mathewhe/aqua_rat huggingface dataset:
Question: Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 40 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 81
(B) 159
(C) 166
(D) 285
(E) 314
Rationale: I solve it using the tough luck technique:
According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject.
80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=110>80
Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books
What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives.
We picked:
50 Botany Books
65 Zoology Books
40 Geology Books
Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!!
Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick
79*2+1 books
Because, we could have picked the books in following order;
1st book picked: Physics
2nd book picked: Chemistry
3rd book picked: Physics
Thus, Total= 50+65+40+79*2+1=155+1+158=314
Ans:E
Answer: (E) 314
Question: The time a passenger train takes to cross another freight train is twice when the passenger train crosses the freight train running in opposite directions. What is the ratio of their speeds?
(A) 1:3
(B) 3:1
(C) 1:4
(D) 4:1
(E) 1:5
Rationale: let speed of freight train=x and speed of passenger train=y, and sum of their length =s so time=s/(x-y),when both are in same direction and time=s/(x+y) when oppsite direction.from question,s/(x-y)=2.s/(x+y) so solving this we get, x/y=3/1.
so x:y=3:1
ANSWER:B
Answer: (B) 3:1
Question: A person took some amount with some interest for 3 years, but increase the interest for 1%, he paid Rs.240/- extra, then how much amount he took?
(A) Rs.8000/-
(B) Rs.6000/-
(C) Rs.4000/-
(D) Rs.7000/-
(E) None of these
Rationale: Explanation:3 years = Rs.240/-year = 240/3Rate of Interest = 1%100/1% × 240/3 = Rs.8000/-P = Rs.8000/- Answer: Option A
Answer: (A) Rs.8000/-
Question: The present worth of a sum due sometime hence is Rs.576 and the banker’s gain is Rs.16.The true discount is
(A) Rs.36
(B) Rs.72
(C) Rs.48
(D) Rs.96
(E) None
Rationale: Solution
T.D	= √P.W xB.G
= √576 x 16
= 96.
Answer D
Answer: (D) Rs.96
Question: In a certain school, 25% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 36. What is the total number of students in the school?
(A) 72
(B) 80
(C) 120
(D) 150
(E) 100
Rationale: Explanation: Let the number of students be x.
Then, Number of students above 8 years of age = (100 - 25)% of x = 75% of x.
75% of x = 36 + 2/3 of 36
75/100x = 60
x = 80.
Answer: Option B
Answer: (B) 80
Question: If 1+2+3+...+n=n (n+1), then
3 (1+3+5+....+99)=?
(A) 7000
(B) 7250
(C) 7500
(D) 7750
(E) 6750
Rationale: Explanation :
To solve this use the formula of AP,
Sn= (n/2)(a+l) ................(1)
To find n, use
=> Tn= a+(n-1)d
=> 99=1+(n-1)2
=> n=50
Use value of n in (1)
then,
Sn = (50/2)(1+99) = 2500
Ans:- 3(Sn) = 7500
Answer : C
Answer: (C) 7500
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 7. How many different 4-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
A. 20
Answer: (A) 20
Question: Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Mukesh?
(A) 900
(B) 100
(C) 1100
(D) 1200
(E) 1500
Rationale: Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000
=>4:5:3
=>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...]
=> 12:5:6
Share of Rajan => 4600*12/23 = 2400
Share of Rakesh => 4600*5/23 = 1000
Share of Mukesh => 4600*6/23 = 1200
ANSWER:D
Answer: (D) 1200
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.9
(B) 31.7
(C) 31.6
(D) 31.54
(E) 31.1
Rationale: 100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer:C
Answer: (C) 31.6
Question: W, B, C are three consecutive positive integers (W>B>C). What is the value of the expression 2W +B +3C?
(A) 6A+7.
(B) 5A+1.
(C) 5A-1.
(D) 6A-5.
(E) 6W-7.
Rationale: => W+W+(W-1)+3(W-2)
Ans E. 6W-7.
Answer: (E) 6W-7.
