mathewhe/aqua_rat huggingface dataset:
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is 1/4 empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent of the gasoline in the tank is brand Z?
(A) 31.25%
(B) 30%
(C) 40%
(D) 50%
(E) 45%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/4
3rd step: brand Z is (1/2)*(1/4) + 1/2 =5/8
4th step: brand Z is (1/2)*(5/8) = 5/16
Answer (A)
Answer: (A) 31.25%
Question: A soccer store typically sells replica jerseys at a discount of 30 percent to 40 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50
Rationale: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 30
and 0.8x = 32
so lowest sale price is 32, which is 40% of 80
hence, C is the answer
Answer: (C) 30
Question: A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 40-sided polygon have?
(A)  875
(B)  740
(C)  1425
(D)  2025
(E)  2500
Rationale: There's a direct formula for this.
Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.
Here, n = 40.
Plugging it in, we get 740 diagonals!
Answer (B).
Answer: (B)  740
Question: The bankers discount of a certain sum of money is Rs. 18 and the true discount on the same sum for the same time is Rs. 15. The sum due is:
(A) 89
(B) 90
(C) 91
(D) 92
(E) 93
Rationale: Sum = (B.D*T.D)/(B.D-T.D)
(18*15)/18-15;
90
ANSWER:B
Answer: (B) 90
Question: A 2member committee comprising of one male & one female member is to be constitute out of 5 males and 3females. Among st the females. Ms.A refuses to be a member of the committee in which Mr.B is taken as the member. In how many different ways can the committee be constituted ?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 19
Rationale: 5C1 * 3C1 -1
= 15-1
= 14
B
Answer: (B) 14
Question: Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A and B combined. Machine D processes work three times as fast as Machine C; Machine D’s work rate is also exactly four times Machine B’s rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 6 hours and 20 minutes. If all four machines work together on the same job simultaneously, how many minutes will it take all of them to complete it?
(A) 15
(B) 17
(C) 19
(D) 21
(E) 24
Rationale: C = A + B
D = 3C = 3(A+B) = 4B
Then B = 3A and C = 4A
The combined rate of the four machines is A + 3A + 4A + 12A = 20A
Machine A can complete the work in 380 minutes, so its rate is 1/380 of the work per minute.
The combined rate is 20/380 = 1/19 so the work will be completed in 19 minutes.
The answer is C.
Answer: (C) 19
Question: At what percent age above the C.P. must an article be marked so as to gain 33% after allowing a customer a discount of 5%?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 40%
Rationale: Let C.P. = $100
Then, S.P. = $133
Let marked price be $x
Then, 95% of x = 133
95x/100 = 133
x = 133*100/95 = 140
Marked price = 40% above the C.P.
Answer is E
Answer: (E) 40%
Question: A student has to obtain 40% of the total marks to pass. He got 150 marks and failed by 50 marks. The maximum marks are?
(A) 500
(B) 650
(C) 400
(D) 575
(E) 610
Rationale: Let the maximum marks be x
Then, 40% of x = 150+50
40x/100 = 200
x = 500
Answer is A
Answer: (A) 500
Question: In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 225 and the slope of line segment AC is 4/3, what is the length of AB?
(A) 12
(B) 180
(C) 24
(D) 28
(E) 40
Rationale: Slope = Change in Vertical Direction/Change in Horizontal Direction = 4/3
Change in Vertical Direction = 4x = AB
Change in Horizontal Direction = 3x = BC
AB^2 + BC^2 = 225^2
16x^2 + 9x^2 = 225^2
25x^2 = 225^2
x^2 = 25*9^2
x = 45
Therefore AB = 45*4 = 180
Answer: B
Answer: (B) 180
Question: In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?
(A) 1 : 2
(B) 2 : 1
(C) 1 : 3
(D) 3 : 1
(E) 2 : 3
Rationale: Explanatory Answer
Let there be 1 litre of the solution after mixing 20% methyl alcohol and 50% methyl alcohol..
If the concentration of methyl alcohol in it is 40%, then 0.4 litres of the resultant mixture is methyl alcohol.
Let x litres of the solution containing 20% methyl alcohol be mixed with (1 - x) litres of the solution containing 50% methyl alcohol to get 1 litre of the solution containing 40% methyl alcohol.
X litres of 20% methyl alcohol solution will contain 20% of x = 0.2x litres of methyl alcohol in it.
(1 - x) litres of 50% methyl alcohol solution will contain 50% of (1- x) = 0.5(1 - x) litres of methyl alcohol.
