mathewhe/aqua_rat huggingface dataset:
Question: 16 is what % of 90?
(A) 16
(B) 17.78
(C) 17
(D) 18.5
(E) 18.23
Rationale: We assume that 90 is 100%
assume 'x' is value we looking for
here,
90 = 100% and
x% = 16
therefore,
100/x = 90/16
100/x = 5.625
x = 17.78
B
Answer: (B) 17.78
Question: The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 22 kmph
(B) 40 kmph
(C) 78 kmph
(D) 50 kmph
(E) 23 kmph
Rationale: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph
Answer:D
Answer: (D) 50 kmph
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
(A) 20
(B) 28
(C) 29
(D) 49
(E) 48
Rationale: There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee =
6C3= (6 * 5 * 4)/6 = 20.
Answer:A
Answer: (A) 20
Question: The average age of a class of 24 students is 23 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
(A) 40
(B) 41
(C) 48
(D) 52
(E) 43
Rationale: Total age of all students =24Ã—23
Total age of all students + Age of the teacher =25Ã—24
Age of the teacher
=25Ã—24âˆ’24Ã—23=24(25âˆ’23)=24Ã—2=48
Answer is C.
Answer: (C) 48
Question: Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
S1 ---------------------- 2 ------------------------------------------ 5,000
S2 ---------------------- 5 ------------------- ---------------------- 12,000
S3 ---------------------- 5 ------------------------------------------ 15,000
S4 ---------------------- 4 ------------------------------------------ 16,000
A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What’s the expected number of defective chips in a shipment of 60,000 chips?
(A) 14
(B) 20
(C) 22
(D) 24
(E) 25
Rationale: for a total of 51000 chips (adding S1,S2,S3,S4) total number of defective chips is 17 ((adding defective chips of S1,S2,S3,S4) so ratio is 16/48000 or 1 every 3000 chips.
Keeping this ratio constant for 60000 chips number of defective chips will be (1/3000) * 60000 = 20
B
Answer: (B) 20
Question: 10 2 = 0.3010, the value of log10 80 is:
(A) 1.602
(B) 1.903
(C) 2.903
(D) 3.903
(E) 4.903
Rationale: log10 80	= log10 (8 x 10)
= log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
Answer: Option B
Answer: (B) 1.903
Question: Steve traveled the first 5 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
(A) 53.33 mph
(B) 88 mph
(C) 60 mph
(D) 64 mph
(E) 66.67 mph
Rationale: Average Speed = Total distance/ Total time = (40 * 5 + 80 * 3)/(5 + 3) = 440/5 = 88
Answer: B
Answer: (B) 88 mph
Question: A wheel that has 24 cogs is meshed with a larger wheel of 48 cogs. When the smaller wheel has made 12 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 6
(B) 5
(C) 3
(D) 7
(E) 4
Rationale: A
6
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
48 : 24 :: 12 : x <-> 48 x x = 12 x 24
x = (12x 24)/48
x = 6
Answer: (A) 6
Question: 2+4
(A) 8
(B) 13
(C) 28
(D) 6
(E) 2
Rationale: D
Answer: (D) 6
Question: (1.00001)(0.99999) - (1.00004)(0.99996) =
(A) 0
(B) 10^-10
(C) 3(10^-10)
(D) 15(10^-10)
(E) 3(10^-5)
Rationale: (1.00001*0.99999)-(1.00004*0.99996)
= (1+0.00001)(1-0.00001) - (1+0.00004)(1-0.00004)
= 1 - (0.00001)^2 - 1 + (0.00004)^2
= -(0.0000000001) + (0.0000000016)
= 0.00000000015=15(10^-10)
Answer D
Answer: (D) 15(10^-10)
Question: In a village of 100 households, 75 have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y
(A) 55
(B) 45
(C) 65
(D) 35
(E) 25
Rationale: x= (75+55+80-100-z)/2 for z=0 ->55
y=the same for z=100 ->10
Therefore x-y=45
ANSWER:B
Answer: (B) 45
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 78000, then the share of B is?
