mathewhe/aqua_rat huggingface dataset:
Question: A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability E that the sum of the two integers will equal 9 ?
(A)  0.15
(B)  0.20
(C)  0.25
(D)  0.30
(E)  0.33
Rationale: Rearrange the first set:
A = {5,4,3,2}
B = {4,5,6,7, 8}
As you can see numbers in each column (the numbers of the same color) give the sum of 9. So there are 4 such pares possible, total # of pairs is 4*5=20. E=favorable/total=4/20=0.2.
Answer: B.
Or: we can select ANY number from set A (4/4=1) but in this case we must select its matching pair from set B (the number of the same color) and since there are only one matching pair of this particular number in B then the probability of this is 1/5. So, overall: E=1*1/5.
Answer: B.
Answer: (B)  0.20
Question: Two digits in John's age are the same as the digit in the Wilson's age, but in reverse order. In 21 years John will be twice as old as Wilson will be then. what is the difference in their current age ?
(A) 25
(B) 43
(C) 14
(D) 36
(E) 12
Rationale: John's age= 10x+y so Wilson's age= 10y+x..
after 21 years , 10x+y+21=2*(10y+x+21)....
so 21+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=5... so ages are 51 and 15 and ans as found correctly by u is D..36
Answer: (D) 36
Question: The function f is defined for all positive integers x by the following rule. f(x) is the number of positive integers each of which is less than x and has no positive factor in common with x other than 1. If p is any prime, number then f(p)=
(A) 2
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) p-1
Rationale: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.
This question for instance basically asks: how many positive integers are less than given prime number p which have no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
For example: if p=3 how many numbers are less than 3 having no common factors with 3: 1, 2, --> 3-1=2.
Answer: E.
Answer: (E) p-1
Question: The present worth of a certain bill due sometime hence is Rs.800 and the true discount is Rs.36.The banker’s discount is
(A) Rs.34.38
(B) Rs.38.98
(C) Rs.37
(D) Rs.37.62
(E) None
Rationale: Solution
B.G	= [(T.D)² / P. W]
= Rs. (36 x 36 / 800)
= Rs.1.62
B.D
Given, T.D =36	= (T.D + B.G)
= Rs. (36 + 1.62)
= Rs.37.62.
Answer D
Answer: (D) Rs.37.62
Question: Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
(A) 3 : 4
(B) 4 : 3
(C) 5 : 3
(D) Data inadequate
(E) None of these
Rationale: Explanation:
(20 x 16) women can complete the work in 1 day.
1 woman's 1 day's work =1/320
(16 x 15) men can complete the work in 1 day.
1 man's 1 day's work =	1/240
So, required ratio
=	1/240 =1/320
=1/3 : 1/4
= 4 : 3 (cross multiplied)
ANSWER IS B
Answer: (B) 4 : 3
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 18
(B) 74
(C) 15
(D) 44
(E) 63
Rationale: Explanation:
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Correct Option : D
Answer: (D) 44
Question: What is the smallest integer T greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10?
(A) 21
(B) 41
(C) T=121
(D) 241
(E) 481
Rationale: Or u can just use the answer choices here. Since the answers are already arranged in ascending order, the first number which gives remainder T as 1 for all three is the correct answer. In the given question, the first number which gives a remainder of 1 for 6,8 and 10 is 121.C
Answer: (C) T=121
Question: What is the minimum percentage increase in the mean of set A {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A)  25%
(B)  50%
(C)  75%
(D)  100%
(E)  200%
Rationale: Mean of A is (-4-1+0+6+9)/5=2;
In order the increase to be minimal we should replace two smallest elements of A, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.
Percent increase=(4-2)/2*100=100%.
Answer: D.
Answer: (D)  100%
Question: If [[x]] = x^2 + 2x + 4, what is the value of [[2]]?
(A) 3
(B) 9
(C) 12
(D) 19
(E) 25
Rationale: These functions questions might look intimidating, but they just test your knowledge about how well you can substitute values
[[x]] = x^2 + 2x + 4
[[2]] = 2^2 + 2*2 + 4 = 12. Option C
Answer: (C) 12
Question: If anangletis defined as 1 percent of 1 degree, then how many anglets are there in a fifth circle?
