mathewhe/aqua_rat huggingface dataset:
Question: Sam deposited $12,000 to open a new savings account that earned eight percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Sam account one year after the account was opened?
(A)  $13,128
(B)  $12,763
(C)  $12,968
(D)  $12,942
(E)  $12,865
Rationale: Approach #1:
8 percent annual interest compounded semi-annually --> 2.5% in 6 moths.
For the first 6 moths interest was 4% of $12,000, so $480;
For the next 6 moths interest was 4% of $12,000,plus8% earned on previous interest of $480, so $480+$8=$488;
Total interest for one year was $480+$488=$968, hence balance after one year was $12,000+ $968=$12,968.
Answer: C.
Answer: (C)  $12,968
Question: A shopkeeper expects a gain of 22½% on his cost price. If in a week, his sale was of Rs.392, what was his profit?
(A) Rs.18.20
(B) Rs.70
(C) Rs.72
(D) Rs.88.25
(E) None
Rationale: Solution
C.P	= Rs.(100/122.50x392)
= Rs.(1000/1225×392)
= Rs.320.
Therefore, Profit	= Rs.(392-320)
= Rs.72.
Answer C
Answer: (C) Rs.72
Question: If a and y are different prime numbers less than ten, what must be true about the sum of a and y?
(A) the sum is even
(B) the sum is odd
(C) the sum is less than ten
(D) the sum is greater than ten
(E) the sum is less than 13
Rationale: This has to be solved by checking for each option:
Prime numbers less that 10 = 2, 3, 5, 7
A. the sum is even
May or may not be true. a = 3, y, = 5 -> True.
a = 2, y = 3 - True
B. the sum is odd
May or may not be true. a = 3, y, = 5 -> False.
a = 2, y = 3 - True
C. the sum is less than ten
May or may not be true a= 5, y = 7, Sum = 12
a = 2, y = 3. Sum = 5
D. the sum is greater than ten
May or may not be true a= 5, y = 7, Sum = 12
a = 2, y = 3. Sum = 5
E. the sum is less than 13
This will always be true.
Maximum sum = 7 + 5 = 12.
This is always less than 13.
Correct Option: E
Answer: (E) the sum is less than 13
Question: If a^2 is divisible by 240 what is the least possible value of integer a?
(A) 120
(B) 30
(C) 90
(D) 60
(E) 12
Rationale: 240 can be written as (2^4)*3*5.
For a^2 to be divisible by 240 it should contain at least 2^4 and 3 and 5 in its factors. We can leave out option E because 12 doesnt have 5 as one of its factor. Now if we check for option B, 30 can be written as 2*3*5, hence 30^ 2 will have 2 as the maximum power of 2, so we can leave out this option too.
Option D is the right answer if we follow the same method as we followed for other two previous options.
60 = (2^2)*3*5; 60^2 = (2^4)*(3^2)*(5^2). So it shows that 60^2 is divisible by 240 and hence the answer.
Answer : D
Answer: (D) 60
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 420. What was Simran share in the profit?
(A) s 180
(B) s 100
(C) s 120
(D) s 190
(E) s 290
Rationale: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Simran's share = Rs.420 x	3/7	= Rs. 180.
ANSWER :A
Answer: (A) s 180
Question: The salaries of A and B together amount to $4000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary?
(A) $1000
(B) $1250
(C) $2500
(D) $3000
(E) $1200
Rationale: Let A's salary is x
B's salary = 4000-x
(100-95)% of x = (100-85)% of (4000-x)
x = $3000
Answer is D
Answer: (D) $3000
Question: Albert is 2 times Mary’s age but only 4 times as old as Betty. Mary is 16 years younger than Albert. How old is Betty?
(A) 8
(B) 12
(C) 10
(D) 15
(E) 18
Rationale: given that A=2M=4B..AND M=A-16..
substituting the values M=16,A=32 AND B=8..
Answer is A
Answer: (A) 8
Question: A chair is bought for Rs.900/- and sold at Rs.810/- find the loss percentage
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (810 ~ 900)/900 = 10% Loss
A
Answer: (A) 10%
Question: Fresh grapes contain 70% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 30kgs of raisins?
