 + 6)/2 = 7
Answer: E
Answer: (E) 7
Question: How many total number of ways in which a distinct objects can be put into two different boxes is
(A) n2
(B) 2a
(C) 2n
(D) 3n
(E) None of these
Rationale: Let the two boxes be B1 and B2. There are two choices for each of the a objects. So, the total number of ways is
2 × 2 ×.....× 2 (a times ) = 2a
Answer B
Answer: (B) 2a
Question: An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 20% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?
(A) 119.45%
(B) 129.56%
(C) 138.24%
(D) 141.92%
(E) 145.36%
Rationale: 0.8*1.2^3 = 1.3824
The answer is C.
Answer: (C) 138.24%
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
(A) 10
(B) 12
(C) 14
(D) 13
(E) 16
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13
Question: A merchant has selected two items to be placed on sale, one of which currently sells for 30 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?
(A) 22 %
(B) 30%
(C) 42 6/7%
(D) 70%
(E) 130%
Rationale: Expensive item = $100;
Cheap item = $70;
We must increase $70 to $100, so by $30, which is approximately 40% increase: (100-70)/70 = 3/7 = ~0.42.
Answer: C.
Answer: (C) 42 6/7%
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 18:16
(C) 18:17
(D) 18:18
(E) 18:12
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer:A
Answer: (A) 18:11
Question: Find a sum for first 3 prime number'ss?
(A) 25
(B) 10
(C) 15
(D) 12
(E) 36
Rationale: Required sum = (2 + 3 + 5) = 10
Note: 1 is not a prime number
Option B
Answer: (B) 10
Question: Father is aged square times more than his son john. After 3 years, he would be three times of John's age. what would be the age of John's Father after 15 years ?
(A) 18
(B) 36
(C) 40
(D) 57
(E) 45
Rationale: Let Father's age be J and John's' age be D...
Given J + 3 = 3(D + 3 ) => J - 6 = 3D -> Eq1.
Given J-6 = (D-6)^2 --> Eq 2..
sub J-6 value in eq 2... 3D = D^2 - 12D + 36.
0 = D^2 - 15D + 36 => D = 12 or D = 3.
When D = 12 we get from eq 1... J+3 = 45 => J =42..
When D = 3 ..we get from eq 1.. J+3 = 18 => J = 15...
In the above options only 42 exits..
IMO option D is correct answer..
Answer: (D) 57
Question: An outlet pipe can empty 2/3 of a cistern in 16 minutes. In 8 minutes, what part of the cistern will be emptied?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 2/5
(E) 3/10
Rationale: 8/16 * 2/3 = 1/3
The answer is B.
Answer: (B) 1/3
Question: What is the probability that a 4-person committee chosen at random from a group consisting of 6 men, 7 women, and 5 children contains at least 1 woman?
(A) 11/102
(B) 77/204
(C) 77/102
(D) 91/102
(E) 31/34
Rationale: Total Members = 6+7+5 = 18
Total ways of making 4 person committee = 18C4 = 3060
Total Members without women = 6+5 = 11
Total ways of choosing e person committee without any women = (6+5)C4 = 330
favorable probability = 1- (330/3060) = 1- (11/102) = 91/102
Answer: option D
Answer: (D) 91/102
Question: The sum of two numbers is 30 and their difference is 10. Find their product.
(A) 104
(B) 108
(C) 114
(D) 325
(E) 200
Rationale: Sol.
Let the numbers be x and y.
Then, x + y = 30 and
x - y = 10
2x = 40 +> x =20 , so y = 10
x y = 20*10 = 200
Answer : E
Answer: (E) 200
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
(A) 4 1/5 Km
(B) 4 1/7 Km
(C) 3 1/5 Km
(D) 3 1/7 Km
(E) 3 2/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
C)
Answer: (C) 3 1/5 Km
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 49%
(C) 57%
(D) 59%
(E) 61%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.400, find the number of 10 paise coins ?