(A) A)34500
(B) B)36099
(C) C)36000
(D) D)38007
(E) E)42000
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 78000
Share of B = 6/13 (78000)
= Rs. 36000
Answer:C
Answer: (C) C)36000
Question: A man can row 36 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of the stream?
(A) 14 kmph
(B) 12 kmph
(C) 18 kmph
(D) 1 kmph
(E) None of these
Rationale: Explanation:
Let man's rate upsteam be X kmph
Then his rate of downstream = 3X kmph
Rate still water = 1/2 (3X + X) = 2X
2X = 36
X = 18
Rate of upstream = 18
Rate of downstream = 54
Rate of stream 1/2 ( 54 - 18) = 18 kmph
Answer: Option C
Answer: (C) 18 kmph
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 4704 sq m, the cost of fencing it at 50 ps per meter is?
(A) 287
(B) 1287
(C) 140
(D) 988
(E) 271
Rationale: 3x * 2x = 4704 => x = 28
2(84 + 56) = 280 m
280 * 1/2 = Rs.140
Answer: C
Answer: (C) 140
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 16 years?
(A) 6.25%
(B) 1.25%
(C) 4%
(D) 5%
(E) 3.25%
Rationale: 150 = (750*16*R)/100
R = 1.25%
Answer: B
Answer: (B) 1.25%
Question: A group of 8 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the seven other students from the group?
(A) 5.67%
(B) 3.57%
(C) 15.17%
(D) 2.07%
(E) 2.57%
Rationale: The question basically asks about the probability that Bob and Lisa sit at the ends.
The total # of sitting arrangements is 8!.
Desired arrangement is either BUVWXYZL or LUVWXYZB. Now, UVWXYZ can be arranged in 6! ways, therefore total # of favorable arrangements is 2*6!.
P=(favorable)/(total)=(2*6!)/8!=1/28.
Answer: B.
Answer: (B) 3.57%
Question: Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 1: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?
(A) 3: 10 p.m.
(B) 5: 00 p.m.
(C) 5: 20 p.m.
(D) 5: 35 p.m.
(E) 6: 00 p.m.
Rationale: the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 1:20 +2=3:20
Hence answer is A.Hope i am correct
Answer: (A) 3: 10 p.m.
Question: Hockey Stick and ball cost $50. If the Stick cost $49 more than the ball.
what is the cost of each ?
(A) Hockey Stick $48.50 & ball $1.50
(B) Hockey Stick $49.00 & ball $1.00
(C) Hockey Stick $48.00 & ball $2.00
(D) Hockey Stick $49.50 & ball $0.50
(E) Hockey Stick $41.50 & ball $8.50
Rationale: D
Hockey Stick $49.50 & ball $0.50
Answer: (D) Hockey Stick $49.50 & ball $0.50
Question: A single discount equivalent to the discount series of 20%, 12% and 5% is?
(A) 33.12
(B) 31.1
(C) 31.6
(D) 31.2
(E) 31.9
Rationale: Explanation:
100*(80/100)*(88/100)*(95/100) = 66.88
100 - 66.88 = 33.12
Answer: A
Answer: (A) 33.12
Question: The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 684. What is the banker's discount?
(A) 1240
(B) 1120
(C) 1190
(D) 1634
(E) None of these
Rationale: Explanation :
TD = (BG ×100)/TR = (684×100)/(6×12) = Rs. 950
BG = BD – TD
=> 684= BD - 950
=> BD = 684 + 950 = 1634 Answer : Option D
Answer: (D) 1634
Question: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability that at least one will be orange?