(A) 75 kgs
(B) 64kgs
(C) 72 kgs
(D) 65 kgs
(E) 70 kgs
Rationale: The weight of non-water in 30 kg of dried grapes (which is 100-25=75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-70=30% of whole weight),
so 30*0.75 = x*0.3
--> x = 75.
Answer: A.
Answer: (A) 75 kgs
Question: Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age?
(A) 1
(B) 2
(C) 4
(D) 5
(E) 6
Rationale: Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
(4x + 8) = 5 (x + 8)
2
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2.
B
Answer: (B) 2
Question: If 5 less than x is 1 greater than y, then a number z that is 5 greater than x reduced by y is equal to
(A) 4
(B) 9
(C) 14
(D) 11
(E) y + 14
Rationale: 11 it is....nice one....
D
Answer: (D) 11
Question: In how many different ways can 5 females and 5 males form a circle such that the males and the females alternate?
(A) 1400
(B) 2800
(C) 1200
(D) 3000
(E) 4012
Rationale: circle 5 males can be arranged in 4!
gvn that the males and females alternate then 5 places for females
=> female arranged in 5 !
tot no of ways = 4! * 5 ! = 24 * 120 = 2880
ANSWER B
Answer: (B) 2800
Question: Ratio between Rahul and Deepak is 4:3, After 2 Years Rahul age will be 26 years. What is Deepak present age.
(A) 14
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 2 = 26 => x = 6
So Deepak age is = 3(6) = 18
Option B
Answer: (B) 18
Question: A and B invest money in the ratio 8:9 and they has loss of Rs.6900 at the end of year. what is the share of loss of B?
(A) Rs.1600
(B) Rs.1500
(C) Rs.1400
(D) Rs.1300
(E) None of the above
Rationale: et ratio of A and B be 8x & 9x
so net loss = 8x+9x= 6800
x=400
A=3x=3(400)=1200
B= 4x=4(400)=1600
so, B= 1600
ANSWER:A
Answer: (A) Rs.1600
Question: Two bullet train s 140 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
(A) 15.8 sec.
(B) 12.8 sec.
(C) 11.88 sec.
(D) 10.8 sec.
(E) 08.8 sec.
Rationale: Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.
Distance covered in crossing each other = (140 + 190) m = 330 m.
Required time = 330x9/250 = 54/5 = 11.88 sec.
ANSWER C
Answer: (C) 11.88 sec.
Question: A $77.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased?
(A) 15%
(B) 23%
(C) 25%
(D) 60%
(E) 80%
Rationale: Listed selling price of chair = 77.95 $
Discounted selling price of chair = 59.95 $
Discount = 77.95 - 59.95 = 18 $
% decrease in price of chair = (18/77.95) * 100% = 23 % approx
Answer B
Answer: (B) 23%
Question: In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability W at least one of the shirts he draws will be blue?
(A) 25/153
(B) 28/153
(C) 5/17
(D) 4/9
(E) W=12/17
Rationale: P(at least one blue) = 1- P(0 blue) = 1 - 10/18*9/17 =W= 12/17.
Answer: E.
Answer: (E) W=12/17
Question: In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 5 hours a day, the number of men required is:
(A) 24
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Explanation :
Let the required number of men be x.
Less days, More men (Indirect Proportion)
More working hrs per day, Less men (Indirect Proportion)
Days 8 : 10
Working Hrs 5 : 8 :: 12 : x
=> 8 x 5 x x = 10 x 8 x 12
=> x = 10 x 8 x 12 / (8 x 5)
=> x = 24
Answer : A
Answer: (A) 24
Question: The perimeter of a square is 72 m. Find the area of the square.
(A) 161 mÂ².
(B) 324 mÂ².
(C) 166 mÂ².
(D) 169 mÂ².
(E) 273 mÂ².
