mathewhe/aqua_rat huggingface dataset:
Question: Which of the following must be an integer if the integer x is divisible by both 18 and 12?
(A) x/252
(B) x/189
(C) x/126
(D) x/36
(E) x/81
Rationale: the integer has to be multiple of LCM of 18 and 12, which is 36..
so x/36 will be an integer
ans D
Answer: (D) x/36
Question: A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 360 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?
(A) 400
(B) 475
(C) 480
(D) 625
(E) 700
Rationale: Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour.
7A+11B=360 ---(1)
8A+22C=600 ---(2)
Dividing (2) by 2
4A+11C=300.....(3)
Adding (1)(3)
11A+11B+11C = 660
A+B+C=60 per hour
So for eight hrs = 60*8 = 480 = Answer = C
Answer: (C) 480
Question: The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 876 m
(B) 157 m
(C) 225 m
(D) 156 m
(E) 167 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2
=> 2(150 + x) = 750 => x
= 225 m.
Answer: C
Answer: (C) 225 m
Question: A thief steels a car at 6a.m. and drives it at 50kmph. The theft is discovered at 7a.m. and the owner sets off in another car at 100 kmph. When will he overtake the thief?
(A) 9a.m.
(B) 9.30a.m.
(C) 10a.m.
(D) 8 a.m.
(E) 10.15a.m.
Rationale: Suppose the thief overtakes x hours after 6a.m.
Distance covered by the thief in x hrs = distance covered by the owner in (x-1 hours)
50x = 100(x-1)
50x = 100
x = 2 hrs
Thief is overtaken at 8a.m.
Answer is D
Answer: (D) 8 a.m.
Question: Riya purchase 20 jars in a store then she returned 4 jars to store .Now how many jars she had?
(A) A)5
(B) B)11
(C) C)19
(D) D)16
(E) E)4
Rationale: 20-4=16. Answer is D
Answer: (D) D)16
Question: Tom, who has 50 math questions, will get 5 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 3 points per question. Then, which of the following can be the score if he solves all the 50 questions?
(A) 192
(B) 193
(C) 194
(D) 195
(E) 196
Rationale: Let x be the correctly answered questions. y be the wrongly answered/ skipped ones.
We have x + y = 50;
Score = 5x-3y
3x+3y = 150; 5x-3y = Score;
==> 8x = 150+Score;
check for answer choices where 150+Score is divisible by 8
Choice (C) 194 fits the equation !
Answer: (C) 194
Question: What is the probability of drawing a "Queen" from a deck of 52 cards?
(A) 2/7
(B) 1/13
(C) 3/5
(D) 2/8
(E) 1/7
Rationale: Explanation :
Total number of cards, n(S) = 52
Total number of "Queen" cards, n(E) = 4
P(E) =n(E)/n(S)=4/52=1/13
Answer: B
Answer: (B) 1/13
Question: In covering a distance of 60 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
(A) 5 km/h
(B) 8 km/h
(C) 10 km/h
(D) 15 km/h
(E) 25 km/h
Rationale: Let A's speed be X km/hr.
Then, 60/x - 60/2x = 2
6x = 60
x = 10 km/hr.
Answer : C
Answer: (C) 10 km/h
Question: A man bets on no. 16 on a roulette wheel 14 times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes?
(A) Either 37 ;30:1
(B) Either ;35:1
(C) Either 15;15:12
(D) Either 21;35:1
(E) Either 17;35:12
Rationale: Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.
Either ;35:1
B)
Answer: (B) Either ;35:1
Question: How long does a train 130 m long running at the speed of 98 km/hr takes to cross a bridge 160 m length?
(A) 13.9 sec
(B) 13.1 sec
(C) 17.9 sec
(D) 61.9 sec
(E) 47.98 sec
Rationale: Speed = 98 * 5/18 = 27 m/sec
Total distance covered = 130 + 160 = 290 m.
