mathewhe/aqua_rat huggingface dataset:
Question: Set A {3,3,3,4,5,5,5} has a standard deviation of 1. What will the standard deviation be if every number in the set is multiplied by 5?
(A) A)1
(B) B)2
(C) C)4
(D) D)8
(E) E)5
Rationale: Points to remember -
1. If oneAdd/Subtractthe same amont from every term in a set, SD doesn't change.
2. If oneMultiply/Divideevery term by the same number in a set, SD changes by same number.
Hence the answer to the above question is E
Answer: (E) E)5
Question: If a certain manager had received a 10% raise instead of the 12% raise that she actually received, her salary would have been $65000. What was her actual salary after the raise?
(A) 60000
(B) 66181.8
(C) 66800
(D) 68000
(E) 59000
Rationale: salary(let X) included 10% increase can be written as
(1+10/100)X=65000
X=65000/1.10------>59090.9
if there is 12% rise in 59090.90
then the salary now is 12% of 59090.9
12*59090.90/100=7090.90
then toal salary after increment=59090.9+7090.90----->66181.8
Ans B
Answer: (B) 66181.8
Question: Multiplication of 2 numbers is 9375 and the quotient, when the larger one is divided by the smalleris 15. Find the sum of the numbers?
(A) 200
(B) 300
(C) 400
(D) 500
(E) 600
Rationale: Let the numbers be x and y.
Then, xy = 9375 and	x	= 15.
y
xy	=	9375
(x/y)	15
y2 = 625.
y = 25.
x = 15y = (15 x 25) = 375.
Sum of the numbers = x + y = 375 + 25 = 400.
C
Answer: (C) 400
Question: x-1-x=5-then-x-4-3x-3-5x-2-3x-1-x-4-1
(A) -20
(B) -22
(C) -25
(D) -27
(E) -29
Rationale: x-1-x=5
x(1-1/x-1)=5
x(x-1-x)=5x
x^2-x-x^2=5x
cancelling x^2 we get -x=5x
6x=0
so x=0
now -x-4-3x-3-5x-2-3x-1-x-4-1= -13x-20
=0-20
= -20
ANSWER:A
Answer: (A) -20
Question: (164)^2 - (163)^2 =
(A) 1
(B) 100
(C) 229
(D) 327
(E) 349
Rationale: Using the formula:
(a+1)^2 - a^2 = 2a+1
So, Answer = 163*2 + 1
= 326+1 = 327 = Answer = D
Answer: (D) 327
Question: 45 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?
(A) 80 litres
(B) 90 litres
(C) 120 litres
(D) 170 litres
(E) None of these
Rationale: Explanatory Answer
To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*45 = 60 litres.
However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.
i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.
Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*60 = 90 litres.
Answer B
Answer: (B) 90 litres
Question: If q and s are positive integers such that (2^q)(4^s) = 16, then 2q + s =
(A)  2
(B)  3
(C)  4
(D)  5
(E)  6
Rationale: lets get the eq into simplest orm..
(2^q)(4^s) = 16..
(2^q)(2^2s) = 2^4..
or q+2s=4..
since q and s are positive integers, only q as 2 and s as 1 satisfy the Equation..
so 2q+s=2*2+1=5..
D
Answer: (D)  5
Question: Find the smallest positive integer n such that tn of the arithmetic sequence 20,19¼ ,18½ ,… is nagative
(A) 27
(B) 28
(C) 29
(D) 30
(E) 31
Rationale: Here we have , a= 20 = d = 19 ¼-20=-3/4
We	want	to	find	the	first	positive	integer	n such thattn<0
20+(n-1)(-3/4)<0
n>27.33
hence, 28th term is first negative term
ANSWER B 28
Answer: (B) 28
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19.7
(B) 19.9
(C) 20.9
(D) 21.9
(E) 22
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A)
Answer: (A) 19.7
Question: If A(k)=(2k+1)^K, and k=0, what is the value of A(A(A(k)))?
(A) 343
(B) 199
(C) 121
(D) 69
(E) 249
Rationale: A(A(A(0)))=A(A(1))=A(3)=(6+1)^3=343.
Thus, the answer is A.
Answer: (A) 343
Question: What is the sum of the different positive prime factors of 1080?
(A) 6
(B) 4
(C) 8
(D) 9
(E) 10
Rationale: I think answer is E: 10
1080 = 2*2*2*3*3*3*5
Sum of theDIFFERENTpositive prime factors = 2 + 3 + 5 = 10
Answer: (E) 10
Question: The side of a square has the length of 7. What is the area of the region shaded?