Rationale: Perimeter of square = 72 m
But perimeter of square = 4 Ã— side
Therefore, 4 Ã— side = 72 m
Therefore, side= 72/4 m = 18m
Now, the area of the square = (side Ã— side)
Therefore, area of the square = 18 Ã— 18 mÂ² = 324 mÂ².
ANSWER : OPTION B
Answer: (B) 324 mÂ².
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
(A) 39
(B) 28
(C) 27
(D) 80
(E) 71
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer: D
Answer: (D) 80
Question: 14, 35, 56, 63, 91, 126
In the sequence above, each term is related with the others. Which of the following could not be a term in the sequence?
(A) 402
(B) 259
(C) 322
(D) 686
(E) 847
Rationale: Simplifying the question into easier words we just need to find which of the numbers is not divisible by 7
clearly the answer is 402 because if we divide 402 by 7 we get a remainder of 57.42
Correct answer - A
Answer: (A) 402
Question: Two pipes can fill a tank in 30 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?
(A) 5 Hours
(B) 7 Hours
(C) 8 Hours
(D) 9 Hours
(E) 15 Hours
Rationale: In 1 hour it fill 1/30 + 1/12 - 1/20 = 1/15
So fill tank fill up in 15 Hours
ANSWER:E
Answer: (E) 15 Hours
Question: 9log9(4) = ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Exponential and log functions are inverse of each other. Hence
aloga(x) = x , for all x real and positive.
and therefore
9log9(4) = 4
correct answer D
Answer: (D) 4
Question: The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/8. What is the probability of Michael passing his driving test?
(A) 1/24.
(B) 1/2.
(C) 1/3.
(D) 2/3.
(E) 2/5
Rationale: 1/4 *1/m= 1/8 , 1/m = 1/2
Answer B
Answer: (B) 1/2.
Question: A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts three hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
(A) 3
(B) 4.5
(C) 6
(D) d) 5.5
(E) e) 5
Rationale: The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.
We know their rates are 30, 40 and 60.
Say the time taken by B is T hrs. Then A takes 3+T hrs. And we need to find the time taken by K.
Distance covered by A = Distance covered by B
30*(3+T) = 40*T
T = 9 hrs
Distance covered by B = Distance covered by K
40*T = 60*Time taken by K
Time taken by K = 40*9/60 = 6 hrs
Time taken by A = 3+T = 3+9 = 12 hrs
Time taken by K = 6 hrs
So K starts 12-6 = 6 hrs after A. (answer C)
Answer: (C) 6
Question: Steve traveled the first 2 hours of his journey at 40 mph and the last 2 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
(A) 53.33 mph
(B) 56.67 mph
(C) 60 mph
(D) 64 mph
(E) 66.67 mph
Rationale: Average Speed = Total distance/ Total time = (40 * 2 + 80 * 2)/(2 + 2) = 240/4 = 60
Answer: C
Answer: (C) 60 mph
Question: The present age of a father is 3 years more than five times the age of his son. Three years hence, father's age will be 17 years more than thrice the age of the son. Find the present age of the father.
(A) 33
(B) 38
(C) 29
(D) 40
(E) 53
Rationale: if the present age be x years.
father's will be (5x+3)years..
so, (5x+3+3)=3(x+3)+17
or, x=10
so the fathers present age =(5x+3)=(5*10+3)years =53years..
ANSWER : OPTION E
Answer: (E) 53
Question: A large tank can filled by A and B in 30 minutes and 45 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
(A) 30min
(B) 20min
(C) 25min
(D) 40min
(E) 45min
Rationale: Part filled by A+B in 1 minute = 1/30 + 1/45 = 1/45
Suppose the tank is filled in x minutes
Then, x/2(1/45 + 1/45) = 1
x/2 * 2/45 = 1
x = 45 min
Answer is E
Answer: (E) 45min
Question: What percent of 40 is 80?
(A) 133 1⁄3
(B) 75
(C) 200
(D) 33 1⁄3
(E) 25
Rationale: To find out the % of 80 in 40
Do 80/40 = 200%
Answer C)
Answer: (C) 200
Question: A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1640 had it been put at the rate of interest compounded annually?