Required time = 290/22 = 13.1 sec.
Answer:B
Answer: (B) 13.1 sec
Question: A scale 6 ft. 8 inches long is divided into 4 equal parts. Find the length of each part
(A) 17 inches
(B) 20 inches
(C) 15 inches
(D) 18 inches
(E) 19 inches
Rationale: Explanation:
Total length of scale in inches = (6*12) + 8 = 80 inches
Length of each of the 4 parts = 80/4 = 20 inches
ANSWER: B
Answer: (B) 20 inches
Question: A bag contains 6red, 5blue and 2green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 2/21
(B) 3/41
(C) 5/26
(D) 3/31
(E) 5/32
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
(A) 89%
(B) 10%
(C) 70%
(D) 80%
(E) 73%
Rationale: A B C D
90 100 80 100
A D
90 ----- 100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
Answer:C:
Answer: (C) 70%
Question: The greatest possible length which can be used to measure exactly the length 6m, 2m 25cm, 10 m 90 cm is
(A) 15 cm
(B) 5 cm
(C) 25 cm
(D) 42 cm
(E) 43 cm
Rationale: Explanation:
Required Length = H.C.F of 600 cm, 225 cm and 1090 c
= 5 cm. Answer: B
Answer: (B) 5 cm
Question: The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?
(A) 10
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: 39x = 5 + 12 + 15 + 19 + (x â€“ 4)44
x = 25
ANSWER B
Answer: (B) 25
Question: Find the term next in series..
1,1/2,3/2,2,5,1/3, 16/3, 15,12,1/4,25/4,?
(A) next number is 48
(B) 58
(C) 40
(D) 43
(E) 44
Rationale: [1,1/2,3/2,2],[5,1/3/16/3,15],[12,1/4,25/4,x]
1+1/2=3/2. .....1/1/2=2
5+1/3=16/3. ....5/1/3=15
12+1/4=25/4....12/1/4=48
ANSWER:A
Answer: (A) next number is 48
Question: A bag contains 600 coins of 25 p denomination and 1200 coins of 50 p denomination. If 12% of 25 p coins and 24% of 50 p coins are removed, the percentage of money removed from the bag is nearly :
(A) 21.6 %
(B) 21.9 %
(C) 21.7 %
(D) 21.2 %
(E) 21.1 %
Rationale: Explanation:
Total money = = Rs. 750.
25 paise coins removed == 72.
50 paise coins removed = = 288.
Money removed = = Rs.162.
Required percentage = % = 21.6 %.
Answer: A)
Answer: (A) 21.6 %
Question: The selling price of 13 apples is the same as the cost price of 26 mangoes . The selling price of 16 mangoes is the same as the cost price of 12 apples. If the profit on selling mangoes is 20%, What is the profit on selling apples?
(A) 20%
(B) 25%
(C) 40%
(D) 50%
(E) 60%
Rationale: Given that S.P of 13 apples = C.P of 26 mangoes
S.P of an apple = 2*C.P of the mango
S.P of 16 mangoes = C.P of 12 apples
C.P of the apple = 4/3 *S.P of the mango
Mango Apple
C.P x 4/3*y
S.P y 2x
Given that y = 1.2x
C.P of apple = 4/3*1.2x =1.6x
Profit on each apple = (S.P – C.P)/C.P*100,
= (2x –1.6x)/1.6*100 = 0.4/1.6 *100 =25%
ANSWER:B
Answer: (B) 25%
Question: Sudhir started a business with Rs.50,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be
(A) 3:2
(B) 5:2
(C) 4:3
(D) 3:4
(E) 3:5
Rationale: 50000*12:60000*(12-8)
=600000 :240000
=5:2
ANSWER:B
Answer: (B) 5:2
Question: Michael drives to hospital in 30 minutes at certain speed & he doubles his speed while returning. Calculate the total time taken for the round trip
(A) 30 minutes
(B) 20 minutes
(C) 45 minutes
(D) 60 minutes
(E) 40 minutes
Rationale: s1 = d1/t1;
s2 = d2/t2
Speed = distance / time taken
In this case d1= d2
Total time = t1 + t2
t1 = 30 minutes & t2 = 15 minutes (since speed is doubled over the same distance)
T= 30 + 15 = 45 minutes
ANSWER: C
Answer: (C) 45 minutes
Question: y=x/(x-k),where k is a constant,and x is real number.show that.
