mathewhe/aqua_rat huggingface dataset:
Question: A jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is
(A) 1/3
(B) 2/3
(C) 2/5
(D) 1/4
(E) 1/2
Rationale: 1 st jar (alchohol) = 40%
2nd jar = 19%
after mix = 26%
mean = 7:14=1:2=>2/1+2=2/3
ANSWER B
Answer: (B) 2/3
Question: It takes Greg 6 minutes to run a mile, and it takes Pete 8 minutes. If Greg and Pete both begin running at exactly 8:30 a.m. without pausing, when is the first time at which they will finish running a mile simultaneously?
(A) 8:36 am
(B) 8:38 am
(C) 8:48 am
(D) 8:54 am
(E) 9:00 am
Rationale: Since Greg will run s miles after s × 6 minutes and Pete will run c miles after c × 8 minutes, they both will finish running a mile at the same time when s × 6 = c × 8. Since s and c must be integers (they represent the number of miles finished) this question is asking you to find a common multiple of 6 and 8. The question asks for the first time they will finish running a mile simultaneously, so you must find the least common multiple. The least common multiple of 6 and 8 is 24, so in the context of the question, this would be 24 minutes. Therefore, the first time they will finish running a mile at the same time is 8:30 + 24 minutes, or 8:54 a.m. The answer is (D).
Answer: (D) 8:54 am
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
(A) 9000
(B) 9400
(C) 9600
(D) 9800
(E) 9900
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
Answer: Option C
Answer: (C) 9600
Question: If the man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let the distance be x
Difference Between time = 12 min, which is 12/60 in hour which is 1/5
Now x/5-x/6 = 1/5
6x-5x/30 = 1/5
x/30 = 1/5
x = 30/5
x=6 So the required distance = 6
ANSWER:C
Answer: (C) 6
Question: 85% of a number is added to 24, the result is the same number. Find the number?
(A) 257
(B) 267
(C) 187
(D) one hundred sixty (160)
(E) 122
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Answer: (D) one hundred sixty (160)
Question: A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, what should be his speed in km/hr?
(A) 12 km/hr
(B) 14 km/hr
(C) 10 km/hr
(D) 8 km/hr
(E) 9 km/hr
Rationale: Explanation:
The person needs to cover 6 km in 45 minutes
Given that he covers one-half of the distance in two-thirds of the total time
=> He covers half of 6 km in two-thirds of 45 minutes
=> He covers 3 km in 30 minutes
Hence, now heneed to cover the remaining 3 km in the remaining 15 minutes
Distance = 3 km
Time = 15 minutes = 1/4 hour
Required Speed=Distance/Time = 3/(1/4) = 12 km/hr
Answer: Option A
Answer: (A) 12 km/hr
Question: The units digit of (3)^(44) + (10)^(46) is:
(A) 2
(B) 4
(C) 1
(D) 8
(E) 0
Rationale: any power of anything ending in zero always has a units digit of 0. So the first term has a units digit of 0.
The period is 4. This means, 3 to the power of any multiple of 4 will have a units digit of 1.
3^44 has a units digit of 1
.
Of course 0 + 1 = 1
C
Answer: (C) 1
Question: What is the greatest prime factor of 1+2+3+。。。+22?
(A) 17
(B) 29
(C) 23
(D) 37
(E) 11
Rationale: find the sum from direct formula = n(n+1)/2 = 22(22+1)/2 = 11*23...
23 is a PRIME number, so ans is 23..
C is the answer
Answer: (C) 23
Question: Peter invested a certain sum of money in a simple interest bond whose value grew to $400 at the end of 3 years and to $ 600 at the end of another 2 years. What was the rate of interest in which he invested his sum?
(A) 100%
(B) 12.5%
(C) 67%
(D) 25%
(E) 33%
Rationale: Lets assume the Principal Amount (initial amount invested) to be P
rate of interest to beRand time as T. We need to find R
Now After a time of 3years the principal P amounts to $400 and after a time of 5years ( question says after another 5years so 3+2) P becomes $600.
Formulating the above data
Amount (A1) at end of 3years
A1= P(1 + 3R/100) = 400
Amount (A2) at end of 8years
A2 = P(1 + 5R/100) = 600
Dividing A2 by A1 we get
(1 + 5R/100)/(1 + 3R/100) = 6/8
after cross multiplication we are left with R =100
Option: A
Answer: (A) 100%
Question: Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
(A) 9 minutes
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. x(2/75 + 1/45) + (30 - x). 2/75 = 1 11x/225 + (60 - 2x)/75 = 1 11x + 180 - 6x = 225. x = 9.