Question: Find the compound interest on $ 16,000 at 20% per annum for 9 months, compounded quarterly
(A) 2532
(B) 2552
(C) 2524
(D) 2522
(E) 2512
Rationale: Principal = $ 16000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = $ [16000 x (1+(5/100))^3] = $ 18522.
CI. = $ (18522 - 16000) = $ 2522.
Answer D.
Answer: (D) 2522
Question: Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?
(A) 109
(B) 12
(C) 99
(D) 81
(E) 22
Rationale: Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.
Answer: B
Answer: (B) 12
Question: A man can row 4.8 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?
(A) 1.9
(B) 1.7
(C) 1.2
(D) 1.5
(E) 1.6
Rationale: Speed of boat in still water (b) = 4.8 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.6 km/hr.
Answer: E
Answer: (E) 1.6
Question: What is the area of an equilateral triangle whose one side length is 40?
(A) 100√3
(B) 200√3
(C) 300√3
(D) 350√3
(E) 400√3
Rationale: -> -> The area of an equilateral triangle with one side length of a is √3a2/4. Thus, √3(40^2)/4=400√3 and the answer is E.
Correct Option:	E
Answer: (E) 400√3
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $ 231
(B) $ 545
(C) $ 145
(D) $ 643
(E) $ 112
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
correct answer C
Answer: (C) $ 145
Question: A, B, C are three consecutive positive integers (A>B>C). What is the value of the expression 2A +B - 2C?
(A) 6A+7.
(B) A+3.
(C) 5A-1.
(D) 6A-5.
(E) 6A-7.
Rationale: B = A-1
C= A-2
Putting these values in 2A +B -2C we get A +3
B is the answer
Answer: (B) A+3.
Question: 50, 47, 45, 42, 40, 37, 35, ?
(A) 33
(B) 32
(C) 31
(D) 30
(E) 29
Rationale: This is an alternating number subtraction series. The pattern is -3, -2, -3, -2, ....
The answer is B.
Answer: (B) 32
Question: ramesh,ram,kareem and Mohan collected coins of different countries. they collected 100 together. none collected less than 10.each collected an even number. each collected a different number. based on these, we can say that the number of coins collected by the boy who collected the most could not have exceeded
(A) 54
(B) 64
(C) 58
(D) 60
(E) 62
Rationale: as other three must have collected atleast 10+12+14=36 coins
the number of coins collected by the boy who collected the most could not have exceeded
100-36=64
ANSWER:B
Answer: (B) 64
Question: 64 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 13.25
(B) 28
(C) 30
(D) 13.2
(E) 14
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 64 = 28
ANSWER:B
Answer: (B) 28
Question: A woman is 18 years older than her son. In 3 years, her age will be twice the age of her son. The present age of her son is
(A) 18
(B) 17
(C) 15
(D) 16
(E) 14
Rationale: Explanation:
Let the son's present age be x years. Then, woman's present age = (x + 18) years
=> (x + 18) + 3 = 2(x + 3)
=> x + 21 = 2x + 6
So, x = 15. Answer: C
Answer: (C) 15
Question: Rs.8000 become Rs.9724 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 6 YEARS
(B) 7
(C) 5
(D) 3
(E) 4
Rationale: Explanation:
9724 = 8000(21/20)N
(21/20)4 = (21/20)N => N = 4
Answer: Option E
Answer: (E) 4
Question: Robert ate 7 chocolates, Nickel ate 5 chocolates. How many more chocolates did Robert ate than nickel?
(A) A)4
(B) B)7
(C) C)9
(D) D)5
(E) E)2
Rationale: 7-5=2. Answer is E
Answer: (E) E)2
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of numbers is?
(A) 22
(B) 67
(C) 40
(D) 88
(E) 11
Rationale: Let the numbers be 2x and 3x.
Then, their L.C.M = 6x. So, 6x = 48 or x = 8.
The numbers are 16 and 24.
Hence, required sum = (16 + 24) = 40.
Answer:C
Answer: (C) 40
Question: What is the Positive integer that can be Added by 595 to make it a perfect square?