1.y increase with increase in x.
2.y decreases first and then increase with the value of x.
3.y increase then decrease with the value of x.
4.it remains constant.
(A) 2
(B) 18
(C) 1
(D) 77
(E) 33
Rationale: Typical question. Taking k =5 and we draw the graph,
If x increases y decreases but when x equal to k, y value becomes infinite. But when x is greater than k, y value slowly reaches to 1. So it decrease from infinite to 1.
Answer:B
Answer: (B) 18
Question: Calculate Ruth's average score in an exam if she obtained the following marks 69, 89, 65, 82 and 58 out of 100 in different subjects.
(A) 75.6
(B) 72.6
(C) 71.6
(D) 73.6
(E) 74.6
Rationale: Explanation:
(69+89+65+82+58)/5=72.6
Answer: Option B
Answer: (B) 72.6
Question: A meeting has to be conducted with 4 managers. Find the number of ways in which the managers may be selected from among 8 managers, if there are 2 managers who refuse to attend the meeting together.
(A) 48
(B) 55
(C) 58
(D) 62
(E) 70
Rationale: The total number of ways to choose 4 managers is 8C4 = 70
We need to subtract the number of groups which include the two managers, which is 6C2 = 15.
70 - 15 = 55
The answer is B.
Answer: (B) 55
Question: In a rectangular axis system, what is the area of a parallelogram with the coordinates: (3,5), (9,5), (2,7), (8,7) ?
(A) 21.
(B) 28.
(C) 35.
(D) 12.
(E) 52.
Rationale: Delta x will give us the dimension of one side of the parallelogram = 9-3= 6 unit
Delta y will give us the dimension of the other side of parallelogram = 7-5=2 unit
Area of parallelogram = 6*2 = 12
ANSWER IS D
Answer: (D) 12.
Question: If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a six-percent vinegar solution, what was the concentration of the original solution?
(A) 19.3%
(B) 31%
(C) 16.67%
(D) 15.5%
(E) 12.5%
Rationale: Let X be the quantity of non-vinegar in the strong vinegar solution
Thus vinegar quantity will be 12 - X
When 50 ounces of water were added the percentage of vinegar becomes 6%, thus (12 - X)/62 = 6/100
From this equation X = 8.28
Answer (12-8.28)/12 = 31%
ANSWER:B
Answer: (B) 31%
Question: A circular path of 20 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
(A) Rs.49
(B) Rs.40
(C) Rs.44
(D) Rs.42
(E) Rs.66
Rationale: Explanation:
π (22^2 - 20^2) = 22/7 *(484-400) = 264
264 * 1/4 = Rs.66
Answer: Option E
Answer: (E) Rs.66
Question: 2: 3 = 4/5: x. The value of x is?
(A) 6/5
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x * 2 = 3 * 4/5
x *2= 12/5
x=6/5
ANSWER:A
Answer: (A) 6/5
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) 2000
(B) 3377
(C) 2667
(D) 2887
(E) 2677
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer:A
Answer: (A) 2000
Question: If a certain sample of data has a mean of 30.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
(A) (14.0; 16.5)
(B) (14.5; 21.0)
(C) (14.0; 26.5)
(D) (16.5; 26.0)
(E) (21.0; 36.5)
Rationale: 2.5 standard deviation equals to 2.5*2=5;
2.5 standard deviations from the mean, so5 points, from the mean is the range from {mean-5} to {mean+5}, so from 25 to 35:
The correct answer choice must cover all this range: only answer choice E does this.