The sum of these quantities of methyl alcohols added up to the total of 0.4 litres in the resultant mixture.
Therefore, 0.2x + 0.5(1 - x) = 0.4 litres
0.2x + 0.5 - 0.5x = 0.4
0.5 - 0.4 = 0.5x - 0.2x
x = 0.1/0.3 = 1/3 litres
And 1 - x = 1 - 1/3 = 2/3 litres.
So, the two solutions are mixed in the ratio of 1 : 2.
correct choice is (A)
Answer: (A) 1 : 2
Question: A call center has two teams. Each member of Team A was able to process 7/5 calls as compared to each member of Team B. If Team A has 5/8 as many number of call center agents as Team B, what fraction of the total calls was processed by Team B?
(A) 3/2
(B) 3/4
(C) 8/15
(D) 1/2
(E) 1/5
Rationale: Let team B has 8 agents, so team A has 5 agents
Let each agent of team B picked up 5 calls, so total calls by team B = 40
So, each agent in Team A picked up 7 calls, so total calls for team A = 35
Fraction for team B = 40/(40+35) = 8/15 = Answer = C
Answer: (C) 8/15
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) Rs.547
(B) Rs.548
(C) Rs.527
(D) Rs.540
(E) Rs.522
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer: D
Answer: (D) Rs.540
Question: A man goes downstream at 13 kmph, and upstream8 kmph. The speed of the stream is
(A) 0kmph
(B) 4kmph
(C) 16kmph
(D) 2.5kmph
(E) 26kmph
Rationale: Speed of the stream = 1/2(13-8)kmph
=2.5kmph.
correct option :D
Answer: (D) 2.5kmph
Question: A student committee on academic integrity has 72 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: xC1 * (x-1)C1=72
x^2 -x -72 =0
(X-9) (X+8) = 0
X= 9 , -8
-8 can't possible.
C
Answer: (C) 9
Question: If x is equal to the sum of the integers from 20 to 30, inclusive, and y is the number of EVEN integers from 20 to 30, inclusive, what is the value of x+y ?
(A) 171
(B) 281
(C) 361
(D) 461
(E) 561
Rationale: sum s= n/2{2a+(n-1)d} = 11/2{2*20+ (11-1)*1} =11*25=275 =X
number of even number =( 30-20)/2 +1 = 6= Y
X+Y = 275+6 =281
B
Answer: (B) 281
Question: Pipes P and Q can fill a tank in 10 and 20 hours respectively. Pipe Q can empty it in 24 hours. If all the three pipes are opened together, then the tank will be filled in what time?
(A) 9 3/7
(B) 5 2/7
(C) 5 6/7
(D) 9 3/13
(E) 3
Rationale: Pipe----------P---------Q--------R--------------(P+Q-R)--
Time--------10--------20-------24----------------x
*
Rate---------12--------6---------5---------------13
Work--------120------120------120--------------120
Time required to fill the tank if all the 3 pipes are open = 120/13
= 9 3/13
Ans -D
Answer: (D) 9 3/13
Question: All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 156 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
(A) 1248
(B) 1723
(C) 1129
(D) 2613
(E) 1372
Rationale: A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 156 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 156 = 3k + 156 => 2k = 312 => k = 156
The initial quantity of milk in A = 8k = 8 * 156 = 1248 liters.
Answer: (A) 1248
Question: When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in a hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of a?
(A) 3/4
(B) 1[1/5]
(C) 1[2/5]
(D) 1[3/4]
(E) 2
Rationale: Rate*Time=Work
Let Painter W's rate be W and Painter X's rate be X
R*T = Work
W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2
X * a = 1 => X = 1/a
When they both work together then their rates get added up
Combined Rate = (W+X)
R*T = Work
(W+X) * 3/4 = 1
=> W+X = 4/3
=> 1/2 + 1/a = 4/3
=> 1/a = (8-3)/6 = 5/6
=> a = 6/5 = 1[1/5]
Answer B
Answer: (B) 1[1/5]
Question: A case contains c cartons. Each carton contains b boxes, and each box contains 400 paper clips. How many paper clips are contained in 2 cases?
(A) 400bc
(B) 400b/c
(C) 800bc
(D) 800b/c
(E) 800/bc
Rationale: 2 cases * c cartons/case * b boxes/carton * 400 clips/box = 800bc paper clips
The answer is C.
Answer: (C) 800bc
Question: Find the ratio of the surfaces of the inscribed and circumscribed spheres about a cube.