(A) 48-8π
(B) 48-6 π
(C) 24+6π
(D) 48-7π
(E) 64-8π
Rationale: The area of a square whose side is 7 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded
The correct answer is D.
Answer: (D) 48-7π
Question: Two friends plan to walk along a 33-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 20% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: If Q complete x kilometers, then P completes 1.2x kilometers.
x + 1.2x = 33
2.2x=33
x = 15
Then P will have have walked 1.2*15=18 km.
The answer is D.
Answer: (D) 18
Question: The ratio between the sale price and the cost price of an article is 6:5. What is the ratio between the profit and the cost price of that article?
(A) 2:9
(B) 1:5
(C) 3:6
(D) 2:0
(E) 2:1
Rationale: Let C.P. = Rs. 5x and S.P. = Rs. 6x.
Then, Gain = Rs. x
Required ratio = x : 5x = 1:5
Answer:B
Answer: (B) 1:5
Question: How many 7 in between 1 to 90?
(A) 19
(B) 20
(C) 22
(D) 23
(E) 24
Rationale: 7,17,27,37,47,57,67,
70,71,72,73,74,75,76,77(two 7's),78,79,87,
19 7's between 1 to 90
ANSWER:A
Answer: (A) 19
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :
(A) 2500
(B) 2700
(C) 2900
(D) 3100
(E) 3500
Rationale: Explanation:
Total number of votes = 7500
Given that 20% of Percentage votes were invalid
=> Valid votes = 80%
Total valid votes = 7500 X80/100
1st candidate got 55% of the total valid votes.
Hence the 2nd candidate should have got 45% of the total valid votes
=> Valid votes that 2nd candidate got = total valid votes x 45/100
=7500 X 80/100 X 45/100 =2700
ANSWER IS B
Answer: (B) 2700
Question: If the compound interest on a certain sum of money for 4 years at 10% per annum be Rs. 993, what would be the simple interest?
(A) Rs. 880
(B) Rs. 890
(C) Rs. 1200
(D) Rs. 900
(E) None
Rationale: Let P = Principal
A - Amount
We have a = P(1 + R/100)3 and CI = A - P
ATQ 993 = P(1 + R/100)3 - P
? P = 3000/-
Now SI @ 10% on 3000/- for 4 yrs = (3000 x 10 x 4)/100
= 1200/-
Answer: C.
Answer: (C) Rs. 1200
Question: ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 6. How many different 5-digit numbers areSvennumbers?
(A) 20
(B) 80
(C) 160
(D) 220
(E) 250
Rationale: ASvennumber is defined as a five-digit number which goes according to the following rules: the leftmost digit is even, any digit to the right of an even digit must be an odd digit, and any digit to the right of an odd digit can only be one of the digits 1 or 7. How many different 5-digit numbers areSvennumbers?
4/9*5/10*2/10*2/10*2/10=160/9000
B. 80
Answer: (B) 80
Question: How many words can be formed from the letters of the word "AFTER", so that the vowels never comes together
(A) 48
(B) 52
(C) 72
(D) 120
(E) None of these
Rationale: Explanation:
We need to find the ways that vowels NEVER come together.
Vowels are A, E
Let the word be FTR(AE) having 4 words.
Total ways = 4! = 24
Vowels can have total ways 2! = 2
Number of ways having vowel together = 48
Total number of words using all letter = 5! = 120
Number of words having vowels never together = 120-48
= 72
Option C
Answer: (C) 72
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
(A) 9:37
(B) 9:31
(C) 9:33
(D) 9:78
(E) 9:32
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B
Answer: (B) 9:31
Question: The speed of a train that is 250 meter in length passing from a railway platform is 150 km/hour. The length of platform is 500 meter. What is the time taken by the train to cross the platform?
(A) 1 minute
(B) 2 minute
(C) 3 minute
(D) 4 minute
(E) 5 minute
Rationale: The time starts when the head of first compartment enters the platform from one side. To cover platform, the train has to cover its own length plus the length of the compartment, that is 250 meter + 500 meter = 750 meter. To cover 150 km or 150x1000 meter=15000 meter, train takes 60 minutes or 60x60=3600 seconds. Therefore, to cover 750 meter, the train would take 180 seconds or 3 minutes.
Answer: C.