Answer: E.
Answer: (E) (21.0; 36.5)
Question: An article is listed at Rs. 920. A customer pays Rs. 742.90 for it after getting two successive discounts. If the rate of first discount is 15%, the rate of 2nd discount is:
(A) 3%
(B) 5%
(C) 8%
(D) 12%
(E) None
Rationale: Solution: MP = 920.
After first discount Marked Price (MP) become,
= 920 - 15% of 920 = 782.
The Selling Price (SP) = 742.90.
Let second discount was x% on 782.
782 - x% of 782 = 742.90
782x/100 = 39.1
782x = 3910
x = 5%.
Second Discount = 5%.
Answer: Option B
Answer: (B) 5%
Question: A question paper consists of two sections A and B having respectively 3 and 4 questions.Four questions are to be solved to qualify in that paper.It is compulsory to solve at least one question from section A and 2 questions from section B .In how many ways can a candidate select the questions to qualify in that paper?
(A) 30
(B) 40
(C) 42
(D) 44
(E) 46
Rationale: here two cases are possible.
case 1) 1 question from section A and 3 question from section B are solved = 3C1.4C3
case 2) 2 question from section A and 2 question from section B are solved = 3C2.4C2
thus total number of ways = 3C1.4C3 + 3C2.4C2 = 30
ANS:A
Answer: (A) 30
Question: Q-1) Of the 84 parents who attended a meeting at a
school, 35 volunteered to supervise children during
the school picnic and 11 volunteered both to supervise
children during the picnic and to bring refreshments to
the picnic. If the number of parents who volunteered
to bring refreshments was 2 times the number of
parents who neither volunteered to supervise children
during the picnic nor volunteered to bring
refreshments, how many of the parents volunteered to
bring refreshments?
(A) 25
(B) 40
(C) 38
(D) 42
(E) 45
Rationale: i used the following formula: total = group1 + group2 + neither - both
using the information from the question stem, we have:
84 total people
35 who supervise (group1)
x who neither supervise nor bring refreshments
2 x people who bring refreshments (group2)
11 who supervise AND bring refreshments (both)
therefore...
84 = 35 + 2x + x - 11
solving, we get x = 20
since we want the value of those who bring refreshments AND supervise:
2(20) = 40
answer is B
Answer: (B) 40
Question: A fruit seller had some mangoes. He sells 30% mangoes and still has 280 mangoes. Find the number of mangoes he had.
(A) 588 mangoes
(B) 400 mangoes
(C) 672 mangoes
(D) 700 mangoes
(E) None of these
Rationale: Explanation:
Suppose originally he had X mangoes.
Then, (100 – 30)% of X = 280
70/100 * X = 280
X = (280 * 100) / 70 = 400
ANSWER: B
Answer: (B) 400 mangoes
Question: 3^15 + 3^15 + 3^15 =
(A) 3^20
(B) 9^12
(C) 3^18
(D) 9^15
(E) 3^16
Rationale: Since we have 3^15 added together 3 times, we can factor out a 3 and we get 3(3^15) which is equal to 3^16.
The answer is E.
Answer: (E) 3^16
Question: Rahul can finish one-fifth of hhis homework in one hour.Neha can finish three-seventh of her homework in one hout thirty minutes and riya can finish three fourth of her homework in three hours thirty minutes.If all of them start their homework at 12:00pm and can go to play as soon as they all finish their homework,when can they start to play,if they take a break at 3:30pm for thirty minutes?