(A) 4.5
(B) 3.5
(C) 3
(D) 2
(E) 1.5
Rationale: We can form equations as following:
Initial amount = P, Total amount after interest = T, Interest per year = I
T = P+I
Given T1 = P+2I = 1400T2 = P+ 5I = 2000
From this we get, P = 1000I = 200 $
Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually)
consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$.
To get a 240 $ compound interest the duration have to be > 1 year and < 2 years.
Only option fitting : Option E.
Answer: (E) 1.5
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 20 . The largest number is:
(A) 24
(B) 32
(C) 36
(D) 42
(E) 45
Rationale: Explanation:
Let the numbers be 4x, 5x and 6x. Therefore,
(4x+5x+6x)/3 = 20
15x = 60
x = 4
Largest number = 6x = 24.
ANSWER A
Answer: (A) 24
Question: P has $42 more than what Q and R together would have had if both B and C had 1/8 of what P has. How much does P have?
(A) $44
(B) $48
(C) $52
(D) $56
(E) $60
Rationale: P = (2/8)*P+42
(6/8)*P=42
P=56
The answer is D.
Answer: (D) $56
Question: Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers k did Carl drive each way?
(A)  350
(B)  345
(C)  320
(D)  280
(E)  240
Rationale: Let us backsolve here.
The answer option has to be divisible by 7 to give us 1/2.
Let us try k=280 km. Time taken will be 3.5 hours and 4 hours.
Hence D is the answer.
Answer: (D)  280
Question: 3/4 of 1/2 of 2/5 of 5040 = ?
(A) 392
(B) 229
(C) 756
(D) 493
(E) 540
Rationale: C
756
? = 5040 * (2/5) * (1/2) * (3/4) = 756
Answer: (C) 756
Question: If a2 + b2 + c2 = 250 and ab + bc + ca = 3, then a + b + c is
(A) 4
(B) 8
(C) 16
(D) 32
(E) 64
Rationale: by formula ,
(a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),
since, a^2 + b^2 + c^2 = 250 and ab + bc + ca = 3,
(a + b + c)^2 = 250 + 2(3)
= 256
= 16^2
therefore: a + b + c = 16
ANSWER:C
Answer: (C) 16
Question: which of the following could be the perimeter of the triangle?If two sides of a triangle have lengths 6 and 12.
I. 30
II. 25
III. 18
(A) I only
(B) II only
(C) II and III only
(D) none
(E) I, II, and III
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Therefore:
(12-6) < {third side} < (12+6).
6< {third side} < 18.
Perimeter = {third side} + 6 + 18= {third side} + 24.
30< {perimeter} < 42
Answer: D.
Answer: (D) none
Question: In what time will a railway train 120 m long moving at the rate of 70 kmph pass a telegraph post on its way?
(A) 3 sec
(B) 4 sec
(C) 5 sec
(D) 6 sec
(E) 7 sec
Rationale: T = 120/70 * 18/5 = 6 sec
ANSWER:D
Answer: (D) 6 sec
Question: If n = 3^6 – 2^6 which of the following is NOT a factor of n?
(A) 97
(B) 7
(C) 35
(D) 5
(E) 19
Rationale: 3^6 - 2^6
= (3^3)^2 - (2^3)^2
=(3^3 + 2^3)(3^3 - 2^3)
=(27+8)(27-8)
=35*19
=7*5*19
Therefore, 97 is Not a factor of n.
A
Answer: (A) 97
Question: Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 30 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks
(A) 1/3
(B) 3
(C) 4
(D) 45/14
(E) 12
Rationale: In 15 mins, Timothy travels=9/4 miles.
Now, let his mother takes x hours to reach him, traveling at 30mph.
So, 30x=9x+9/4
x=3/28 hrs.
Thus, the distance traveled by his mother to reach= 30*3/28=45/14 miles. Ans D
Answer: (D) 45/14
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.3 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:
(A) 2:5
(B) 2:3
(C) 2:4
(D) 4:5
(E) 2:9
Rationale: Let the ratio be k : 1. Then,
k * 16.3 + 1 * 15.4 = (k + 1) * 15.8
= (16.3 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.5 = 4/5
Required ratio = 4/5 : 1 = 4:5.
