mathewhe/aqua_rat huggingface dataset:
Question: A group of 5 friends—Archie, Betty, Jerry, Moose, and Veronica—arrived at the movie theater to see a movie. Because they arrived late, their only seating option consists of 3 middle seats in the front row, an aisle seat in the front row, and an adjoining seat in the third row. If Archie, Jerry, or Moose must sit in the aisle seat while Betty and Veronica refuse to sit next to each other, how many possible seating arrangements are there?
(A) 32
(B) 36
(C) 48
(D) 72
(E) 120
Rationale: First, place one person in the isle seat - 3 possibilities.
Second, place the two girls Betty and Veronica (more specifically separate them) and then place the remaining two persons - the girls can sit either in the middle seats, one seat apart, or one girl in the third row and then the other girl with the remaining two guys in the middle seats - which is 2*2! + 2*3! = 16.
Total number of possibilities 3*16 = 48.
Answer C
Answer: (C) 48
Question: Mr. Peterson deposits $ 200 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
(A) $118.00
(B) $120.00
(C) $242.00
(D) $122.00
(E) $140.00
Rationale: Using Formula - A = P(1+r/n)^nt
Given
P=200
n=2
t=1
r=0.2
Substituting value in formula
A = 200(1+0.2/2)^2
A= 242.00$=C
Answer: (C) $242.00
Question: Vijay sells a cupboard at 14% below cost price. Had he got Rs.2086 more, he would have made a profit of 14%. What is the cost price of the cupboard?
(A) 7458
(B) 7456
(C) 7450
(D) 7454
(E) 7453
Rationale: Explanation:
Cost price = 2086/(0.14 + 0.14) = 2086/0.28
= Rs.7450
ANSWER: C
Answer: (C) 7450
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
(A) 1266
(B) 3000
(C) 2866
(D) 2999
(E) 2678
Rationale: 4 --- 2000
5 --- ? => 3000
Answer: B:
Answer: (B) 3000
Question: In a kilometer race, A beats B by 100 meters or 10 seconds. What time does A take to complete the race?
(A) 90 sec
(B) 190 sec
(C) 290 sec
(D) 490 sec
(E) 390 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/100
= 100 sec.
Time taken by A = 100 - 10
= 90 sec.
Answer:A
Answer: (A) 90 sec
Question: A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B. Which of the following could be the difference of A and B ?
(A) 72
(B) 46
(C) 33
(D) 24
(E) 92
Rationale: A and B are positive two-digit integers such that the tens digit in A is the same as the units digit in B, and the units digit in A is the same as the tens digit in B:
A = 10x + y
B = 10y + x
A - B = (10x + y) - (10y + x) = 9(x - y). As you can see the difference must be a multiple of 9. Only option A is a multiple of 9.
Answer: A.
Answer: (A) 72
Question: Find the average of first 4 multiples of 8?
(A) 20
(B) 12.6
(C) 22.5
(D) 31.3
(E) 40.8
Rationale: average = (8+16+24+32)/4 = 20
Answer is A
Answer: (A) 20
Question: A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 3 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought.
(A) 2/11
(B) 4/15
(C) 6/17
(D) 8/21
(E) 10/25
Rationale: The total number of ways to sell 6 bottles from 10 is 10C6 = 210.
The number of ways to sell 3 bottles of apple juice is 6C3*4C3 = 20*4 = 80
P(selling 3 bottles of apple juice) = 80/210 = 8/21
The answer is D.
Answer: (D) 8/21
Question: You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 5 coins. How many coins do you have at the end?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Solution
Start with 11 coins.
Sharon takes 3 coins from you: 11 - 3 = 8 coins.
Steven takes 5 coins from you: 8 - 5 = 3 coins.
So you have 3 at the end.
Correct answer : B
Answer: (B) 3
Question: A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 8% of bananas were rotten. Find the percentage of fruits in good condition?