(A) 1:2
(B) 1:3
(C) 1:4
(D) 1:5
(E) None of these
Rationale: Answer: A)
Answer: (A) 1:2
Question: Two boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction. What time will they take to be 20 km apart?
(A) 10
(B) 11
(C) 14
(D) 15
(E) 20
Rationale: Explanation:
Relative speed = 7.5 - 5.5 = 2 kmph (because they walk in the same direction)
distance = 20 km
time = distance / speed=20/2=10 hr
Answer :A
Answer: (A) 10
Question: If the average of r, b, c, 14 and 15 is 12. What is the average value of r, b, c and 29
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: r+b+c+14+15 = 12*5 = 60
=>r+b+c = 60-29 = 31
r+b+c+29 = 31+29= 60
Average = 60/4 = 15
Answer D
Answer: (D) 15
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 17:6
(B) 18:5
(C) 17:9
(D) 17:1
(E) 17:3
Rationale: P:Q = 85000 : 15000 = 17:3.Answer:E
Answer: (E) 17:3
Question: A man bought some apples of which 13% of then were rotten. He sold 75% of the balance and was left with 261 apples. How many apples did he have originally?
(A) 1000
(B) 1100
(C) 1200
(D) 1300
(E) 1400
Rationale: Ans.
Now take initial number of apples x.
Then x×(100−13)%×(100−75)%=261
⇒x=261/(87)%×(25)%⇒261×100×100/87×25⇒1200
Answer C
Answer: (C) 1200
Question: Two isosceles Triangles have equal vertical angles and their areas are in the ratio 16:49. Find the ratio of their corresponding heights .
(A)  4/5
(B)  5/4
(C)  3/2
(D)  4/7
(E)  2/3
Rationale: We are basically given that the triangles are similar.
In two similar triangles, the ratio of their areas is the square of the ratio of their sides and also, the square of the ratio of their corresponding heights.
Therefore, area/AREA=height^2/HEIGHT^2=16/49 --> height/HEIGHT=4/7.
Answer: D.
Answer: (D)  4/7
Question: 13 Examiners check 650 abswer books in 5 days working 4 hours daily. How many more Examiners are required to check 7200 answer books in 12 days working 3 hours daily
(A) 48
(B) 68
(C) 67
(D) 47
(E) 57
Rationale: Needed Examiners =(7200*5*4*13 )/650*12*3 =80 More Examiners needed =80-13 =67 Answer : C
Answer: (C) 67
Question: Mantu starts a month with provisions expected to last for the entire month. After few days, it is discovered that the provisions will, in fact short by 12 days and it is calculated that if the stock of provisions left is immediately tripled, it will be possible to exactly make up for the shortfall. If the stock of provisions left is doubled instead of being tripled, and simultaneously the strength of the Mantu is decreased by 25, then the provisions will fall short by :-
(A) 2 days
(B) 1 days
(C) 3 days
(D) 4 days
(E) None of these
Rationale: Explanation :
At the moment the shortfall is discovered, let there be n days worth of provision left.
Now, 3n−n=2n extra days worth of provisions lasts for the 12 additional days.
Thus, 3n lasts for 18 days i.e. 18 days are left for the month to end.
But if the provisions are only doubled and the strength becomes (3/4)th then the provisions will last for :-
=>12×(4/3).
=>16 days.
i.e. short fall of 18−16= 2 days.
Answer : A
Answer: (A) 2 days
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is ?
(A) 8 kmph
(B) 6 kmph
(C) 7.5 kmph
(D) 5.5 kmph
(E) 6.5 kmph
Rationale: Explanation:
Speed of the stream = 1
Motor boat speed in still water be = x kmph
Down Stream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph
ANSWER IS B
Answer: (B) 6 kmph
Question: A train passes a station platform in 46 sec and a man standing on the platform in 16 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 227
(B) 240
(C) 460
(D) 450
(E) 455
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 16 = 240 m.
Let the length of the platform be x m . Then,
(x + 240 )/46= 15=> x = 450 m.
Answer:D
Answer: (D) 450
Question: A dealer originally bought 80 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many dollars was each battery sold?
(A) 3q/160
(B) 3q/2
(C) 120q
(D) q/80
(E) 120/q
Rationale: The cost of each battery was q/80.
Each battery was sold for 1.5q/80 = 3q/160.
The answer is A.
Answer: (A) 3q/160
Question: Two persons A and B can complete a piece of work in 15 days and 30 days respectively. If they work together, what part of the work will be completed in 5 days?