Answer: (C) 3 minute
Question: The difference between the place values of two sixes in the numerical 81369206 is
(A) 0
(B) 599
(C) 5994
(D) 59994
(E) None of them
Rationale: Required difference = (60000-6)
=59994.
Answer is D
Answer: (D) 59994
Question: A 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds. What is the length of the platform?
(A) 39.9
(B) 37.88
(C) 35
(D) 38.88
(E) 38.09
Rationale: Speed = [200 / 42] m/sec = 100/21 m/sec.
Let the length of the platform be x meters.
Then, x + 200 / 50 = 100/21
21(x + 200) = 5000 è x = 38.09 m. Answer: E
Answer: (E) 38.09
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 28 sec
(B) 37 sec
(C) 17 sec
(D) 23 sec
(E) 27 sec
Rationale: E
Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds.
Answer: (E) 27 sec
Question: Pipe A can fill a tank in 4 hours, pipe B in 6 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 1.2
(B) 1.4
(C) 1.6
(D) 1.8
(E) 2
Rationale: The part filled by A + B + C in 1 hour is 1/4 + 1/6 + 1/12 = 1/2
All the three pipes together will fill the tank in 2 hours.
The answer is E.
Answer: (E) 2
Question: In a business, A and C invested amounts in the ratio 4 : 3 , whereas the ratio between amounts invested by A and B was 1 : 2 . If Rs 182100 was their profit, how much amount did B receive?
(A) 97120
(B) 100000
(C) 90000
(D) 95000
(E) None of these
Rationale: Explanation :
Assume that investment of A = x
Then, investment of B =2x
Investment of C = 3x/4
A:B:C = 1x : 2x : 3x/4 = 1 : 2 : 3/4 =4 : 8 : 3
B's share = 182100 * 8/(4+8+3) = 182100*8/15
= 12140*8 = 97120.
Answer : Option A
Answer: (A) 97120
Question: The third proportional to 1 and 2 is?
(A) 2
(B) 1
(C) 4
(D) 8
(E) 7
Rationale: (2*2)/1 = 4
Answer: C
Answer: (C) 4
Question: 160% of 5/8 =
(A) 0.2
(B) 0.5
(C) 0.6
(D) 0.75
(E) 1.0
Rationale: Should be simple.
1.6*5/8 = 8/8 =1.0
Correct Option : E
Answer: (E) 1.0
Question: What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?
(A) 3
(B) 27
(C) 30
(D) 21
(E) 18
Rationale: Explanatory Answer
Useful result pertaining to remainders
You can solve this problem if you know this rule about remainders.
Let a number x divide the product of A and B.
The remainder will be the product of the remainders when x divides A and when x divides B.
Using this rule,
The remainder when 33 divides 1044 is 21.
The remainder when 33 divides 1047 is 24.
The remainder when 33 divides 1050 is 27.
The remainder when 33 divides 1053 is 30.
∴ the remainder when 33 divides 1044 * 1047 * 1050 * 1053 is 21 * 24 * 27 * 30.
Note: The remainder when a number is divided by a divisor 'd' will take values from 0 to (d - 1). It cannot be equal to or more than 'd'.
The value of 21 * 24 * 27 * 30 is more than 33.
When the value of the remainder is more than the divisor, final remainder will be the remainder of dividing the product by the divisor.
i.e., the final remainder is the remainder when 33 divides 21 * 24 * 27 * 30.
When 33 divides 21 * 24 * 27 * 30, the remainder is 30.
Choice C
Answer: (C) 30
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) 399
(B) 272
(C) 999
(D) 277
(E) 311
Rationale: Answer: Option C
Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999 Answer: C
Answer: (C) 999
Question: P is three times as fast as Q and working together, they can complete a work in 18 days. In how many days can Q alone complete the work?
(A) 24
(B) 77
(C) 88
(D) 55
(E) 778
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 18 days, which means Q can do the work in 72 days.
Hence, P can do the work in 24 days.
Answer:A
Answer: (A) 24
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 19/35
(C) 18/30
(D) 78/35
(E) 18/55
Rationale: Explanation:
If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer: Option A
Answer: (A) 18/35
Question: A composer’s guild is planning its spring concert, and ten pieces have been submitted for consideration. The director of the guild knows that they will only have time to present four of them. If the pieces can be played in any order, how many combinations of pieces are possible?
(A) 40
(B) 210
(C) 1090
(D) 5040
(E) 10000
Rationale: Combination question..
10C4 = 210..
ANS option B is correct..