(A) 5.00pm
(B) 5:30pm
(C) 4.40pm
(D) 6.30pm
(E) 3.30pm
Rationale: Let the work be 1
Then Rahul do 1/5 work in 60min
So Rahul do 1 work in 300 min
Then Neha do 3/7 work in 90min
So Neha do 1 work in 210min
Then Riya do 3/4 work in 210min
So Riya do 1 work in 280 min
By 300min i.e 5hr all will complete their work so
12-1,1-2,2-3,3-3:30, 4-4:30,4:30-5:30
By 5:30 they all go to play
ANSWER:B
Answer: (B) 5:30pm
Question: Five kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms?
(A) 4.9
(B) 4.8
(C) 2.5
(D) 2
(E) 0.2
Rationale: If C is the answer, then the question means that the concentration of water the newt day became 96%.
Out of 5 kilograms 98%, or 4.9 kilograms was water and 0.1 kilograms was non-water.
The next day, after some water evaporated, oranges became 96% water and 4% of non-water, so the next day 0.1 kilograms of non-water composed 4% of oranges, which means that the new weight of the oranges was x*0.04=0.1 --> x=2.5 kilograms.
Answer: C.
Answer: (C) 2.5
Question: Aravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he
take along with him?
(A) $ 3500
(B) $ 3600
(C) $ 3800
(D) $ 3000
(E) $ 4000
Rationale: Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000.
D)
Answer: (D) $ 3000
Question: A train 140 m long is running with a speed of 50 km/hr. In what time will it pass a man who is running at 4 km/hr in the direction opposite to that in which the train is going?
(A) 8.1
(B) 7.0
(C) 9.33
(D) 8
(E) 9
Rationale: Speed of train relative to man = 50 +4 = 54 km/hr.
= 54 * 5/18 = 15 m/sec.
Time taken to pass the men = 140 * 1/15 = 9.33 sec.
Answer: Option C
Answer: (C) 9.33
Question: A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by­­ ________ each working now for 10 hours daily, the work can be completed in time.
(A) 140 workers
(B) 150 workers
(C) 160 workers
(D) 155 workers
(E) 130 workers
Rationale: total man work in 90 days is = 90*75*8==>54000 man work
remaining work =1-2/7=5/7
now, 2/7 work have 54000 man work
5/7 work will have (54000*7/2)*5/7 ==> 135000 man work
days left =60 and 10 hrs per day
so, no. of workers = 135000/(60*10)==>225
this is total workers.
so, workers needed ==>225-75= 150 workers
ANSWER:B
Answer: (B) 150 workers
Question: Steve Purchased a house for $15000 and he like to resell it with 20% profit. And what price he want to sell that?
(A) 16000
(B) 17500
(C) 18000
(D) 19500
(E) 21000
Rationale: Explanation:
C.P= 15000
Profit% = 20% = (Profit*C.P) / 100
Profit= (Profit% * C.P) / 100 = (20*15000) / 100 = 3000
S.P = C.P + Profit = 15000+3000 = 18000 . Answer: C
Answer: (C) 18000
Question: The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
(A) 101
(B) 107
(C) 111
(D) 185
(E) 192
Rationale: Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.
Answer: Option C
Answer: (C) 111
Question: A certain company items price list has an average of 6 and a standard deviation of d (d is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than d?
(A) (-6;0)
(B) (0;0)
(C) (0;6)
(D) (0;12)
(E) (6;6)
Rationale: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.
Answer: E.
Answer: (E) (6;6)
Question: An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discount offered on it, find its SP?
(A) Rs. 60
(B) Rs. 69
(C) Rs. 72
(D) Rs. 89
(E) Rs. 92
Rationale: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
C
Answer: (C) Rs. 72
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 1/15
(B) 2/13
(C) 5/26
(D) 6/27
(E) 6/13
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: In how many ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?
(A) 736
(B) 768
(C) 792
(D) 840
(E) 876
Rationale: three letters can be arranged in 3! ways.
only one combination EIU is required.
7 letters can be arranged in 7! ways.
thus 7!/ 3! * 1 = 840.
D
Answer: (D) 840
Question: Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 2 hours?