(A) 7/10
(B) 3/5
(C) 2/5
(D) 3/10
(E) 1/10
Rationale: Probability of the first ball being orange = 2/5
The first all is not replaced, hence the total number of balls for the second pick = 1/4
Therefore the total probability is 2/5 x 1/4 = 1/10
Hence E
Answer: (E) 1/10
Question: The average weight of 20 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
(A) 48.79286
(B) 42.25
(C) 50.87364
(D) 51.25
(E) 52.25474
Rationale: Explanation:
Average weight of 20 boys = 50.25
Total weight of 20 boys = 50.25 × 20
Average weight of remaining 8 boys = 45.15
Total weight of remaining 8 boys = 45.15 × 8
Total weight of all boys in the class = (50.25 × 20)+ (45.15 × 8)
Total boys = 20 + 8 = 28
Average weight of all the boys = (50.25×20)+(45.15×8)/28
=
Answer: Option A
Answer: (A) 48.79286
Question: How many factors of 880 are odd numbers greater than 1?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: When factorized, 880 has 6 prime factors. Of these prime factors 2 are odd and 4 are even. Hence total number of odd factors is 2*2(4), which includes 4. The total number of odd factors greater than 1 are 3.(option A)
Answer: (A) 3
Question: The average of six number is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. what is the average of the remaining four number ?
(A) 2.3
(B) 4.6
(C) 4.7
(D) 4.8
(E) None of these
Rationale: solution:
Sum of the remaining four numbers = (3.95 × 6) - [(3.4 × 2) + (3.85 ×2)]
=23.70 -(6.8 + 7.7) = 23.70 - 14.5 = 9.20.
∴ Required average =9.2/4 = 2.3 Answer A
Answer: (A) 2.3
Question: The operation # is defined for all nonzero q and y by #y = q + q/y. If a>0, then 1#(1#a) =
(A) a
(B) a+1
(C) a/(a+1)
(D) (a+2)/(a+1)
(E) (2a+1)/(a+1)
Rationale: q#y = q + q/y. If a>0, then 1#(1#a) =
You can see that a stands for y and 1 stands for q. I like to work with numbers so I did q=1 a=2 and a=y so y=2
1#a= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3
So now you can check by filling in a, which is 2:
A. a --> 2
B. a+1 --> 2+1=3
C. a/(a+1)-->2/(2+1)=2/3
D. (a+2)/(a+1)-->(2+2)/(2+1)=4/3
E. (2a+1)/(a+1)-->(2*2+1)/(2+1)=5/3
So E is the answer.
Answer: (E) (2a+1)/(a+1)
Question: Find the value of x: x² + 4x + 4.
(A) 2
(B) 4
(C) -2
(D) -4
(E) 0
Rationale: That quadratic is factored as follows:x² + 4x +4 = (x+2)(x+2).Lesson 17.Now, it is easy to see that the second factor will be 0 when x = -2.The solution is:x	=	-2 C
Answer: (C) -2
Question: A clerk multiplied a number by ten when ten should have divided it. The answer he got was 100.what should the ans have been?
(A) 3
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: let the number be x
actually form = x/10
but x*10=100
=>x=10
means the number the should be divided is 10
=>the answer would have been (10/10)=1
ANSWER:B
Answer: (B) 1
Question: The sale price at which a store sells an article is 25% more than its cost price. If the sale price is an integer, which of the following cannot be the cost price?
(A) $12
(B) $16
(C) $31
(D) $56
(E) $92
Rationale: Sale Price = (5/4)*(Cost Price)
If the sale price is an integer, then the cost price must be divisible by 4.
The answer is C.
Answer: (C) $31
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 80,47 kmph
(B) 80,80 kmph
(C) 80,42 kmph
(D) 80,40 kmph
(E) 83,40 kmph
Rationale: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph.Answer:D
Answer: (D) 80,40 kmph
Question: If 24 men can do a piece of work in 25 hours, in how many hours will 15 men
do it ?
(A) 40 hours
(B) 45 hours
(C) 50 hours
(D) 55 hours
(E) 60 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
15 : 24 : : 25 : x<=>(15 x x) =(24 x 25)<=>(24 x 25)/15 = 40
Hence, 15 men can do it in 60 hours
Answer is A.