Answer: (B) 210
Question: Kathleen can paint a room in 2 hours, and Anthony can paint an identical room in 3 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?
(A) 8/15
(B) 4/3
(C) 12/5
(D) 9/4
(E) 15/4
Rationale: (1/2 + 1/3)t=2
t=12/5
Answer: C
Answer: (C) 12/5
Question: 5/4 of all married couples have more than one child. 2/5 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?
(A) 1/5
(B) 1/4
(C) 17/20
(D) 3/5
(E) It cannot be determined from the given information.
Rationale: Plug in simple numbers. Take 100 couples for example.
5/4 of 100 couples have more than one child = 125 couples.
2/5 of 100 couples have more than 3 kids = 40 couples.
This implies that 40 couples are a subset of 125 couples
We need to find couples that have 2 or 3 kids, so essentially, it is 125 - 40 = 85. Fraction will be 85/100 = 17/20.
Option C
Answer: (C) 17/20
Question: Tough and Tricky questions: Exponents.
If 2^m3^m3^m = 9^n, then m/n =
(A) 1/3
(B) 2/3
(C) 1
(D) 3/2
(E) 3
Rationale: I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!
What I did was to test powers of 3 that would lead to 9.
So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n
What I did was test 3 raised to the power of 2 like this:
3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=3/2.
D
Answer: (D) 3/2
Question: The sum of two numbers is 25 and their difference is 13. Find their product.
(A) 104
(B) 114
(C) 315
(D) 325
(E) 400
Rationale: Explanation:
Let the numbers be x and y.
Then x + y = 25 and x - y = 13.
x = 19; y = 6
xy = 19 * 6 = 114
ANSWER IS B
Answer: (B) 114
Question: Find curved surface area of a cylinder with diameter of base 14 cm and height 60 cm.
(A) 2601cm2
(B) 2610cm2
(C) 2620cm2
(D) 2630cm2
(E) 2640cm2
Rationale: Volume = πR2H= π x 72 x 60 = 9240	cm3
Curved surface area = 2πRH = (2 π x 7 x 60) cm2 =2640 cm2
answer :E
Answer: (E) 2640cm2
Question: Raman travelled for 10 hours. He covered the first half of the distance at 20 kmph and remaining half of the distance at 15 kmph. Find the distance travelled by Raman?
(A) 161.42
(B) 181.42
(C) 178.42
(D) 191.42
(E) 171.42
Rationale: Let the distance travelled be x km.
Total time = (x/2)/20 + (x/2)/15 = 10 => x/40 + x/30 = 10 => (3x + 4x)/120 = 10
=> x = 171.42 km
Answer:E
Answer: (E) 171.42
Question: A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings?
(A) 16
(B) 56
(C) 112
(D) 28
(E) 38
Rationale: In 8 different toppings, selecting 2 diff toppings = 8c2
formula is n!/(n-c)!
n = total number of toppings
C = number chosen in a grouping.
n=8 and c=2 so we get
8!/(8-2)! = (8*7*6*5*4*3*2*1)/(6*5*4*3*2*1)
= 8*7 =56
ANSWER:B
Answer: (B) 56
Question: A clock store sold a certain clock to a collector for 30 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 60 percent of what the collector had paid. The shop then sold the clock again at a profit of 90 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $150, for how much did the shop sell the clock the second time?
(A) $1010.46
(B) $505.23
(C) $2020.92
(D) $800.46
(E) $1515.69
Rationale: Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 30% profit.
This means the clocks' selling price was C (1.3) and this becomes cost price for the collector.
Now, when the collector tries to sell the same clock to the store, the store buys it for 60% the price at which the collector bought it.
Thus, you get = 1.3*0.6*C = 0.78 C
Furthermore, the store sells the clock for the second time for 90% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.9 = 1.9 * 0.78 C
Finally given that C - 0.78 C = 150 ----> C = 681.82$
Thus, the cost of the clock the second time around = 1.9*0.78 C = 1.9 * 0.78 * 681.82 = 1010.46$. Hence A is the correct answer.
Answer: (A) $1010.46
Question: Which of the following is not a prime number ?
(A) 2
(B) 3
(C) 11
(D) 19
(E) 20
Rationale: Clearly, 20 is not a prime number.
Answer : E
Answer: (E) 20
Question: in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 11 people all together .how many people can sit in a bus?