Answer:D
Answer: (D) 4:5
Question: 3 candidates in an election and received 2500, 5000 and 20000 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 72.72%
(B) 50%
(C) 57.57%
(D) 60%
(E) 65%
Rationale: Total number of votes polled = (2500 + 5000 + 20000) = 27500
So, Required percentage = 20000/27500 * 100 = 72.72%
A
Answer: (A) 72.72%
Question: The volume of a cube is 729 cc. Find its surface.
(A) 864
(B) 444
(C) 456
(D) 486
(E) 422
Rationale: a3 = 729 => a = 96a2 = 6 * 9 * 9 = 486Answer: D
Answer: (D) 486
Question: If (x/y)=(6/5), find the value (x^2+y^2)/(x^2-y^2)
(A) 61/11
(B) 51/11
(C) 41/11
(D) 21/11
(E) None of them
Rationale: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(6/5)^2+1] / [(6/5)^2-1]
= [(36/25)+1] / [(36/25)-1] = (61*25)/(25*11) = 61/11
Answer is A.
Answer: (A) 61/11
Question: Find the sum and number of divisors of 544 excluding 1 and 544.
(A) 587
(B) 588
(C) 589
(D) 590
(E) 591
Rationale: if N = p^a * q^b *r^c *...
total no. of factors of N = (a+1)*(b+1)*(c+1)*... &
sum of all of the factors of N =(1+p+p^2+...+p^a)*(1+q+..+q^b)*(1+r+r^2+...+r^c)
544 = 2^5 * 17
number of divisors of 544 excluding 1 and 544 = (5+1)*(1+1) - 2 = 10
sum of divisors of 544 excluding 1 and 544 = (1+2+2^2+2^3+2^4+2^5)*(1+17)-1-544
= 589
ANSWER:C
Answer: (C) 589
Question: The sale price of an article including the sales tax is $ 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
(A) $700
(B) $800
(C) $500
(D) $300
(E) $400
Rationale: C
$500
110% of S.P. = 616
S.P. = (616 * 100)/110 = $ 560
C.P = (110 * 560)/112 = $ 500
Answer: (C) $500
Question: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A and B working together , in how many days will the work be completed?
(A) 23
(B) 22
(C) 12
(D) 24
(E) 25
Rationale: A can finish 1 work in 20 days
B can finish 1/1.5 work in 20 days - since A is 1.5 faster than B
This means
B can finish 1 work in 20*1.5 days = 30 days
Now using the awesome GMAT formula when two machines work together they can finish the job in = AB/ (A+B) = 20*30/(20+30) = 20*30/50 = 12 days
So answer is C
Answer: (C) 12
Question: A marble statue is being carved by a sculptor. In the first week 35% is cut away, in the second week 20% of the remainder is cut away and in the third week 25% of the remainder is cut away and polished to produce the final statue. The weight of the final statue is 48.75 lbs. What was the weight of the original piece of marble?
(A) 134
(B) 167
(C) 125
(D) 113
(E) 111
Rationale: C
lb : reverse the calculations:
So 48.75 ÷ 0.75 = 65,
65 ÷ 0.8 = 81.25 and
81.25 ÷ 0.65 = 125.
Answer: (C) 125
Question: It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill one quarter of the dish?
(A) 10 days
(B) 14 days
(C) 24 days
(D) 28 days
(E) 29 days
Rationale: The bacteria doubles each day, so after 29 days, the dish was half full.
After 28 days, the dish was one quarter full.
The answer is D.
Answer: (D) 28 days
Question: If log x + log y = log (x+y), then,
(A) x=y
(B) xy=1
(C) y= (x-1)/x
(D) y=x/(x-1)
(E) y=1/(x-1)
Rationale: log x + log y = log (x+y)
=> log (x+y) = log (xy)
=> x+y = xy => y(x-1) = x
=> y= x/(x-1)
ANSWER:D
Answer: (D) y=x/(x-1)
Question: From the sale of sleeping bags, a retailer made a gross profit of 16% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag?