(A) 2*3*6
(B) 3*2*5
(C) 5*3*3
(D) 2*3
(E) 3*5*4
Rationale: 596 is added to a number that gives a perfect square
Nearest perfect square is 625.
so,625-596=30
30=2*3*5
Option B is answer
Answer: (B) 3*2*5
Question: Two airplanes take off from one airfield at noon. One flies due east at 203 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?
(A) 166
(B) 332
(C) 406
(D) 483
(E) 566
Rationale: C
In two hours:
the plane flying East will be 406 miles away from airport.
the other plane will be 566 miles away from airport.
566/406= ~1.4 = ~sqrt(2)
This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 406 miles apart.C
Answer: (C) 406
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 7
(D) 9
(E) 5
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.Answer: B
Answer: (B) 6
Question: A grocer stacked oranges in a pile. The bottom layer was rectangular with 5 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?
(A)  2
(B)  4
(C)  6
(D)  7
(E)  9
Rationale: Bottom Layer = 5 x 5 = 25
IInd Layer = (5-1) x (5-1) = 16
IIIrd Layer = (4-1) x (4-1) = 9
Answer = 9 = E
Answer: (E)  9
Question: If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction.
(A) 1/12
(B) 1/8
(C) 1/6
(D) 1/4
(E) 1/2
Rationale: X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
ANSWER:A
Answer: (A) 1/12
Question: In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/12 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
(A) 23/30
(B) 11/15
(C) 47/60
(D) 1/6
(E) 2/15
Rationale: 1/5 -- cable TV (This includes some data from video cassette recorder)
1/10 -- video cassette recorder including 1/3(equiped with cable tv) i.e. 1/3(1/5) = 1/15
therefore only video cassette recorder = 1/12 - 1/15 = 1/60
Total = 1/5+1/60+neither cable tv nor videocassette recorders
1 =13/60+ neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-13/60 = 47/60
Hence C.
Answer: (C) 47/60
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1792?
(A) 1600
(B) 2777
(C) 2889
(D) 27670
(E) 2771
Rationale: 1792 = P [1 + (5*12/5)/100]
P= 1600.Answer:A
Answer: (A) 1600
Question: The ratio of ducks and frogs in a pond is 31 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ?
(A) 148
(B) 152
(C) 156
(D) 169
(E) None
Rationale: Solution:
Ratio of Ducks and Frogs in Pond,
= 31 : 39.
Average of Ducks and Frogs in Pond,
= 152.
So, total number of Ducks and Frogs in the Pond,
= 2* 152 = 304.
Therefore,
Number of Frogs, = (304 *39)/70 = 169.
Answer: Option D
Answer: (D) 169
Question: If n is an integer greater than 7, which of the following must be divisible by 3?
(A) 1. n (n+1) (n-4)
(B) 2. n (n+2) (n-1)
(C) 3. n (n+3) (n-5)
(D) 4. n (n+4) (n-2)
(E) 5. n (n+5) (n-6)
Rationale: We need to find out the number which is divisible by three,
In every 3 consecutive integers, there must contain 1 multiple of 3.
So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three
1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1)
2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1)
3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n)
4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1)
5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2)
from the above onlyoption Ais product of consecutive three numbers.
D
Answer: (D) 4. n (n+4) (n-2)
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 four times, approximately what is the probability that the product of the four winning sectors’ integers will be even?
(A) 50%
(B) 67%
(C) 80%
(D) 90%
(E) 95%
Rationale: The only way to have an odd product is if all 4 integers are odd.
P(odd product) = 5/9*5/9*5/9*5/9 = 625/6561
P(even product) = 1 - 625/6561 = 5936/6561 which is about 90%
The answer is D.
Answer: (D) 90%
Question: The sum of the first 50 positive even integers is 2550. What is the sum of even integers from 102 to 200 inclusive?
(A) 5100
(B) 7550
(C) 10100
(D) 15500
(E) 20100
Rationale: First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
2550+(100*50)=7550;ANSWER:B
Answer: (B) 7550
Question: The product of two numbers is 468 and the sum of their squares is 289. The sum of the number is?
(A) A)23
(B) B)25
(C) C)27
(D) D)31
(E) E)35
Rationale: Let the numbers be x and y.