(A) 914
(B) 714
(C) 718
(D) 724
(E) 814
Rationale: 50*3k + 20*4k + 10*5k = 40000
280k = 40000 => k = 142.85
50p coins = 3k = 3*142.85 = 428
20p coins = 4k = 4*142.85 = 571
10p coins = 5k = 5*142.85 = 714
ANSWER:B
Answer: (B) 714
Question: The decimal d is formed by writing in succession all the positive, even integers in increasing order after the decimal point; that is d = 0.246810121416...
What is the 100th digit of d to the right of decimal point?
(A) 6
(B) 1
(C) 0
(D) 2
(E) 8
Rationale: One-digit even numbers: There are (1)(10/2) = 4 even one-digit numbers.
0.2468
4 digits down, 96 remaining. The next 5 even numbers will be 10, 12, 14, 16, and 18, ... so it follows that: (2)(5) = 10 digits.
Two-digit numbers: 90 digits, which brings us to the number 98.
Three-digit numbers: we only need 6 more digits. The next even numbers are 100, and 102, thus 2 is the 100th digit.
Answer: D
Answer: (D) 2
Question: The length of the bridge, which a train 120 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 255
(B) 267
(C) 255
(D) 277
(E) 211
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec
Time = 30 sec
Let the length of bridge be x metres.
Then, (120 + x)/30 = 25/2
=> x = 255 m. Answer:C
Answer: (C) 255
Question: The speed of a boat in still water is 65kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 22 kmph
(B) 40 kmph
(C) 78 kmph
(D) 15 kmph
(E) 45 kmph
Rationale: Speed downstream = 65 + 20 = 85 kmph
Speed upstream = 65 - 20= 45 kmph
Answer:E
Answer: (E) 45 kmph
Question: Two motor cycles were sold for Rs 9,900 each, gaining 10% on one and losing 10% on the other. The gain or loss per cent in the whole transaction is
(A) Neither loss nor gain
(B) 1% profit
(C) 100/99 % profit
(D) 1% loss
(E) None of these
Rationale: C.P. of the 1st Motor Cycle = (9900 x 100)/(100 + 10) = Rs 9000
C.P. Of the 2nd Motor Cycle = (9900 x 100)/(100 - 10) = Rs 11000
Total C.P = Rs 20,000
Total S.P = Rs 19,800
Therefore, Loss per cent = (200/20000) x 100 = 1
ANSWER:D
Answer: (D) 1% loss
Question: A sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $600?
(A) $3,000
(B) $3,150
(C) $4,000
(D) $4,150
(E) $5,000
Rationale: Total salary = $150+ 15% (x) where x = all the sales she makes.
How much x should be for total to be 600
$150+15%(x) = $600
15%(x) = $450
x = $3000
Answer :A
Answer: (A) $3,000
Question: A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 30 days, then together ,all will finish the work in :
(A) 13 1/3 days
(B) 12 1/3 days
(C) 15 days
(D) 12 days
(E) 30 days
Rationale: C alone can finish the work in 30 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
Aâ€™s 1 dayâ€™s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 dayâ€™s work = (1/60) + (1/30) + (1/30) = 1/12
All the three together will finish it in 1/12 = 12 days.
ANSWER:D
Answer: (D) 12 days
Question: Merry invested Rs. 8000 in a scheme for 3 years at compound interest rate 7% p.a. How much amount will Merry get on maturity of the fixed deposit?
(A) s.8980
(B) s.9800.34
(C) s.9841
(D) s.8900
(E) s.8820
Rationale: Amount = [8000 * (1 + 7/100)3]
= 8000 * 107/100 * 107/100 * 107/100
= Rs.9800.34
Answer:B
Answer: (B) s.9800.34
Question: The number 4 is the smallest positive
integer that has exactly three factors:
1, 2, and 4. If k is the next-highest integer
that also has exactly three factors, what is
the sum of the three factors of k?