(A) 92.5%
(B) 87.8%
(C) 85.2%
(D) 96.8%
(E) 78.9%
Rationale: Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 8% of 400
= 8/100 × 400
= 3200/100
= 32
Therefore, total number of rotten fruits = 90 + 32 = 122
Therefore Number of fruits in good condition = 1000 - 122 = 878
Therefore Percentage of fruits in good condition = (878/1000 × 100)%
= (87800/1000)%
= 87.8%
Answer:B
Answer: (B) 87.8%
Question: A trader bought a car at 20% discount on its original price. He sold it at a 30% increase on the price he bought it. What percent of profit did he make on the original price?
(A) A)4%
(B) B)12%
(C) C)14%
(D) D)20%
(E) E)22%
Rationale: Original price = 100
CP = 80
S = 80*(130/100) = 104
100 - 104 = 4%
A)
Answer: (A) A)4%
Question: A package contains 8 black and 12 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 5/9
(B) 3/5
(C) 6/8
(D) 7/9
(E) 1/3
Rationale: Let number of balls = (8+12) = 20.
Number of white balls = 12.
P (drawing a white ball) =	12/20=3/5
B
Answer: (B) 3/5
Question: In an acoustics class, 120 students are male and 100 students are female. 25% of the male students and 20% of the female students are engineering students. 20% of the male engineering students and 25% of the female engineering students passed the final exam. What percentage of engineering students passed the exam?
(A) 5%
(B) 10%
(C) 16%
(D) 22%
(E) None of these
Rationale: Explanation :
The number of female engineering students in the class is (20/100)×100=20.
Now, 25% of the female engineering students passed the final exam: 25.
Hence, the number of female engineering students who passed is 5.
There are 120 male students in the class. And 25% of them are engineering students.
Hence, the number of male engineering students is (1/4)×120=30.
Now, 20% of the male engineering students passed the final exam :- 20.
Hence, the number of male engineering students who passed is 6.
Hence, the total number of engineering students who passed is:
(Female Engineering students who passed)+ (Male Engineering students who passed)
=>5+6=11.
The total number of engineering students in the class is:
(Number of female engineering students)+ (Number of male engineering students)=
=>30+20=50
Hence, the percentage of engineering students who passed is :-
=>(Total number of engineering students passed/ Total number of engineering students) ×100.
=>(11/50)×100.
=> 22%.
Answer : D
Answer: (D) 22%
Question: The edge of a cube is 3a cm. Find its surface?
(A) 24a8
(B) 24a4
(C) 24a1
(D) 54a2
(E) 24a7
Rationale: 6a2 = 6 * 3a * 3a = 54a2
Answer:D
Answer: (D) 54a2
Question: If f is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
(A) √n + 1
(B) n + 1
(C) n^2 + 1
(D) f + 2√f + 1
(E) n^2 + 2n + 1
Rationale: If f is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
f = (x)^2 where x is a positive integer
To calculate -
(x+1)^2 = x^2 + 2x + 1
root(f) = x
Ans - f + 2 root(f) + 1
This should beD
Answer: (D) f + 2√f + 1
Question: x+(1/x) = 3 find x^2 + (1/x^2)
(A) 2.25
(B) 7
(C) 4.25
(D) 5.25
(E) 6.25
Rationale: squaring on both sides (x+1/x)^2=3^2
x^2+1/X^2=9-2
x^2+1/X^2=7
ANSWER:B
Answer: (B) 7
Question: Peter read W books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
(A) W > 35N
(B) W < N − 35
(C) W > N + 35
(D) W = N − 35
(E) W = N + 35
Rationale: Peter read W books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
A. W > 35N
B. W < N − 35
C. W > N + 35
D. W = N − 35
E. W = N + 35
Since Peter read more books than Nikki we have W>N. Moreover since Peter reads 35 more books than Nikki easily we can have W=N+35.
So the answer is (E).
Answer: (E) W = N + 35
Question: There are 4 physics books and 1 chemistry book on shelf P and 3 physics books on shelf Q. One book is moved from shelf P to shelf Q. A student picks up a book from shelf Q. What is the probability that the chemistry book is taken by the student?
(A) 1/9
(B) 1/10
(C) 1/12
(D) 1/15
(E) 1/20
Rationale: P(a chemistry book is moved to shelf Q) = 1/5
P(a chemistry book is then chosen from shelf Q) = 1/4
P(the student takes a chemistry book) = 1/5 * 1/4 = 1/20
The answer is E.