Then, xy = 468 and x2 + y2 = 289.
(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 468) = 1225
x + y = 35.
Option E
Answer: (E) E)35
Question: In what time will a train 120 meters long cross an electric pole, if its speed is 184 km/hr
(A) 5 seconds
(B) 4.5 seconds
(C) 3 seconds
(D) 2.3 seconds
(E) None of these
Rationale: Explanation:
First convert speed into m/sec
Speed = 184*(5/18) = 51 m/sec
Time = Distance/speed
= 120/51 = 2.3 seconds
Option D
Answer: (D) 2.3 seconds
Question: A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally?
(A) 15 days
(B) 16 days
(C) 17 days
(D) 18 days
(E) 19 days
Rationale: clearly 11mornings and 12 afternoons = 23 half days
since 13 days raining means 13 half days.
so 23-13 =10 halfdays ( not effecetd by rain )
so 10 halfdays =5 fulldays
total no. of days = 13+5 =18 days
ANSWER:D
Answer: (D) 18 days
Question: A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose?
(A) 1.4
(B) 1.5
(C) 1.6
(D) 1.8
(E) 1.0
Rationale: Let the speed be 's' and let the distance between rose and poppy be 'x'
The problem boils down to:
Rose to Poppy: s+3=x/6 ------- 1
Daisy to Rose: s=(x+18)/10------ 2
so from 1 we can re write x as x=6s+18
substitute the value of x in 2 gives us s=1.8 m/s
D
Answer: (D) 1.8
Question: A train 100m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
(A) 45kmph
(B) 55kmph
(C) 32kmph
(D) 61kmph
(E) 70kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
100/[(x+5)*5/18] = 6
30(x+5) = 1800
x = 55kmph
Answer is B
Answer: (B) 55kmph
Question: A, B, C hired a car for Rs.520 and used it for 7,8 and 11 hours respectively. Hire charges paid by B were
(A) Rs.140
(B) Rs.160
(C) Rs.180
(D) Rs.220
(E) None
Rationale: Solution
A : B : C	= 7 : 8 : 11.
Hire charges paid by B	= Rs(520×8/26)
= Rs.160.
Answer B
Answer: (B) Rs.160
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.7. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal?
(A) 0.12
(B) 0.24
(C) 0.28
(D) 0.66
(E) 0.72
Rationale: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )
=0.6*0.2+0.4*0.3+0.6*0.7
= 0.12+0.12+0.42
=0.66
D
Answer: (D) 0.66
Question: A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 3.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?
(A) (320 - y)/(5x)
(B) (y +220)/(5x)
(C) 5(80 - y)/(4x)
(D) (y + 400)/(4x)
(E) (4y + 320)/(5x)
Rationale: Ans B
Plug some numbers
Let y = 40 houses and x = 20
then they painted 20 houses per week
as painters were added to the group , the rate of the group increased to 3.25 x => 3.25 * 20 = 65 houses per week
total time they took = (40/20) + (40/65) = 2.6 weeks
Putting the values of x and y in equation B
(y +220)/(5x) = (40+220)/5*20 = 260/100 = 2.6
Answer: (B) (y +220)/(5x)
Question: In the xy-plane, a line has slope 3 and x-intercept 6. What is the y-intercept of the line?
(A) -18
(B) -3
(C) 0
(D) 3
(E) 9
Rationale: Let the line be represented by a general equation y=mx+b, where m = slope (3) and b=y intercept. We are also given the value of x-intercept 6.
Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.
Putting these values in the equation : 0 = 3*6 + b => b = -18. Hence A.
Answer: (A) -18
Question: On a purchase of $110, a store offered a payment plan consisting of a $10 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?
(A) 9.5%
(B) 10.5%
(C) 11.5%
(D) 9.1%
(E) 12.5%
Rationale: 12*10 + 10 = 130
(10/110)* 100 = 9.1
Answer : D
Answer: (D) 9.1%
Question: If the price of an article went up by 50%, then by what percent should it be brought down to bring it back to its original price?