(A) 13
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: The greatest of the five possible answers is 20, so k is less than 20. Use trial and error to
find the value of k:
Factors of 5: 1 5
Factors of 6: 1 2 3 6
Factors of 7: 1 7
Factors of 8: 1 2 4 8
Factors of 9: 1 3 9
Thus, k = 9, and the sum of the factors of k is 1 + 3 + 9 = 13.
correct answer A)13
Answer: (A) 13
Question: A 15 lt mixture contains water with 20% of alcohol.If 5 more lts of water added to the mixture what is the percentage of alcohol?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: Initially the mixture contains 20% of 15=15*(20/100)=3 lts of alcohol
after mixing another 5 lts of water...
the total liquid is 20 lts..
so alcohol percentage=(3/20)*100=15%
ANSWER:B
Answer: (B) 15%
Question: Two pipes can fill a tank in 12 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?
(A) 5.5 Hours
(B) 7.5 Hours
(C) 8.5 Hours
(D) 9.5 Hours
(E) 6.5 Hours
Rationale: In 1 hour it fill 1/12 + 1/12 - 1/20 = 7/60
So fill tank fillup in 60/7 = 8.5 Hours
ANSWER:C
Answer: (C) 8.5 Hours
Question: A set of 17 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
(A) 32
(B) 37
(C) 40
(D) 45
(E) 50
Rationale: The correct answer is D.
A set of 17 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
Given 15 different integers, lets say
n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12, n13, n14, n15
Also given median is 25 i.e. n8 = 27
n1, n2, n3, n4, n5, n6, n7, 25, n9, n10, n11, n12, n13, n14, n15
As each integer is different we need to find the maximum values for all those numbers before the median.
the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..
18, 19, 20, 21, 22, 23, 24, 25, n9, n10, n11, n12, n13, n14, n15
Also given the range is 25 i.e. n15 - n1 (18) = 27
The maximum value n15 can have is 27 + n1 (18) = 45
D
Answer: (D) 45
Question: P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 140 days, in how many days can R alone complete the remaining work?
(A) 50 days
(B) 102.7 days
(C) 100 days
(D) 150 days
(E) 80 days
Rationale: P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days
Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days
P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 390 days
P works for 60 days--> 60/200 work done => 30%
Q works for 140 days--> 140/250 work done => 56%
260% work left ... R alone will take 26% * 395 = 102.7 days
Answer is (B)
Answer: (B) 102.7 days
Question: Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of b - a ?
(A) -10
(B) 10
(C) -19
(D) 20
(E) 21
Rationale: Yes! there is really a faster way to solve it.
Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2
Here A = sum of even ints from 2 to 20, inclusive
number of even ints = 10,
first int + last int = 2+20 = 22
A = 10*22 / 2 = 110
B = sum of odd ints from 1 to 19, inclusive
number of odd ints = 10,
first int + last int = 1+19 = 20
A = 10*20 / 2 = 100
B - A = 100 - 110 = -10
Ans :A
Answer: (A) -10
Question: A goods train runs at the speed of 72 km/hr and crosses a 300 m long platform in 26 sec. What is the length of the goods train?
(A) 382
(B) 782
(C) 278
(D) 270
(E) 220
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 300)/26 = 20
x = 220 m.
Answer: E
Answer: (E) 220
Question: The successive discounts 20% and 15% are equal to a single discount of?
(A) 22
(B) 27
(C) 32
(D) 997
(E) 232
Rationale: Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.Answer: C
Answer: (C) 32
Question: Find the mean proportional between 25 & 36?
(A) A)59
(B) B)30
(C) C)63
(D) D)65
(E) E)67
Rationale: Formula = √a×b
A = 25 and B = 36
√25×36 = 5 × 6 = 30
B
Answer: (B) B)30
Question: What is the units digit of 222^(333)*333^(222)?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits.
Here's another way to organize the information.
We're given [(2222)^333][(3333)^222]
We can 'combine' some of the pieces and rewrite this product as....
([(2222)(3333)]^222) [(2222)^111]
(2222)(3333) = a big number that ends in a 6
Taking a number that ends in a 6 and raising it to a power creates a nice pattern:
6^1 = 6
6^2 = 36
6^3 = 216
Etc.
Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6.