Answer: (E) 1/20
Question: If 3a – 2b – 4c = 32 and √3a-√(2b+2c)=4, what is the value of a + b + c?
(A) 3
(B) 9
(C) 10
(D) 12
(E) 14
Rationale: when we look at the two equations, we can relize some similarity, so lets work on it..
3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32
{√3a-√(2b+2c)}{√3a+√(2b+2c)}=32..
or 4*√3a+√(2b+2c)=32..
or √3a+√(2b+2c)=8..
now lets work on these two equations
1)√3a-√(2b+2c)=4..
2)√3a+√(2b+2c)=8..
A) add the two eq..
√3a+√(2b+2c)+√3a-√(2b+2c)=12..
2√3a=12..
or √3a=6..
3a=36..
a=12.
B) subtract 1 from 2..
√3a+√(2b+2c)-√3a+√(2b+2c)=4..
2√(2b+2c)=4..
√(2b+2c)=2..
2b+2c=4..
or b+c=2..
from A and B a+b+c=12+2=14..
D
Answer: (D) 12
Question: If a car had traveled 35 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 105 km, at what speed did it travel?
(A) 50 kmh
(B) 55 kmh
(C) 60 kmh
(D) 65 kmh
(E) 70 kmh
Rationale: Time = Distance/Speed
Difference in time = 1/2 hrs
105/x - 105/(x + 35) = 1/2
Substitute the value of x from the options. --> x = 70 --> 105/70 - 105/105 = 3/2 - 1 = 1/2
Answer: E
Answer: (E) 70 kmh
Question: To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of Y dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?
(A) Y/T
(B) Y/(T-S)
(C) SY/(T-S)
(D) SY/T(T-S)
(E) Y(T-S)/T
Rationale: Since no absolute values are given in the question we can replace the given parameters with assumed numbers,
Let Total colleagues be 100 (T)
Let total contribution be 600 (Y) (point to note is that its total cost not per person)
Those who dont pay are S (30)
Per person cost = Y/T = 600/100 = 6
So cost for those who failed to pay = (Y/T) * S = SY/T = 30*6=180
The equation for people who would bear the total cost after S people fail = (T-S)=70
There fore the solution is (SY/T)/ (T-S) = SY/T(T-S) = 180/70
Answer D
Hope this helps !!!
Answer: (D) SY/T(T-S)
Question: The ratio of two quantities is 2 : 3. If each of the quantities is increased by 6, what is the ratio of the new quantities?
(A) 2 : 3
(B) 6 : 7
(C) 8 : 9
(D) 8 : 3
(E) It cannot be determined from the information given
Rationale: let quantities are 2x and 3x
ratio of quantities after each is increased by 6 = (2x+6)/(3x+6)
For x = 1, (2x+6)/(3x+6) = 8/9
For x = 2, (2x+6)/(3x+6) = 10/12
The value of final expression is dependent on the value of x which can't be determined as per given information. Hence, The answer can not be determined
Answer: Option E
Answer: (E) It cannot be determined from the information given
Question: If $1000,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
(A) 10,000(x^n)
(B) 10,000(x/100)^n
(C) 10,000n(x/100)
(D) 1,000,000n(x/100)
(E) 10,000n(1+x/100)
Rationale: I think answer D is for compound interest (which i assumed)
and answer D is for simple interest because it is not compounding.
Answer: (D) 1,000,000n(x/100)
Question: How many bricks each measuring 30cm x 12cm x 10cm, will be needed to build a wall 6m x 4m x 20.5m
(A) 5655
(B) 1366
(C) 6444
(D) 7266
(E) None of these
Rationale: Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (600 x 400 x 20.5) / (30 x 12 x 10) = 1366
Answer: B
Answer: (B) 1366
Question: A and B starts a business with Rs.8000 each, and after 5 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 22:13
(C) 23:12
(D) 36:23
(E) 11:10
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 5 months and then withdraws Rs.4000. So, the investment of B for remaining 13 months is Rs.4000 only.