(A) 2/3%
(B) 2/8%
(C) 2/1%
(D) 33.3%
(E) 2/7%
Rationale: Let the price of the article be Rs. 100.
50% of 100 = 50.
New price = 100 + 50 = Rs. 150
Required percentage = (150 - 100)/150 * 100
= 50/150 * 100= 33.33%.
Answer:D
Answer: (D) 33.3%
Question: A man 24 years older than his son. In two year his age will be twice of his son. what is the present age of his son?
(A) 23
(B) 22
(C) 21
(D) 20
(E) 32
Rationale: Correct Answer : B
present age of son = x years
present age of man = ( x +24 )years
In two year his age will be twice of his son.
(x +24)+2=2(x+2)
x=22
Answer: (B) 22
Question: The total of the ages of Jayant, Prem and Saransh is 75 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Prem?
(A) 25 years
(B) 32 years
(C) 34 years
(D) 38 years
(E) None
Rationale: Solution
Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,
(2x + 10)+(3x + 10)+(4x + 10)	= 75.
‹=›9x = 45
x = 5.
∴ Prem's present age = 3x + 10 = 25 years.
Answer A
Answer: (A) 25 years
Question: 6^b + 6^b + 6^b + 6^b + 6^b + 6^b =
(A) 7^b
(B) 7^(b + 1)
(C) 7^(7b)
(D) 6^(b + 1)
(E) 49^B
Rationale: Easy one.
6*6^b = 6^(b+1)
Ans. D
Answer: (D) 6^(b + 1)
Question: A chemical is composed of hydrogen, oxygen and nitrogen. If 20 moles of the chemical is to be made containing twice as much hydrogen as oxygen and three times as much oxygen as nitrogen how many moles of oxygen is required?
(A) 5 moles
(B) 6 moles
(C) 8moles
(D) 2 moles
(E) 1.5 moles
Rationale: Amount of chemical=20 moles
hydrogen=2 oxygen
oxygen=3 nitrogen
hydrogen+oxygen+nitrogen=20
2 oxygen+oxygen+1/3 oxygen=20
10 oxygen=20
oxygen=2
Answer is D
Answer: (D) 2 moles
Question: 3889 + 12.597 - ? = 3854.002
(A) A)47.095
(B) B)47.595
(C) C)47.932
(D) D)47.95
(E) of the above
Rationale: Let 3889 + 12.597 - x = 3854.002.
Then x = (3889 + 12.597) - 3854.002
= 3901.597 - 3854.002
= 47.595.
Answer = B
Answer: (B) B)47.595
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 8 runs. His new average is:
(A) 22 runs
(B) 24 runs
(C) 26 runs
(D) 28 runs
(E) 30 runs
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 8
= 11x + 88 = 10x + 108
= x = 20.
New average = (x + 8) = 28 runs.
Answer:D
Answer: (D) 28 runs
Question: If 1 added to the age of the elder sister, then the ratio of the ages of two sisters becomes 0.5:1, but if 2 is subtracted from the age of the younger one, the ratio becomes 1:3, the age of the younger sister will be?
(A) 7 years
(B) 5 years
(C) 8 years
(D) 10 years
(E) 4 years
Rationale: Explanation :
Let, the age of the elder sister be x year, and younger sister be y year.
Now, according to the question,
y/(x+1)=0.5/1.
=>y/(x+1)=1/2.
=>2y= x + 1
=>x−2y =−1 -------(i)
And,
=>(y−2)/x=1/3.
=>x−3y =−6 -------(ii)
On solving these equations, we get :-
x=9 and y=5
Hence, the age of the younger sister is 5 years.
Answer : B
Answer: (B) 5 years
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 7
(B) 6
(C) 8
(D) 5
(E) 3
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
Answer: (C) 8
Question: There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible?
(A) 100
(B) 90
(C) 50
(D) 45
(E) 25
Rationale: 1. first child out of 10 - 10 possibilities
2. second child out of 9 - 9 possibilities. the total number of pairs = 9*10=90
3. exclude xy yx cases: 90/2=45
Second way
N=10C2=10!/(8!2!)=10*9/2=45
ANS:D
Answer: (D) 45