Answer:A
Answer: (A) 9 minutes
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 5
(B) 18
(C) 12
(D) 24
(E) 10
Rationale: Explanation:
Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
Correct Option : E
Answer: (E) 10
Question: What is 82% of 3/5?
(A) 6.9
(B) 0.492
(C) 0.6845
(D) 0.6859
(E) 0.69
Rationale: 82%*(3/5)=0.82*0.6=0.492
Answer :B
Answer: (B) 0.492
Question: Last year for every 100 million vehicles that travelled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, hom many of those vehicles were involved in accidents (1 billion=1,000,000,000)?
(A) 288
(B) 320
(C) 2880
(D) 3200
(E) 28800
Rationale: Explanation:
If r is halved then it is possible to substitute 1/2r for r in the formula and simplify:
1/(2(1/2r))^3=1/(8(1/8r^3))=1/r^3
Compared to the original where:
V=1/(2r)^3=1/(8r^3), the new value of V is 1/r^3 or
8(1/(8r^3))=8V
When r is halved then V is multiplied by 8.
Answer: Option B
Answer: (B) 320
Question: A train 100 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
(A) 6 sec.
(B) 7 sec.
(C) 9 sec.
(D) 11 sec.
(E) None
Rationale: Solution
Speed of the train relative to man	=( 68 - 8 )
= 60 Kmph
= 60 x 5 / 18
=50/3 m/sec.
Time taken by it to cover 100 m at (50 /3)m/sec
= (100 x 3/50)sec
= 6 sec.
Answer A
Answer: (A) 6 sec.
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
(A) 1800
(B) 900
(C) 2500
(D) 2700
(E) None of these
Rationale: Explanation :
Let required number of bottles be x
More machines, more bottles(direct proportion)
More minutes, more bottles(direct proportion)
⇒ 6 × 1 × x = 10 × 4 × 270
⇒ x = (10 × 4 × 270)/6 = (10 × 4 × 90)/2 = 10 × 4 × 45 = 1800. Answer : Option A
Answer: (A) 1800
Question: When 242 is divided by a certain divisor the remainder obtained is 15. When 698 is divided by the same divisor the remainder obtained is 27. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor?
(A) 11
(B) 17
(C) 13
(D) 23
(E) 37
Rationale: let that divisor be x
since remainder is 15 or 27 it means divisor is greater than 27.
now 242-15=227 =kx (k is an integer and 234 is divisble by x)
similarly 698-27=671 = lx (l is an integer and 689 is divisible by x)
adding both 698 and 242
= (227+671)+15+27
=x(k+l) + 42
when we divide this number by x then remainder will be equal to remainder of (42 divided by x) = 5 hence x = 42-5 = 37
hence E
Answer: (E) 37
Question: If 4 less than x is 4 greater than y, then a number z that is 2 greater than x reduced by y is equal to
(A) 4
(B) 9
(C) 14
(D) y + 9
(E) 10
Rationale: 10 it is....nice one....
E
Answer: (E) 10
Question: John had a stock of 800 books in his bookshop. He sold 62 on Monday, 62 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold?
(A) 26.5%
(B) 36.5%
(C) 71.7%
(D) 56.5%
(E) 70.0%
Rationale: Let N be the total number of books sold. Hence
N = 75 + 50 + 64 + 78 + 135 = 272
Let M be the books NOT sold
M = 960 - N = 960 - 402 = 688
Percentage
Books not sold / total number of books = 688/960= 0.72 = 71.7%
correct answer C
Answer: (C) 71.7%
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) 240
(B) 270
(C) 295
(D) 360
(E) 300
Rationale: Explanation:
Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
ANSWER IS B
Answer: (B) 270
Question: Valerie buys 3 new dresses on average every year for the last 5 years. In order to increase her average to 4 dresses per year, how many dresses should Valerie buy next year?
(A) 1
(B) 5
(C) 6
(D) 9
(E) 12
Rationale: Solution
Average of 6 years = 4 .
âˆ´ Required number of dresses= (6x4)-(5x3)
= 24- 15
= 9.
Answer D
Answer: (D) 9
Question: A contractor undertook to make 15 km of roadway in 40 weeks. In 10 weeks, 3 km was complete by 180 men working 8 hours a day. The men then agreed to work 1 hour a day overtime, And some boys were engaged to assist them, the work was finished in the stipulated time(40 weeks). How many boys were employed, if the work of 3 boys is equal to that of 2 men?
(A) 48
(B) 50
(C) 22
(D) 27
(E) 221
Rationale: Explanation:
Let the capacity of man = 3 units, and boy = 2 units per hour.