A : B
8000*18 : (8000*5) + (4000*13)
144000 : 92000
A:B = 36:23
ANSWER:D
Answer: (D) 36:23
Question: When 1/10 percent of 1,000 is subtracted from 1/10 of 1,000, the difference is
(A) 10
(B) 100
(C) 999
(D) 99
(E) 9
Rationale: (1/10)*1000 - (1/10)%*1000 =
100 - (1/1000)*1000 =
100 - 1 = 99
The answer is D.
Answer: (D) 99
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:8
(B) 3:4
(C) 3:5
(D) 3:2
(E) 3:1
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B
=6000 : 8000 => 3:4
Answer:B
Answer: (B) 3:4
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 9 a.m.
(B) 10 a.m.
(C) 10.30 a.m.
(D) 11 a.m.
(E) 11.30 a.m
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
=> 45x = 135
=> x = 3.
So, they meet at 10 a.m.
Answer: Option B
Answer: (B) 10 a.m.
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 11
(B) 16
(C) 18
(D) 10
(E) 14
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Answer:B
Answer: (B) 16
Question: Quarters (US $ 0.25) are stacked in 18 columns. The first column has 10 quarters and each subsequent column has 3 quarters more than the previous column. Find the total number of quarters.
(A) 648
(B) 630
(C) 578
(D) 639
(E) 646
Rationale: Number of coins in the 18 columns forms an AP with first number 10 and last 61
Avg is 35.5 and the total number of coins is 35.5*18
Answer is D
Answer: (D) 639
Question: In a room are five chairs to accommodate 3 people, one person to a chair. How many seating arrangements are possible?
(A) 45
(B) 60
(C) 72
(D) 90
(E) 120
Rationale: I actually solved this problem by the following thoughts (derived from factorials):
First Person: 5 Chairs to choose
Second Person: 4 Chairs to choose
Third Person: 3 Chairs to choose
Then I simply multiplied this values and got the answer. Basically it’s 5! – 2!.=60
Answer: B.
Answer: (B) 60
Question: A can do a job in 15 days and B can do it in 30 days. A and B working together will finish twice the amount of work in days?
(A) 20
(B) 22 1/2
(C) 22 1/0
(D) 22 1/9
(E) 22 1/1
Rationale: 1/15 + 1/30 = 3/30 = 1/10
10= 10 *2 = 20 days
Answer: A
Answer: (A) 20
Question: A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(A) 50%
(B) 40%
(C) 60%
(D) 70%
(E) 45.45%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 110 - (60)
= 50
Now, we need to calculate 50 is what percent of 110.
=> 50/110 x 100 = 45.45 %
ANSWER:E
Answer: (E) 45.45%
Question: For integers x and y, when x is divided by y, the remainder is odd. Which of the following statement is not wrong?
(A) x is odd
(B) xy is odd
(C) x and y share no common factors other than 1
(D) either integer x or integer y is odd
(E) The sum x + y is odd
Rationale: either integer x or integer y is odd
D
Answer: (D) either integer x or integer y is odd
Question: A miniature roulette wheel is divided into 9 equal sectors, each bearing a distinct integer from 1 to 9, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun three times, approximately what is the probability that the product of the three winning sectors’ integers will be even?
(A) 50%
(B) 67%
(C) 83%
(D) 90%
(E) 96%
Rationale: The only way to have an odd product is if all 3 integers are odd.
P(odd product) = 5/9*5/9*5/9 = 125/729
P(even product) = 1 - 125/729 = 604/729 which is about 83%
The answer is C.
Answer: (C) 83%
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability T that exactly two visitors will buy a pack of candy?
(A) 0.343
(B) 0.147
(C) 0.189
(D) 0.063
(E) 0.027
Rationale: 3C2 * (3/10)^2 * 7/10
= 3 * 9/100 * 7/10
= 189/1000
= 0.189=T
Answer - C
Answer: (C) 0.189
Question: Find the average of all the numbers between 9 and 26 which are divisible by 5.
(A) 15
(B) 19
(C) 18
(D) 22
(E) None
Rationale: Sol.