(A) 450
(B) 750
(C) 1,800
(D) 5,900
(E) 7,500
Rationale: 8 machines/ 360 cans = 5 machines/ x cans
8x= 1800
x=225
(225)(2 hours)= 450 cans. The answer is A.
Answer: (A) 450
Question: If s and t are positive integers such that s/t = 64.28, which of the following could be the remainder when s is divided by t?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: 0.28 = 28/100 = 7/25
The remainder must be divisible by 7.
The answer is D.
Answer: (D) 21
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
(A) 7%
(B) 9%
(C) 4%
(D) 2%
(E) 4%
Rationale: 150 = (750*5*R)/100
R = 4%
Answer: C
Answer: (C) 4%
Question: If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $81, how much does one shirt cost?
(A) $10
(B) $12
(C) $13.20
(D) $21
(E) $16.80
Rationale: 3J + 2S = 69
2J + 3S = 81
----------------
5J + 5S = 150 ----(divide by 5)---> J + S = 30
3J + 2S = J + 2(J + S) = J + 60 = 69 ---> J = 9
3*9 + 2S = 69
27 + 2S = 69
2S = 42
S = 21
Answer: D
Answer: (D) $21
Question: In May, the grounds keeper at Spring Lake Golf Club built a circular green with an area of 49π square feet. In August, he doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
(A) 100PI
(B) 144PI
(C) 196 PI
(D) 80
(E) 90
Rationale: AREA OF CIRCLE 49PI SQ FEET =PI R^2 THEREFORE R =7
NOW GREEN RADI DOUBLED I.E R =14 AREA =196 PI
C
Answer: (C) 196 PI
Question: 8 * 8 * 8 * 8 = 2^ ?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: Solution :
2^3 * 2^3 * 2^3 * 2^3 = 2^(3+3+3+3) = 2^12
Answer : 12
Option : E
Answer: (E) 12
Question: A wheel makes 1200 revolutions in covering a distance of 60 km. Find the radius of the wheel.
(A) 10.5m
(B) 11m
(C) 11.25m
(D) 11.45m
(E) None of these
Rationale: Explanation: Distance covered in one revolution =((60X 1200)/1000)= 72m.
2πR = 72 => 2 x (22/7) x R = 72 => R = 72 x (7/44) = 11.45 m.
Answer: Option D
Answer: (D) 11.45m
Question: (2^2-1)(2^2+1)(2^4+1)(2^11+1)=
(A) 2^19 - 1
(B) 2^16 + 1
(C) 2^32 - 1
(D) 2^128 - 1
(E) 2^16(2^16-1)
Rationale: A: is correct
(2^2-1)* (2^2+1)=(2^4-1)
(2^4-1)*(2^4+1)=2^8-1
(2^8-1)*(2^11 +1)=2^19-1
You can apply to this formula: a^2- b^2=(a-b)*(a+b)
Answer: (A) 2^19 - 1
Question: Pipe A can fill a tank in 4 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2.4 hours
(B) 2.8 hours
(C) 3.2 hours
(D) 4.8 hours
(E) 5.2 hours
Rationale: The part filled by A + B + C in 1 hour
= 1/4 + 1/8 + 1/24
= 10/24
All the three pipes together will fill the tank in 24/10 = 2.4 hours.
The answer is A.
Answer: (A) 2.4 hours
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 24 years. The present age of the husband is
(A) 40
(B) 32
(C) 45
(D) 55
(E) 65
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) years = 90 years.
Sum of the present ages of wife and child = (24 * 2 + 5 * 2) years = 58 years.
Husband's present age = (90 - 58) years = 32 years
Option B
Answer: (B) 32
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) Rs.5800
(B) Rs.5480
(C) Rs.5400
(D) Rs.5900
(E) Rs.5430
Rationale: 100x + 400
= 12(x – 5)
x = 50
100 * 50 + 400
= 5400
Answer:C
Answer: (C) Rs.5400