2^111 requires us to figure out thecycleof the units digit...
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....).
111 = 27 sets of 4 with a remainder of 3....
This means that 2^111 = a big number that ends in an 8
So we have to multiply a big number that ends in a 6 and a big number that ends in an 8.
(6)(8) = 48, so the final product will be a gigantic number that ends in an 4.
Final Answer:
C
Answer: (C) 4
Question: The simple interest on Rs. 26 for 6 months at the rate of 7 paise per rupeeper month is
(A) 1.2
(B) 10.92
(C) 12.98
(D) 12.38
(E) None
Rationale: Sol.
S.I. = Rs. [26 * 7/100 * 6] = Rs. 10.92
Answer B
Answer: (B) 10.92
Question: 1*2+ 2*2^2+ 3*2^3+ 4*2^4……………………+2012*2^2012
(A) 8100312
(B) 8100313
(C) 8100412
(D) 8200312
(E) 8300312
Rationale: take 2 outside as common
we get 2(1+2*1^2+3*1^3+.........2012*1^2012)
then 2(1+2+.....2012)
we get 8100312
ANSWER:A
Answer: (A) 8100312
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
(A) 338
(B) 187
(C) 120
(D) 882
(E) 272
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer: C
Answer: (C) 120
Question: There are 20 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
(A) 10
(B) 30
(C) 190
(D) 60
(E) 90
Rationale: 20 players are there.
two players play one game with one another.
so 20C2=20*19/2
=190
SO OPTION C is correct
Answer: (C) 190
Question: In a sequence, each term is obtained by adding 7 to the preceding one. If the sum of the first 30 terms is equal to 705, what is the result of the addition of the first 40 terms?
(A) 2000
(B) 2250
(C) 2340
(D) 2400
(E) 2440
Rationale: a is first term and d = 7 since the preceding number is always greater than the previous one..
Now 30th term is a+29(7).
Sum of n terms is n/2(first term + last term)and here we have to get sum of 30 terms , we get 30/2 ( a + a+203) = 705 ( given sum of 30 terms is 705)
=> 15(2a+203) = 705
=> 2a+203 = 47
=> 2a=-156
=> a = -78
Now to get sum of first 40 terms , we need to get 40th term value i.e. -78+39(7) = 195.
Sum of first 40 terms = 40/2( -78 + 195) =2340 .
Hence option C is correct answer..
Answer: (C) 2340
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 4 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]
(A)  0.22
(B)  0.44
(C)  0.55
(D)  22
(E)  55
Rationale: A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents;
A half-liter of kerosene costs as much as 8 eggs --> 4 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 8 eggs = 8/12*33 = 22 cents.
Answer: D.
Answer: (D)  22
Question: A cube of side two meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
(A) 2878
(B) 2778
(C) 1000
(D) 8000
(E) 8900
Rationale: Along one edge, the number of small cubes that can be cut
=200/10 = 20
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 20 * 20 * 20 = 8000
Answer: D
Answer: (D) 8000
Question: Evaluate 926 + 9.026 + 0.926 + 9.0026
(A) 944.9755
(B) 944.9655
(C) 944.9565
(D) 946.9565
(E) 944.9546
Rationale: 926 + 9.026 + 0.926 + 9.0026 = 944.9546
Option E
Answer: (E) 944.9546
Question: If x is a whole number, then x²(x² - 1) is always divisible by
(A) multiple of 12
(B) 24
(C) 12 - x
(D) 12
(E) none
Rationale: Solution
Putting x = 12,we get 2²(2² - 1)	= 12.
So, x²(x² - 1) is always divisible by 12.
Answer D
Answer: (D) 12
Question: For how many positive integers is the number of positive divisors equal to the number itself ?
(A) none
(B) one
(C) two
(D) three
(E) cannot be determined
Rationale: The factors of 1: {1}. 1 factor. WORKS!
The factors of 2: {1,2}, 2 factors. WORKS!