Now total work = 3×180×8×7×10 = 3 km. - - - - - - - (1)
Let k boys were recruited. Now total work = (3×180+2×k) ×9×7×30 = 12km. - - - - - - (2)
By dividing 2nd equation by 1st,
⇒ (540+2k)×9×7×303×180×8×7×10=4(540+2k)×9×7×303×180×8×7×10=4
⇒ k = 50
Answer: B
Answer: (B) 50
Question: If C + D = 9 and C and D are positive integers, which of the following is a possible value for 5C + 8D?
(A) 55
(B) 61
(C) 69
(D) 90
(E) 97
Rationale: c + d = 11
5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 45 + 3d=D=15
D=15
c+d=9=C+15=9=C=9-15=-6
C=-6
5C + 8D=5(-6)+8(15)=-30+120=90
Hence, D is the right answer.
Answer: (D) 90
Question: If 20% of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together.
(A) 11 1/9
(B) 10 1/9
(C) 12
(D) 15
(E) 18
Rationale: 0.2/A + 0.8/B = 20
1/A + 4/B = 100
0.8/A + 0.2/B = 30
4/A+ 1/B = 150
15/B = 250
B = 3/50 work per day
A = 3/100 work per day
Combined rate = 3/40 + 3/100 = 9/100
Time taken when working together = 100/9 = 11(1/9) days
Answer (A)
Answer: (A) 11 1/9
Question: Sangakara and Ponting select batting by using a dice, but dice is biased. So to resolve,Ponting takes out a coin. What is the probability that coin shows correct option?
(A) 1/2
(B) 1/6
(C) 1/12
(D) 6/10
(E) 3/10
Rationale: as coin has only two faces then probability must be 1/2
ANSWER:A
Answer: (A) 1/2
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday ?
(A) 34
(B) 66
(C) 25
(D) 18
(E) 12
Rationale: Explanation:
M + Tu + W + Th = 4 x 48 = 192
Tu + W + Th + F = 4 x 46 = 184
M = 42
Tu + W + Th = 192 - 42 = 150
F = 184 â€“ 150 = 34
Answer: A
Answer: (A) 34
Question: A certain party consists of four different group of people - 30 students, 35 politicians, 20 actors and 27 leaders. On a particular function day, the total cost spent on party members was Rs.9000. It was found that 6 students spent as much as 7 politicians, 15 politicians spent as much as 12 actors and 10 actors spent as much as 9 leaders. How much did students spent?
(A) 2377.55
(B) 2477.55
(C) 2577.55
(D) 2677.55
(E) 2777.55
Rationale: as question says,
30s+35p=20a+27L =9000 say eqn 1
6s=7p , 15p=12a , 10a=9L
or
6s=7p , 7p=(12*7)/15 a =(28/5)a , (28/5)a= (28/50)*9L
OR
6s=7p=(28/5)a=(252/50)L = K
now
s=(k/6), p= (k/7) , a=(.1785k) , L=(.1984k)
put these value in eqn one you will got value of k is 475.511
now 6s=k
hence s=k/6=79.25
there are 30 students hence 79.25*30=2377.55
ANSWER:A
Answer: (A) 2377.55
Question: If 40% of a certain number is 160, then what is 30% of that number?
(A) 270
(B) 380
(C) 120
(D) 360
(E) 180
Rationale: Explanation:
40% = 40*4 = 160
30% = 30*4 = 120
Answer: Option C
Answer: (C) 120
Question: The instructions state that Cheryl needs 4/9 square yards of one type of material and 2/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 8/18 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
(A) 1/12
(B) 1/9
(C) 2/3
(D) 1 1/9
(E) 2 1/9
Rationale: Total bought = 4/9+2/3
left part 8/18--->4/9
so used part 4/9+2/3-4/9=2/3
ANSWER:C
Answer: (C) 2/3
Question: A train travels from city A to city B. The average speed of the train is 60 miles/hr and it travels the first quarter of the trip at a speed of 90 mi/hr. What is the speed of the train in the remaining trip?
(A) 30
(B) 45
(C) 54
(D) 72
(E) 90
Rationale: Using the RTD chart, with A being the first quarter, B the rest of the trip and All the combinedtrip.
_______R_____T______D
A.........90........3..........270
B.........54.......15.........810
All........60.......18........1080
Let me explain how we fill in the chart:
1) Starting with what we know, we add 90 and 60
2) Picking an easy number for the total distance (6*9=54), so I chose 540. Multiply by 2 to get the whole trip, and we get 1080. Add 1080 for all-distance.
3) 1/4 of the whole distance happened at a Rate of 90. So, 1080/4=270, add 270 under A-D.