(A) 0.36
(B) 7200
(C) 360
(D) 3,600
(E) 36,000
Rationale: 1 degree * 1/100 = 1 anglet
So 1 degree = 100 anglets
=> 72 degrees = 7200 anglets
Answer - B
Answer: (B) 7200
Question: A motorboat can go at 21 kmph and still water. It takes 7 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 3 kmph?
(A) 65 km
(B) 85 km
(C) 55 km
(D) 72 km
(E) 40 km
Rationale: Let the distance between A and B be x km.
Total time = x/(21 + 3) + x/(21 - 3) = 7
=> x/24 + x/18 = 7 => (4x + 3x)/72 = 7 => x = 72 km.
ANSWER:D
Answer: (D) 72 km
Question: A given line L has an equation 3x+4y=5. Which of the following is the equation of line which is perpendicular to the above line?
(A)  4x - 3y = 5
(B)  3x + 4y = 10
(C)  3x + 5y = 5
(D)  3x + 5y = 3
(E)  3x – 4y = 5
Rationale: For lines to be perpendicular ,
slope of line 1 * slope of line 2 = -1
(-3/4) * (x) = -1
x = (4/3)
where x is slope of line 2
Ans - A
Answer: (A)  4x - 3y = 5
Question: The cost price of a radio is Rs.1860 and it was sold for Rs.1340, find the loss %?
(A) 18%
(B) 12%
(C) 22%
(D) 27%
(E) 21
Rationale: 1860 ---- 520
100 ---- ? => 27%
Answer:D
Answer: (D) 27%
Question: A can do a piece of work in 24 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in ?
(A) 3 days
(B) 5 days
(C) 6 days
(D) 7 days
(E) 11 days
Rationale: B's 9 day's work = 9 x (1/12) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/4 work is done by A in = 24 x (1/4) = 6 days.
answer : C
Answer: (C) 6 days
Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.
C's rent = Rs.175 x 9/35 = Rs. 45.
answer :B
Answer: (B) 45
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 11
(B) 14
(C) 18
(D) 12
(E) 19
Rationale: 2 * 22/7 * 14 * x = 1056 => x = 12
Answer: D
Answer: (D) 12
Question: The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is:
(A) 45
(B) 50
(C) 51.4 approx.
(D) 54.6 approx.
(E) 54
Rationale: Let the required means score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 52 * 100
= 1600 + 775 + 55x = 5200
= 55x = 2825
= x = 565/11 = 51.4.
ANSWER:C
Answer: (C) 51.4 approx.
Question: Out of a total 85 children playing badminton or table tennis or both, total number of girls in the group is 70% of the total number of boys in the group. The number of boys playing only badminton is 50% of the number of boys and the total number of boys playing badminton is 60% of the total number of boys. The number of children playing only table tennis is 40% of the total number of children and a total of 12 children play badminton and table tennis both. What is the number of girls playing only badminton?
(A) 16
(B) 14
(C) 17
(D) Data inadequate
(E) None of these
Rationale: Let the number of boys= x
then x + 7x⁄10 = 85 or x = 50
No. of girls = 85 – 50 = 35
Answer B
Answer: (B) 14
Question: If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 900 responses are needed, what is the minimum number of questionnaires that should be mailed?
(A) 1300
(B) 1350
(C) 1400
(D) 1450
(E) 1500
Rationale: Let x be the minimum number of questionnaires to be mailed.
0.6x = 900
x = 1500
The answer is E.
Answer: (E) 1500
Question: There are 35 students in a hostel. If the no. of students increases by 12, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) 259.58
(B) 340.58
(C) 342.58
(D) 345.58
(E) 380.58
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 12) = x – 1
or, 35x + 42 = 47x – 47
or, x = 7.42
Thus the original expenditure of the mess = 35 x 7.42 = Rs. 259.58
A
Answer: (A) 259.58
Question: A and B can do a work in 1 day, B and C in 2 days and C and A in 3 days. In how many days will the work be completed, if all three of them work together?
(A) 12/11
(B) 12/24
(C) 13/16
(D) 18/12
(E) 14/23
Rationale: One day work of A and B = 1/1
One day work of B and C = 1/2
One day work of C and A = 1/3
2(A + B + C) = 1/1+ 1/2 + 1/3
2(A + B + C) = 11/6
(A + B + C) = 11/12
Number of days required = 12/11 days.