Answer: (A) 40 hours
Question: There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set R, which cannot be the range of the set R?
(A) 8
(B) B.11
(C) C.14
(D) D.17
(E) E.21
Rationale: Let Set A has 1,8 as elements
B has 1,14 as elements.. So Range for Combined set R becomes 14-1=13
For range to be 14,
A = 1,8
B= 2,15 (Range=14)
For range to be 17
A=1,8
B= 5,18
For range to be 21:
A=1,8
B= 9 ,22
So we are left with A and B.
Now consider A has elements A= -1,-8 and Thus Range =-1-(-8) =7
So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...
Consider Option A
A=-1,-8
B= y,x where y and x are smallest and largest element in Set B
Elements of Combined Set: -8,-1,y and x
Now x-(-8)=8 or x=0, then x-y=13 or y=-13...
Range of Combined Set: 0-(-13)= 13...
I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B
Answer: (B) B.11
Question: If the radius of the sphere is 14 m. then its total surface area is
(A) 2644
(B) 2446
(C) 2464
(D) 6442
(E) 6424
Rationale: Sphere Total surface area
= 4πr(power2) = 4 × 22/7 × 14 × 14 = 2464
Answer is C.
Answer: (C) 2464
Question: The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
(A) 40
(B) 41
(C) 44
(D) 42
(E) 43
Rationale: Total age of all students =22×21
Total age of all students + Age of the teacher =23×22
Age of the teacher
=23×22−22×21=22(23−21)=22×2=44
Answer is C.
Answer: (C) 44
Question: Find the value of
((0.1)3 + (0.6)3 + (0.7)3 − (0.3)(0.6)(0.7))/((0.1)2 + (0.6)2 + (0.7)2 − 0.006 − 0.42 − 0.07)
(A) 14/10
(B) 14/23
(C) 15/31
(D) 13/15
(E) None
Rationale: ((0.1)3 + (0.6)3 + (0.7)3 − (0.3)(0.6)(0.7))/((0.1)2 + (0.6)2 + (0.7)2 − 0.006 − 0.42 − 0.07)
=> (0.1 + 0.6 + 0.7)3/(0.1 + 0.6 + 0.7)2
=> 0.1 + 0.6 + 0.7 => 1.4 = 14/10
A)
Answer: (A) 14/10
Question: In a clothing store, there are six different colored neckties (red, orange, yellow, green, blue, and indigo) and three different colored shirts (red, orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color?
(A) 719/720
(B) 1/120
(C) 2/233
(D) 1/6
(E) 1/720
Rationale: 6 ties and 6 shirts...
red tie can take any of 6 shirts..
orange can take any of the remaining 5 shirts
yellow any of remaining 4..
and so on till last indigo chooses the 1 remaining..
Total ways= 3*2*1= 6
out of this 6, ONLY 1 way will have same colour tie and shirt..
prob = 1/6
D
Answer: (D) 1/6
Question: The circulation for magazine Z in 1971 was 6 times the average (arithmetic mean) yearly circulation for magazine Z for the years 1972-1980. What is the ratio of the circulation in 1971 to the total circulation during 1971-1980 for magazine Z ?
(A) 4/7
(B) 5/7
(C) 3/7
(D) 2/7
(E) 1/7
Rationale: There are 9 years from 1972-1980, inclusive. Let's say the average circulation every year between 1972-1980 inclusive is x.
So the total circulation is 9x from 1972-1980, inclusive.
In 1971, the circulation is 6x.
So total circulation for 1971-1980 is 6x + 9x = 15x.
Ratio of circulation in 1971 to total circulation during 1971-1980 is 6x to 14x or 6/14=3/7
Answer : C
Answer: (C) 3/7
Question: Evaluate : 37 x 181+ 37 x 319
(A) 22500
(B) 15500
(C) 18500
(D) 25000
(E) None of them
Rationale: 37 x 181 + 37 x 319 = 37 x (181 + 319) = 37 x 500 = 18500.