Average = (10 + 15 + 20 + 25 / 4) = 70 / 4 = 17.5
Answer C
Answer: (C) 18
Question: Reduce 4128/4386 to its lowest terms
(A) 14/13
(B) 13/17
(C) 16/17
(D) 13/18
(E) None of these
Rationale: Explanation:
HCF of 4128 and 4386
4128)4386(1
4128
-----
258)4128(16
4128
----
0
Hence HCF of 4128 and 4386 is 258.
4128/258 = 16
4386/258 = 17
4128/4386 = 16/17
Answer: Option C
Answer: (C) 16/17
Question: If xy+5z = x(y+z), which of the following must be true?
(A) 1. x=0 and z=0
(B) 2. x=5 and z=0
(C) 3. y=1 and z=0
(D) 4. x=1 or y=0
(E) 5. x=1 or z=0
Rationale: xy+5z=x(y+z)
xy+5z=xy+xz
5z=xz
it means x=5 or z=0
Answer B
Answer: (B) 2. x=5 and z=0
Question: There are 23 balls in a box: 10 balls are green, 8 are blue and 5 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?
(A) 7/21
(B) 4/13
(C) 3/13
(D) 5/13
(E) 6/13
Rationale: If 1 green and 1 blue ball are taken from the box, then there are 9 green, 7 blue and 5 white balls, a total of 21 balls. If one ball is selected at random, the probability that it is blue is given by 7 / 21
Answer : A
Answer: (A) 7/21
Question: Find the value of y from (12)^3 x 6^4÷432 = y?
(A) 5618
(B) 5232
(C) 5889
(D) 5184
(E) 5132
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
D
Answer: (D) 5184
Question: Express Airlines has a transcontinental flight between Big City and Urbana - a distance of 1,500 km that it completes in three hours. Akatsuki is going from her home in Urbana to a convention in Big City that starts 5 hours after her plane leaves for Big City and ends 6 hours later. Akatsuki's plane suffers a mechanical failure and is forced to land at the Middlebrook airport, located 750 km away from both Big City and Urbana. What's the longest amount of time that Akatsuki can wait for repairs before she misses her convention?
(A) 10.5 hours
(B) 6 hours
(C) 5 hours
(D) 4.5 hours
(E) 3 hours
Rationale: Airplane's rate of speed: 1,500/3 = 500 km/h
Distance between Middlebrook and Big City: 750 km
Travel time between Middlebrook and Big City/Urbana: 750/500 = 1.5 hours
Time into flight: 1.5 hours.
Time until convention begins: 5 - 1.5 = 4.5 hours
Time until convention ends: 4.5 + 6 = 10.5 hours
IMO, the correct answer is "A."
Answer: (A) 10.5 hours
Question: Compute the number of distinct line segments that can be drawn inside a square such that
the endpoints of the segment are on the square and the segment divides the square into two
congruent triangles.
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: Cutting along opposite corners are the only valid ways, so there are 2 such pairs.
correct answer D
Answer: (D) 2
Question: If v is an integer, which of the following must be an even integer?
(A) v^2-v-1
(B) v^2-4v+6
(C) v^2-5v+5
(D) v^2+3v+8
(E) v^2+2v+10
Rationale: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: v^2-v-1 = -1 { If v = 1 }
B: v^2-4v+6 = 3 { If v = 1 }
C: v^2-5v+5 = 1 { If v = 1 }
D: v^2+3v+8 = 12 { If v = 1 }v^2+3v+8 = 18 { If v = 2 }
E: v^2+2v+10 = 13 { If v = 1 }
Thus the only possible answer is (D)
Answer: (D) v^2+3v+8
Question: Varma can read a book in k minutes. What part of the book can he read in 12 minutes?(k>12)
(A) (k - 8)/k
(B) k/8
(C) 8 + k
(D) 12/k
(E) 8/k
Rationale: Option D
Explanation:
Part of the book he can read in 1 minute = 1/k
Part of the book he can read in 12 minutes =12/k.
Answer: D
Answer: (D) 12/k
Question: Remainder of (6^17+17^6)/7= ?