4) 2080 - 270 = 810, for the rest of the trip. Add 810 under B-D.
5) Claculate the individual Times for A and All, using T=D/R. Add the results, 3 and 18, under A-T and All-T.
6) 18-3=15, this is the remaining Time for B. Add 15 under B-T.
7) Finally, 15R=810 -->R=810/15 --> R= 54ANS C
Answer: (C) 54
Question: Brand X coffee costs twice as much as brand Y coffee. If a certain blend is 1/2 brand X and 1/2 brand Y. what fraction of the cost of the blend is Brand X?
(A) a. 1/3
(B) b. 2/5
(C) 3. 2/3
(D) 4. 1/5
(E) 5. 3/4
Rationale: Assume Cost of X= Ca = 200 , Cost of Y = Cb=100
The blend contains 0.5 X and 0.55 Y ---> Cost of the blend = Cbl = 0.5*200+0.5*100= 150
Thus fraction of X in the blend = 0.5*200/150 = 2/3.
Answer : C
Answer: (C) 3. 2/3
Question: For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:
(A) 32
(B) 38
(C) 44
(D) 52
(E) 63
Rationale: Therefore, since the remainder when q is divided by r is 7, then r>7;
Similarly, since the remainder when s is divided by t is 3, then t>3.
Now, all answers, except 38 can be represented as the product of two multiples one of which is greater than 7 and another is greater than 3:
32=8*4
44=11*4
52=13*4
63=9*7
However, 38=1*38 or 19*2, thus rt cannot equal to 38.
Answer: B.
Answer: (B) 38
Question: In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are accounting majors?
(A) 3
(B) 5
(C) 8
(D) 11
(E) 17
Rationale: pqrs = 1365 = 3* 5 *7 * 13
Since 1< p < q < r < s, the number of students who are accounting majors is p = 3.
The answer is A.
Answer: (A) 3
Question: If the manufacture gains 10%, the wholesale dealers 15% and the retailer 25% then find the cost of production of a table, the retail price of which is $1265 ?
(A) $650
(B) $800
(C) $1200
(D) $950
(E) $1050
Rationale: Let the cost of production of the table be $x
Then, 125% of 115% of 110% of x = 1265
125/100 * 115/100 * 110/100 * x = 1265
253/160 * x = 1265
x = 1265*160/253 = $800
Answer is B
Answer: (B) $800
Question: If a, b, c and d are positive integers less than 4, and 4^a+3^b+2^c+1^d=78 then what is the value of b/c?
(A) 3
(B) 2
(C) 1
(D) 1/2
(E) 1/3
Rationale: Since a, b and c are positive integers less than 4 we have the following possibilities:
4^a=4,16,or 64
3^b=3,9,or 27
2^c=2,4,or 8
Trial and error gives us quite quick the solution of
4^a=64
3^b=9
2^c=4
64+9+4=77
i.e. c=2 and b=2 ----> b/c=1/1=1
The correct answer is C
Answer: (C) 1
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
(A) 12/457
(B) 12/855
(C) 12/455
(D) 12/456
(E) 12/451
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455.Answer: C
Answer: (C) 12/455
Question: A cube of edge 10cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?
(A) 6cm
(B) 8.25cm
(C) 11.25cm
(D) 15.12cm
(E) 3.33cm
Rationale: Increase in volume = volume of the cube = 10*10*10 cm^3
Rise in water level = volume / area = 10*10*10/20*15 = 3.33cm
Answer is E
Answer: (E) 3.33cm
Question: Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 11 from the product of their ages a year from today. What is their age today?
(A) 2.
(B) 4.
(C) 5.
(D) 7.
(E) 9.
Rationale: ad = (a+1) (d+1) -11
0= a+d-10
a+d = 10
a=d (as they are twin brothers)
a=d=5
C is the answer
Answer: (C) 5.
Question: What is the remainder when 1201 × 1202 ×1203 × 1207 is divided by 6?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The remainders when dividing each number by six are: 1, 2, 3, and 1.
The product is 1*2*3*1 = 6
The remainder when dividing 6 by 6 is 0.
The answer is A.
Answer: (A) 0
Question: If f(x) = 7 x +12, what is f-1(x) (the inverse function)?
(A) (x-12)/7
(B) (x-12)/6
(C) (x-12)/5
(D) (x-12)/4
(E) (x-12)/3
Rationale: f(x) = 7 x + 12
take both side f-1(x)
f(f-1(x))= 7 f-1(x) + 12
x= 7(f-1(x)) +12
f-1(x) = (x-12)/7
ANSWER:A
Answer: (A) (x-12)/7
Question: In certain code 'TWICE' is written as '34$5δ' and 'WEARS' is written as '4δ29%'. How is 'SEAT' written in that code?