The factors of 3: {1,3}, 2 factors. Doesn't work
The factors of 4: {1,2,4}, 3 factors. Doesn't work
As we can see, if an integer n has n factors, then the factors of n must be: {1, 2, 3,....., n)
So, we can quickly see that the only positive integers that meet this criterion are 1 and 2
Answer:B
Answer: (B) one
Question: If the average (arithmetic mean) of x^2, 2x^2, and 3x^2 is 200, what is the value of x?
(A) 10
(B) 12
(C) 15
(D) 20
(E) 25
Rationale: AM of x^2, 2x^2 and 3x^2 = x^2 + 2x^2 + 3x^2 / 3 = 6x^2/3
Given that 2x^2 = 200
x^2 = 100
x = 10
Answer is A
Answer: (A) 10
Question: The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 3 terms of the sequence?
(A) 201/100
(B) 99/100
(C) 100/101
(D) 1/10000
(E) 3/4
Rationale: Easy task and accomplish
X1=1-1/2
x2=1/2-1/3
x3=1/3-1/4
sum=X1+X2+X3=1-1/2+1/2-1/3+1/3-1/4= 3/4
E is the answer
Answer: (E) 3/4
Question: Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
(A) 7/125
(B) 4/125
(C) 4/25
(D) 3/25
(E) 2/25
Rationale: The number of ways to select w, x, and y is: 5*5*5=125
The number of ways to choose three different numbers from the set is 5C3=10.
There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.
P(w < x < y) = 10/125 = 2/25
The answer is E.
Answer: (E) 2/25
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
(A) 5/5
(B) 5/9
(C) 5/21
(D) 5/98
(E) 5/1
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer:B
Answer: (B) 5/9
Question: Walking at the rate of 3 kmph a man cover certain distance in 6hr 40min. Running at a speed of 18 kmph the man will cover the same distance in.
(A) 40 min
(B) 25 min
(C) 54 min
(D) 65 min
(E) 58 min
Rationale: Distance = Speed * time
3*20/3= 20km
New Speed = 18 kmph
Therefore time = 20/18 = 10/9= 54min
Answer : C.
Answer: (C) 54 min
Question: The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: For any given day, only the guards patrolling on the previous day won't be available. So, 2 guards who patrolled on Friday won't be available. We are thus left with 5 guards.
To choose 2 out of 5, we will have 5C2 = 10 different pairs.
The answer is C.
Answer: (C) 10
Question: If 20 liters of chemical X are added to 80 liters of a mixture that is 30% chemical X and 70% chemical Y, then what percentage of the resulting mixture is chemical X?
(A) 32%
(B) 35%
(C) 38%
(D) 41%
(E) 44%
Rationale: The amount of chemical X in the solution is 20 +0.3(80) = 44 liters.
44 liters / 100 liters = 44%
The answer is E.
Answer: (E) 44%
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
(A) 3/7
(B) 4/9
(C) 4/7
(D) 5/11
(E) 6/11
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10)	= 4/7
C)
Answer: (C) 4/7
Question: It takes Jake 15 minutes to do one oil change, and it takes Bob 10 minutes. If Jake and Bob both begin doing oil changes at exactly 10:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?
(A) 10:00 a.m.
(B) 10:15 a.m.
(C) 10:30 a.m.
(D) 10:45 a.m.
(E) 11:00 a.m.
Rationale: Since Jake will finish s oil changes after s × 15 minutes and Bob will finish c oil changes after c × 10 minutes, they both will finish doing an oil change at the same time when s × 15 = c × 10. Since s and c must be integers (they represent the number of oil changes finished) this question is asking you to find a common multiple of 15 and 10. The question asks for the first time they will finish a car simultaneously, so you must find the least common multiple. The least common multiple of 15 and 10 is 30, so in the context of the question, this would be 30 minutes. Therefore, the first time they will finish changing the oil of a car at the same time is 10:00 + 30 minutes, or 10:30 a.m. The answer is (C).
Answer: (C) 10:30 a.m.
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 80 kg
(B) 85 kg
(C) 95 kg
(D) 100 kg
(E) 105 kg
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
B)
Answer: (B) 85 kg