(A) 2
(B) 1
(C) 0
(D) 3
(E) 4
Rationale: 6^17/7 = (7-1)^17/7 => (-1)^17/7 = -1/7
17^6/7 = (2*7+3)^6/7 = 3^6/7 = 27^2/7 =(4*7-1)^2/7 =(-1)^2/7 = 1/7
so, (6^17+17^6)/7 = (-1+1)/7 => 0/7 rem = 0
ANSWER:C
Answer: (C) 0
Question: A certain pilot flew 400 miles to City K at an average speed of 450 miles per hour with the wind and made the trip back at an average speed of 250 miles per hour against the wind. Which of the following is closest to the pilot’s average speed, in miles per hour, for the round-trip?
(A) 280
(B) 290
(C) 300
(D) 310
(E) 320
Rationale: Avg speed = total distance/ total time
total distance = 800
total time = 400/450 + 400/250 = 112/45
=> avg speed = (800*45)/112 = 320(approx)
ans is E
Answer: (E) 320
Question: In a bag there are 3 Snicker's bars and 2 Milky Way bars. What is the probability of choosing at least one Snickers when choosing two consecutive candy bars randomly?
(A) 9/10
(B) 16/20
(C) 2/5
(D) 3/5
(E) ½
Rationale: P(at least one Snicker's Bar) = 1 - P(no Snicker's Bar, so 2 Milky Way Bars) = 1- 2/5*1/4 = 9/10.
Answer: A.
Answer: (A) 9/10
Question: The number of permutations of the letters of the word 'MESMERISE' is?
(A) 9!/(2!)2 3!
(B) 9!/(2!)2 8!
(C) 9!/(8!)2 3!
(D) 8!/(2!)2 3!
(E) 9!/(2!)2 1!
Rationale: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = 9!/(2!)2 3!
Answer: A
Answer: (A) 9!/(2!)2 3!
Question: A password for a computer is six digits from 0 and 9. The six digit number is a prime number. What is the approximate probability that the last digit is a 3?
(A) 1/4
(B) 1/6
(C) 1/10
(D) 1/20
(E) 1/50
Rationale: If the last digit is 0, 2, 4, 6, or 8, the number is even and therefore not prime. If the last digit is 5, the number is divisible by 5 and therefore not prime. The only possibilities are 1, 3, 7, and 9. So the probability is approximately 1/4 (answer A). We say approximately because there is a certain degree of randomness in the distribution of prime numbers.
Answer: (A) 1/4
Question: The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what ia the pice of each of these two books ?
(A) 10,12
(B) 10,16
(C) 10,18
(D) 10,19
(E) 10,91
Rationale: Explanation:
Total pice of the two books = Rs. [(12 x 10) - (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
let the price of one book be Rs. x
Then, the price of other book = Rs. (x + 60% of x) = Rs. = Rs.
So,
The prices of the two books are Rs. 10 and Rs. 16
Answer: B) 10,16
Answer: (B) 10,16
Question: A train covers a distance of 15 km in 10 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?
(A) 240m
(B) 150 m
(C) 120 m
(D) 200 m
(E) 165 m
Rationale: Speed = (15/10 * 60) km/hr
= (90 * 5/18) m/sec
= 25 m/sec.
Length of the train
= 20 * 10
= 200m.
Answer: D
Answer: (D) 200 m
Question: If |4x+2| = 46, what is the sum of all the possible values of x?
(A) 2
(B) -1
(C) 4
(D) -5
(E) 6
Rationale: There will be two cases
4x+2= 46 or 4x+2 = -46
=> x =11 or x= -12
sum of both the values will be -12 +11 = -1
Answer is B
Answer: (B) -1
Question: Total of ages of A,B and C at present is 90 years. If ratio of this ages is 2 : 3 : 4 what will be the age of C after 5 years?
(A) 45 years
(B) 42 years
(C) 40 years
(D) 37 years
(E) None of the above
Rationale: 2+3+4=9
4*(90/9)=40yrs
after 5yrs=45
ANSWER:A
Answer: (A) 45 years