Answer is C.
Answer: (C) 18500
Question: A bike covers a certain distance at the speed of 64km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
(A) 80.34 km/h
(B) 85.34 km/h
(C) 90.30 km/h
(D) 92.25 km/h
(E) 97.74 km/h
Rationale: Ans.(B)
Sol. Total distance = 64 × 8 = 512 km
Now speed = 512/6 = 85.34 km/h
Answer: (B) 85.34 km/h
Question: A man can row his boat with the stream at 18 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 3 kmph
(C) 8 kmph
(D) 7 kmph
(E) 5 kmph
Rationale: DS = 18
US = 4
S = ?
S = (18 - 4)/2 = 7 kmph
Answer: D
Answer: (D) 7 kmph
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 288
(B) 277
(C) 200
(D) 150
(E) 982
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: (D) 150
Question: A number is greater than 3 but less than 8. Also the number is greater than 6 but less than 10. What is the number?
(A) 5
(B) 7
(C) 6
(D) 8
(E) 9
Rationale: B 7
Answer: (B) 7
Question: By how much is three-fifth of 340 greater than four-seventh of 210 ?
(A) 90
(B) 100
(C) 110
(D) 120
(E) 84
Rationale: Explanation:
3/5 of 340 - 4/7 of 210 = 204 - 120 = 84.
Answer: E
Answer: (E) 84
Question: Albert invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per
annum. How much Albert will get on the maturity of the fixed deposit
(A) Rs. 8510
(B) Rs. 8620
(C) Rs. 8730
(D) Rs. 8820
(E) None of these
Rationale: Explanation:
=>(8000×(1+5100)2)=>8000×2120×2120=>8820
Answer:D
Answer: (D) Rs. 8820
Question: At the store, Sam bought a shirt and a toaster. There was a 7% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?
(A) 0.93(K – T)
(B) 0.93K – T
(C) 0.93(K – 1.07T)
(D) (K – T)/1.07
(E) (K/1.07) – T
Rationale: 1.07S + 1.07T = K
1.07S = K - 1.07T
S = (K/1.07) - T
The answer is E.
Answer: (E) (K/1.07) – T
Question: V is the volume of a cylinder; the radius of the cylinder is 3.4. The height of the cylinder is 550% more than the radius. Which of the following is true?
(A) 100 < V < 300
(B) 300 < V < 500
(C) 500 < V < 700
(D) 700 < V < 900
(E) 900 < V < 1100
Rationale: Volume of a cylinder is pi*(r^2)*h
h>5.5r+r ---> h>6.5*3.4
So, volume is > 3.14*3.4*3.4*6.5*3.4=800 (approx)
Hence, answer will be D.
Answer: (D) 700 < V < 900
Question: Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 20 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
(A) 10%
(B) 12%
(C) 15%
(D) 27%
(E) 37%
Rationale: Lets assume that candidate got 20% votes and total votes is 100.
Candidate won = 20
Remaining = 80
To get 50%, candidate requires 30 votes from 100 which is 30% and 30 votes from 80.
30/80 = 37.5%
Which is approx 37%. Hence the answer is E
Answer: (E) 37%
Question: 7+2=56
6+3=48
5+5=45
2+1=4
4+9=??
Solve it?
(A) 92
(B) 48
(C) 42
(D) 38
(E) 72
Rationale: x+y=x[y+(x-1)]=x^2+xy-x
7+2=7[2+(7-1)]=49+14-7=56
6+3=6[3+(6-1)]=36+18-6=48
5+5=5[5+(5-1)]=25+25-5=45
2+1=2[1+(2-1)]=4+2-2=4
4+9=4[9+(4-1)]=16+36-4=48
Answer :B
Answer: (B) 48
Question: George baked a total of 175 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: 3/5 of the 175 pizzas cooked on Saturday = 105 pizzas
3/5 of the remaining pizzas on Sunday = 42 pizzas
We're left with (175-105-42) =28 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.