(A) 22
(B) 23
(C) 697
(D) 66P
(E) 82
Rationale: Answer: Option B
Answer: (B) 23
Question: The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 40%. What is the mark up on the cost price?
(A) 40%
(B) 8%
(C) 25%
(D) 16.66%
(E) 26%
Rationale: The most natural way to deal with 'weights' questions is by assuming values.
Say the trader's balance shows 100 gms. It is actually 90 gms because it weighs 10% less. Say, the cost price is $90 ($1/gm). Since he gets a profit of 40%, the selling price must be 90+(40/100)*90 = $126
Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $126, the mark up is simply 26%.
Ans : E
Answer: (E) 26%
Question: If m > 1 and n = 2^(m−3), then 4^m =
(A) 16n^2
(B) 4n^2
(C) 2n^2
(D) 8n^2
(E) 64n^2
Rationale: n = 2^(m-3) = 2^m/8
2^m = 8n
4^m = (2^m)^2 = (8n)^2 = 64n^2
The answer is E.
Answer: (E) 64n^2
Question: A furniture store owner decided to drop the price of her recliners by 20% to spur business. By the end of the week she had sold 60% more recliners. What is the percentage increase of the gross?
(A) 10%
(B) 15%
(C) 20%
(D) 28%
(E) 50%
Rationale: Say a recliner is actually worth $100
If she sells 100 recliners then she earns $10000
After the discount of 20%, she will earn $80 per recliner and she sells 60% more ie.,160 recliners
Hence her sales tields 160*80=$12800
Increase in sales=12800-10000=$2800
So% increase = 2800*100/10000 =28%
D is the answer
Answer: (D) 28%
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 178 votes. Find the total number of valid votes?
(A) 445
(B) 570
(C) 480
(D) 520
(E) 550
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 178 => 4x/10 = 178
=> 4x = 1780 => x = 445.
ANSWER:A
Answer: (A) 445
Question: If Jack walked 6 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?
(A)  4
(B)  4.8
(C)  6
(D)  6.25
(E)  15
Rationale: Distance walked in 1 hour and 15 mins = 6 miles
Speed per hour = Distance/Time = 6/(5/4) = 4.8 miles per hour
Answer B
Answer: (B)  4.8
Question: A man has some hens and cows. If the number of heads be 100 and the number of feet equals 180, then the number of hens will be:
(A) 22
(B) 23
(C) 80
(D) 90
(E) 28
Rationale: Explanation:
Let the number of hens be x and the number of cows be y.
Then, x + y = 100 .... (i)
and 2x + 4y = 220 x + 2y = 110 .... (ii)
Solving (i) and (ii) we get: x = 90, y = 10.
The required answer = 90.
Answer: D
Answer: (D) 90
Question: A clock loses 10 minutes each hour.
If the clock is set correctly at noon,what time is it when it reads 3 PM ?
(A) 3:36 PM
(B) 3:47 PM
(C) 3:45 PM
(D) 2:36 PM
(E) 3:30 PM
Rationale: A
3:36 PM.
The clock loses 10 minutes each hour,
so it loses 5 minutes every half-hour,
and it loses 1 minute very 6 minutes.
It is 12:50 PM at 1:00 o'clock.
It is 1:40 PM at 2:00 o'clock.
It is 2:30 PM at 3:00 o'clock.
It is 2:55 PM at 3:30 o'clock.
It is 3:00 PM at 3:36 o'clock.
Answer: (A) 3:36 PM
Question: The present age of Suraj is 6 times Vijay’s age. The present age of Vijay’s 20 years less than Suraj’s present age. What is the present age of Suraj?
(A) 20 years
(B) 22 years
(C) 18 years
(D) 16 years
(E) None of these
Rationale: S=6V, V=S-20
S=6(S-20)
5S=120
S=24
ANSWER:E
Answer: (E) None of these
Question: A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?
(A) 22 days
(B) 4 days
(C) 13 days
(D) 6 days
(E) 9 days
Rationale: (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).
B's 1 day's work =((1/4)-(1/12))=(1/6)
Hence, B alone can complete the work in 6 days.
Answer is D.
Answer: (D) 6 days
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 7 boys when a boy gets any no. of prizes?
(A) 55
(B) 58
(C) 343
(D) 354
(E) 200
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (7 x 7 x 7) ways = 73 ways = 343 ways Or nr ways = 73 ways = 343 ways
Answer: (C) 343
Question: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/10
II. 1/9
III. 1/11
(A) None
(B) I only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us B as the only possible answer.
Answer: (B) I only