(A) 52
(B) 92
(C) 95
(D) 88
(E) 66
Rationale: Right Side =15 seat
Left Side =15-3 (3 few seat in right side)= 12 seat
Total= 15+12= 27
People can seat in 27 seat= 27*3=81
People can seat in Last Seat = 11
Total People can seat= 81+11=92
ANSWER:B
Answer: (B) 92
Question: P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
(A) 8/15
(B) 7/15
(C) 1/15
(D) 3/15
(E) None of these
Rationale: Explanation:
P's 1-day work = 1/15
Q's 1-day work = 1/20
Work done by (P + Q) in 1 day = 1/15 + 1/20 = 7/60.
Work done by them in 4 days = (7/60) * 4 = 7/15.
Work left = 1 - (7/15) = 8/15.
ANSWER IS A
Answer: (A) 8/15
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is
(A) 30 kg
(B) 31 kg
(C) 37 kg
(D) 39 kg
(E) 41 kg
Rationale: Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
B's weight = 31 kg
B)
Answer: (B) 31 kg
Question: In how many different ways can the letters of the word MISSISSIPPI be arranged if the vowels must always be together?
(A) 48
(B) 144
(C) 210
(D) 420
(E) 840
Rationale: The word MISSISSIPPI has 4 I , 4S , 2P and M .
The only vowel present in the word is I and we have to consider 4 I's as a single group
Number of different ways = 8!/(4!*2!)
=(8*7*6*5)/2
=840
Answer E
Answer: (E) 840
Question: Before 6 years, dog A’s age was 4 times of dog B’s age and after 4 years, dog A’s age will be 3 times of dog B’s age. What is the difference of dog A’s age and dog B’s now?
(A) 36
(B) 42
(C) 54
(D) 60
(E) 64
Rationale: A - 6 = 4(B - 6) --> A - 4B = -18.............1
A + 4 = 3(B + 4) --> A - 3B = 8.............2
(2) - (1) --> B = 26 --> A = 3(30)=90
A - B = 90 - 26 = 64
Answer: E
Answer: (E) 64
Question: In the year 1990 there are 5000 men 3000 women 2000 boys. In 1994 men are increased by 20% women are increased by ratio of boys and women?
(A) 11000
(B) 12000
(C) 13000
(D) 14000
(E) 15000
Rationale: total population in year 1990 = 5000+3000+2000=10000
total population in year 1994 =((5000*120/100)+(3000+(3000*2/3))+(2000))
=13000
ANSWER:C
Answer: (C) 13000
Question: A shirt goes on sale for 70% of its original price. One week later, the sale price is marked down 10%. The final price is what percent of the original price?
(A) 63%
(B) 70%
(C) 62%
(D) 50%
(E) 28%
Rationale: Just assume original price is 100.
Sale price = 70
Then it is marked down by 10% = 70-7=63.
Hence it is 63% od the original price. Hence answer is A.
Answer: (A) 63%
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
(A) 1/5
(B) 1/4
(C) 2/5
(D) 3/7
(E) 3./11
Rationale: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.
C
Answer: (C) 2/5
Question: A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price y. The store sold the first 150 copies in the first week at 80% more than y, and then over the next month, sold a 100 more at 20% more than y. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than y. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?
(A)  30% loss
(B)  10% loss
(C)  10% profit
(D)  20% profit
(E)  60% profit
Rationale: [[y(150)(1.8)+y(100)(1.2)+y(150)(0.6)]/400y] - 1
[50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1
[(5.4 + 2.4 + 1.8)/8] - [8/8]
+1.6/8
+20%
answer is D
Answer: (D)  20% profit
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 15
(B) 44
(C) 40
(D) 27
(E) 12
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: C
Answer: (C) 40
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
(A) 17.6 cm
(B) 18.6 cm
(C) 91.5 cm
(D) 16.5 cm
(E) 14.6 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer:C
Answer: (C) 91.5 cm
Question: A man buys a cycle for Rs. 2000 and sells it at a loss of 10%. What is the selling price of the cycle?
(A) 1800
(B) 1420
(C) 1430
(D) 1440
(E) 1540
Rationale: S.P. = 90% of Rs. 2000 = 90/100 x2000= Rs. 1800
answer : A
Answer: (A) 1800
Question: 6 noun, 4 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??
(A) 412
(B) 432
(C) 472
(D) 524
(E) 554
Rationale: we have to choose one from each set. 1 from 6 nouns and 1 from 4 verbs and 1 from 3 adjectives.
then we have to arrange 3 different set in 3! ways.
so,
6c1*4c1*3c1*3!=432
ANSWER:B
Answer: (B) 432