(A) 1/8
(B) 1/3
(C) 1/6
(D) 1/2
(E) 5/3
Rationale: A's one day's work = 1/15
B's one day's work = 1/30
(A + B)'s one day's work = 1/15 + 1/30 = 1/10
The part of the work completed in 5 days = 5 (1/10) = 1/2.
Answer:D
Answer: (D) 1/2
Question: The cost of 4 bags and 12 purses is Rs.2800, what is the cost of 10 bags and 30 purses?
(A) Rs.7000
(B) Rs.7500
(C) Rs.3800
(D) Rs.7900
(E) None of these
Rationale: Explanation:
Cost of 4 bags + 12 purses = Rs.2800
Multiply each term by 5/2, we get,
Cost of 10 bags + 30 purses = Rs.7000.
Answer: Option A
Answer: (A) Rs.7000
Question: Find the principle on a certain sum of money at 6% per annum for 2 2/5 years if the amount being Rs.1120?
(A) 979
(B) 1288
(C) 2778
(D) 2682
(E) 1021
Rationale: 1120 = P [1 + (6*12/5)/100]
P= 979
Answer: A
Answer: (A) 979
Question: The cost of one photocopy is $0.02. However, a 25% discount is offered on orders of more than 100 photocopies. If Steve and David have to make 80 copies each, how much will each of them save if they submit a single order of 160 copies?
(A) $0.32
(B) $0.40
(C) $0.45
(D) $0.48
(E) $0.54
Rationale: If Steve and David submit separate orders, each would be smaller than 100 photocopies, so no discount. Each would pay (80)*($0.02) = $1.60, or together, a cost of $3.20 --- that's the combined "no discount cost".
If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer = (B).
Answer: (B) $0.40
Question: If a man crosses a 700 m long street in 5 minutes. What is his speed?
(A) 7 km/hr
(B) 7.1 km/hr
(C) 7.2 km/hr
(D) 8 km/hr
(E) 8.4 km/hr
Rationale: distance = 700 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time=700/300=2.3m/s=2.3×18/5 km/hr=8.4 km/hr
E
Answer: (E) 8.4 km/hr
Question: Population is 24000. Population increases by 10% every year, then the population after 3 years is?
(A) 26630
(B) 26640
(C) 36644
(D) 31944
(E) 26844
Rationale: population after 1st year = 24000*10/100 = 2400 ===> 24000+2400 = 26400
population after 2nd year = 26400*10/100 = 2640 ===> 26400+2640 = 29040
population after 3rd year = 29040*10/100 = 2904 ===> 29040+2904 = 31944
ANSWER:D
Answer: (D) 31944
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) 276
(B) 188
(C) 120
(D) 982
(E) 129
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer: C
Answer: (C) 120
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
(A) 7
(B) 8!
(C) 9
(D) 3
(E) 4
Rationale: Total number of letters
= 8
Using these letters the number of 8 letters words formed is 8P8
= 8!.
Answer:B
Answer: (B) 8!
Question: How many multiples of 3 are there between 15 and 246 ?
(A) 128
(B) 94
(C) 89
(D) 76
(E) 60
Rationale: It should be mentioned whether 15 and 246 are inclusive.
If 15 and 246 are inclusive, then the answer is (246-15)/3+1=78.
If 15 and 246 are NOT inclusive, then the answer is (243-18)/3+1=76.
Since OA is D, then we have NOT inclusive case.
Answer: (D) 76
Question: Tom opened a shop investing Rs.3000. Jose joined him 2 months later, investing Rs.4500. They earned a profit of Rs.6300 after completion of one year. What will be Jose's share of profit?
(A) 3500
(B) 2800
(C) 3251
(D) 4251
(E) 3508
Rationale: SoL = ~s- So Anju’s share = [5/9] x 6300 = 3500
A
Answer: (A) 3500
Question: x, a, z, and b are single digit positive integers. x = 1/5 a. z = 1/5 b. (10a + b) – (10x + z) could NOT equal
(A) 36
(B) 33
(C) 44
(D) 64
(E) 56
Rationale: a=5x , b =5z therefore(5x*10+5z) - (10x +z) = (5-1) (10x+z) =.(10x+Z)
number should be divisible by 4
B
Answer: (B) 33
Question: A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was?