(A) 3.0
(B) 3.36
(C) 24.13
(D) 25.0
(E) 31.36
Rationale: Cost price * 1.16 = Selling price --> Cost price * 1.16 = $28 --> Cost price = $24.13.
Answer: C.
Answer: (C) 24.13
Question: In a colony of 70 residents, the ratio of the number of men and women is 4 : 3. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
(A) 1:6
(B) 1:1
(C) 1:8
(D) 1:9
(E) 1:3
Rationale: Number of men in the colony = 4/7 * 70 = 40.
Number of women in the colony = 3/7 * 70 = 40.
Number educated women in the colony = 1/5 * 30 = 6.
Number of uneducated women in the colony = 4/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30.
Number of educated men and uneducated men are in the ratio 10 : 30 i.e., 1:3.
Answer:E
Answer: (E) 1:3
Question: What is the smallest number which when diminished by 24, is divisible 5, 10, 15 and 20?
(A) 276
(B) 84
(C) 88
(D) 90
(E) 342
Rationale: Required Number
= (LCM of 5, 10, 15 and 20) + 24
= 60 + 24 = 84
Option B
Answer: (B) 84
Question: If 35 people play hockey and 10 people play both football and hockey and if 10 people play hockey and cricket and 5 people play all three games then the number of people playing hockey alone is?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: hockey =35 (given)
hockey , cricket , football = 5(given)
hockey , cricket = 10(given)
hockey , football = 10(given)
only hockey = 35 - 5(h,c,f)-5(h,c (10-5)) -5(h,f(10-5))=35-5-5-5=20
ANSWER:C
Answer: (C) 20
Question: A man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes. If the ratio between the length and breadth of the park be 3:2, then its area is:
(A) 1536m2
(B) 15360m2
(C) 153600m2
(D) 163600m2
(E) None of these
Rationale: Perimeter= Distance covered in 8 min
= (12000/60 *8)m= 1600m
Let, length= 3x meters and breadth= 2x meters
Then, 2(3x+2x)= 1600 or x= 160
Therefore, length= 480 m and breadth= 320m
Therefore, area= (480*320)m2 = 153600 m2
ANSWER:C
Answer: (C) 153600m2
Question: At a circular table for twelve will sit ten adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the twelve people be arranged around the table.
(A) 116,120
(B) 124,480
(C) 132,720
(D) 142,240
(E) 161,280
Rationale: Consider the two parents and two children as one unit.
Then there are eight adults and one family unit.
The number of ways 9 can form a line is 9!
Around a circular table, there would be 9 rotations so we divide this number by 9.
There are 8! ways for 9 to sit around the circular table.
Then the two children have two options and the two parents have two options.
Then the total number of ways is 8!*2*2= 161,280
The answer is E.
Answer: (E) 161,280
Question: The present ages of three persons in proportions 2 : 8 : 6. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(A) 10, 40, 30
(B) 16, 28, 36
(C) 16, 28, 35
(D) 16, 28, 34
(E) 16, 28, 33
Rationale: Let their present ages be 2x, 8x and 6x years respectively.
Then, (2x - 8) + (8x - 8) + (6x - 8) = 56
16x = 80
x = 5.
Their present ages are 2x = 10 years, 8x = 40 years and 6x = 30 years respectively.
Answer:A
Answer: (A) 10, 40, 30
Question: There are 20 poles with a constant distance between each pole. A car takes 26 second to reach the 12th pole. How much will it take to reach the last pole.
(A) 44.4543
(B) 44.9091
(C) 44.95128
(D) 44.91288
(E) 44.91222
Rationale: Assuming the car starts at the first pole.
To reach the 12th pole, the car need to travel 11 poles (the first pole doesn't count, as the car is already there).
11 poles 26 seconds
1 pole (26/11) seconds
To reach the last (20th) pole, the car needs to travel 19 poles.
19 pole 19 x (26/11) seconds
= 44.9091 seconds
Answer:B
Answer: (B) 44.9091