M T W TH F
8 7 6 4 3=28
W=6
D
Answer: (D) 6
Question: A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
(A) 24
(B) 77
(C) 66
(D) 89
(E) 12
Rationale: 10/40 + 10/30 + 10/x = 1
x = 24 days
Answer:A
Answer: (A) 24
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
(A) 8 years
(B) 9 years
(C) 6 years
(D) 4 years
(E) 5 years
Rationale: 4 years
Answer:D
Answer: (D) 4 years
Question: The edges of three metal cubes are 1 cm, 2 cm, and 3 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)?
(A) 3.3
(B) 3.5
(C) 3.7
(D) 3.9
(E) 4.1
Rationale: The total volume is 1^3+2^3+3^3=36
The edge of the new cube is the cube root of 36 which is about 3.3 cm.
The answer is A.
Answer: (A) 3.3
Question: Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 2/5
(B) 1/5
(C) 1/9
(D) 1/10
(E) 1/25
Rationale: Total pairs = 10C2 = 45; Same Color Pairs= 5C1*1C1=5; Prob = 1/9
Or 2/10 * 1/9 * 5 = 1/9
Ans C
Answer: (C) 1/9
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
(A) (2x + 3y)2
(B) (2y – x)2 + y(16x + 5y)
(C) 4x(x + 2y) + y(4x + 9y)
(D) (2x + 2y)2 + y(4x + 5y)
(E) (2x – y)2 + 8y(2x + y)
Rationale: Others are requal to 4x2 + 9y2 + 12xy.
Answer B
Answer: (B) (2y – x)2 + y(16x + 5y)
Question: In what time will a railway train 80 m long moving at the rate of 40 kmph pass a telegraph post on its way?
(A) 3
(B) 5
(C) 4
(D) 6.4
(E) 7.2
Rationale: T = 80/40 * 18/5 = 7.2 sec
Answer:E
Answer: (E) 7.2
Question: Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
(A) 2288
(B) 2677
(C) 6000
(D) 2700
(E) 2881
Rationale: 10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x
10 * 20 * 90 = 15 * 2 * x => x = 6000
Answer: C
Answer: (C) 6000
Question: At what rate p.a a sum of Rs. 2400 will become Rs. 3600/- in 5 years.
(A) 10%
(B) 15%
(C) 20%
(D) 12%
(E) 23%
Rationale: Explanation:
principal P = 2400/-
Rate of interest R = ?
Time T = 5 years
Accumulated Amount A = Rs.10400/-
A = P + I
A = P + PTR/100
A = P(1+ TR/100)
2400[ 1 + (5 x R)/100] = 3600
2[(20 + R)/20] = 3
20 + R = 30
R = 10%
Answer: Option A
Answer: (A) 10%
Question: The sum of the squares of three number is 138,while the sum of their products taken two at a time is 131. their sum is :
(A) 20
(B) 30
(C) 40
(D) None of these
(E) Cannot be determined
Rationale: Solution
Let the numbers be a,b and c then, a 2 + b 2+ c 2 = 138 and (ab + b c + ac) = 131.
(a + b+ c)2 = a 2 + b 2 + c 2 + 2(ab + b c + ca) = 138 + 2 * 131 = 400 .
⇒ (a + b + c) = 400/20= 20
Answer A
Answer: (A) 20
Question: What distance will be covered by a bus moving at 72 kmph in 30 seconds?
(A) 287
(B) 600
(C) 289
(D) 276
(E) 207
Rationale: 72 kmph = 72 * 5/18
= 20 mps
D = Speed * time = 20 * 30
= 600 m.
Answer:B
Answer: (B) 600
Question: Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) Rs.21.60
(B) Rs.24.00
(C) Rs.25.20
(D) Rs.27.80
(E) None of these
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 6,000{ [1 + 6/100]2 - 1 - 12/100}
= 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)
= 6,000 (0.0036) = 6 * 3.6 = Rs.21.60
ANSWER:A
Answer: (A) Rs.21.60