(A) 3887
(B) 2768
(C) 15000
(D) 76887
(E) 16711
Rationale: Principal = (100 * 5400) / (12 * 3) = Rs. 15000
Answer: C
Answer: (C) 15000
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
(A) 240
(B) 88
(C) 66
(D) 528
(E) 22
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240.Answer:A
Answer: (A) 240
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 77.
(A) 1666
(B) 1555
(C) 1777
(D) 1444
(E) 1333
Rationale: Number of odd numbers between 1 and 59 is (77+1)/2=38
Therefore Sum of odd numbers 38*38= 1444
ANSWER: D
Answer: (D) 1444
Question: A box has 10 black and 10 white balls. What is the probability of getting two balls of the same color?
(A) 9/18
(B) 9/19
(C) 9/12
(D) 9/11
(E) 9/13
Rationale: ANSWER:B
Answer: (B) 9/19
Question: The G.C.D. of 1.08, 0.32 and 0.9 is:
(A) 0.02
(B) 0.9
(C) 0.18
(D) 0.108
(E) None
Rationale: EXPLANATION
Given numbers are 1.08, 0.32 and 0.90. H.C.F. of 108, 32 and 90 is 2,
H.C.F. of given numbers = 0.02.
Answer A
Answer: (A) 0.02
Question: If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Rationale: 0.[u]225[/u = 0.225225225.....
Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.
Answer E
Answer: (E) 5
Question: List L: ABC, BCA, CAB
In list L above, there are 2 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
(A) 47
(B) 114
(C) 152
(D) 161
(E) 488
Rationale: Let's try to sum the 2 given numbers taking their place values into account:
(100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B)
= 100(A + B + C) + 10(A + B + C) + (A + B + C)
= 111*(A + B + C)
We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152
Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases.
Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3
A, B and C are all even. 2+4+8 = 14. Factors 2 and 7
Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get.
D
Answer: (D) 161
Question: In 1950, Richard was 4 times as old as Robert. In 1955, Richard was 3 times as old as Robert. In which year was Richard 1.3 times as old as Robert?
(A) 1960
(B) 1965
(C) 1970
(D) 1975
(E) 2040
Rationale: In 1950: Ri = 4 Ro -------------- eq1
In 1955: Ri +5 = 3(Ro+5)---------eq2
Thus in 1950, solving eq1 and eq2
Ro= 10 , Ri =40
Now for each year we can calculate:
1960: Ri = 50 , Ro =20
1965: Ri= 55, Ro=25
2040: Ri= 100, Ro = 130
Thus Ans:E
Answer: (E) 2040
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, x
(A) 29
(B) 31
(C) 23
(D) 43
(E) 53
Rationale: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 38 + 5 = 43.
Answer: (D) 43
Question: How many 4-digit numbers are completely divisible by 7?
(A) 1354
(B) 1286
(C) 1178
(D) 1224
(E) None
Rationale: Solution: 4- digit numbers divisible by 7 are: 1001, 1008, 1015….. 9996.
This is an A.P. in which a=1001, d=7, l=9996.
Let the number of terms be n.
Then Tn=9996. .'. a+(n-1)d=9996
=> 1001+(n-1)7= 9996
=>(n-1)7=8995
=>(n-1)= 8995/7= 1285
=> n=1286.
.'. number of terms =1286.
Answer B
Answer: (B) 1286
Question: A certain club has 10 members, including Rarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Rarry will be either the member chose to be secretary or the member chose to be treasurer?
(A) 1/720
(B) 1/80
(C) 1/10
(D) 1/9
(E) 1/5
Rationale: In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9
Probability to become a secretary = (9/10 * 1/9) = 1/10
Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8
probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10
Since, the problem is saying Rarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E
Answer: (E) 1/5
Question: If a and b are positive integers and (2^a)^b = 2^7, what is the value of 2^a*2^b?
(A) 16
(B) 32
(C) 64
(D) 256
(E) 128
Rationale: 2^ab =2^7 therefore ab=7 either a=1 or 7 or b=7 or 1
therefore 2^a* 2^b = 2^(a+b)= 2^8 =256
D
Answer: (D) 256
Question: The average temperature of the first three days is 27∘C and that of the next three days is 29∘C. If the average of the whole week is 28.5∘C, the temperature of the last day of the week is :
(A) 10.5∘C
(B) 21∘C
(C) 31.5∘C
(D) 42∘C
(E) None
Rationale: Explanation:
Let the seventh day temperature be x. Then total temperature for the whole week is
3×27+3×29+1×x=7×28.5
x = 31.5
Correct Option: C
Answer: (C) 31.5∘C