Answer: A
Answer: (A) 12/11
Question: A man speaks truth 3 out of 4 times. He throws a die and reports it to be a 6.
What is the probability of it being a 6?
(A) 3/5
(B) 1/2
(C) 3/4
(D) 3/8
(E) 3/6
Rationale: Explanation :
There are two cases
1) He is telling truth that the die reports 6, its probability = 3/4*1/6 = 1/8
2) He is telling lie that the die reports 6, its probability = 1/4*5/6 = 5/24
So required probability = (1/8)/(1/8)+(5/24) = (1/8)/(1/3) = 3/8
Hencer (D) is the correct answer
Answer : D
Answer: (D) 3/8
Question: What is the sum of all two digit numbers?
(A) 4805
(B) 4815
(C) 4830
(D) 4900
(E) 4905
Rationale: 10 + 11 + 12 + 13 + 14 + 15 + - - - - - - - - + 97 + 98 + 99 + 100
Sn = n/2[a + l]
= 90/2[10 + 99]
= 45[109]
= 4905.
E)
Answer: (E) 4905
Question: Which of the following is not the square of an integer?
(A) 455625
(B) 458623
(C) 227529
(D) 261121
(E) 478864
Rationale: The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
The square of an integer cannot have the units digit of 2, 3, 7, or 8.
The answer is B.
Answer: (B) 458623
Question: If the sum of a number and its square is 240, What is the number?
(A) 15
(B) 77
(C) 25
(D) 87
(E) 171
Rationale: Explanation:
Let the integer be x.
Then, x + x2 = 240
x2 + x - 240 = 0
(x + 16) (x – 15) = 0
x = 15
ANSWER: A
Answer: (A) 15
Question: Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
(A) 30
(B) 25
(C) 24
(D) 35
(E) 40
Rationale: Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.
ANSWER C
Answer: (C) 24
Question: 50% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 70%
Rationale: To maximize the percentage of companies offering both, let's assume that all 50% of companies which offer wireless internet also offer snacks.
The answer is D.
Answer: (D) 50%
Question: A and B invests Rs.8000 and Rs.15000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 32:75
(B) 82:31
(C) 32:45
(D) 34:89
(E) 35:21
Rationale: A : B
(8000*4)+(4000*8) : (15000*6)+(10000*6)
64000 : 150000
32 : 75
Answer:A
Answer: (A) 32:75
Question: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 40
II. 70
III. 92
(A) I only
(B) III only
(C) I and II
(D) I only III
(E) II and III
Rationale: m = 18k + 12 --> Values are 12, 30, 48, 66, 84
n = 24k + 14 --> Values are 14, 38, 62, 86
I. 50 --> Not possible
II. 70 --> Not possible
III. 92 --> 30 + 62 --> Possible
Answer: B
Answer: (B) III only
Question: The edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?
(A) 120
(B) 278
(C) 378
(D) 368
(E) 367
Rationale: 4*5*6
= 120
Answer: A
Answer: (A) 120
Question: One fourth of a solution that was 11% salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent salt by weight?
(A) 24%
(B) 34%
(C) 22%
(D) 31%
(E) 8.5%
Rationale: consider total solution to be 100 liters and in this case you'll have: 75*0.11+25*x=100*0.16 --> x=0.31.
Answer:D.
Answer: (D) 31%
Question: A train crosses a platform 100 m long in 60 seconds at a speed of 45 km/hr. The time taken by the train to cross an electric pole is :
(A) 36 sec
(B) 38 sec
(C) 44 sec
(D) 52 sec
(E) None
Rationale: Sol.
Speed = [45 * 5/18] m/sec = [25/2] m/sec.
Let the length of the train be x metres.
Then, x + 100 / [25/2] = 60 or x = 650 m
∴ time taken by the trian to cross an electric pole
= [650 * 2/25] sec =52 sec.
Answer D
Answer: (D) 52 sec
Question: David invested a certain sum of money in a bank that paid simple interest. The amount grew to $300 at the end of 2 years. He waited for another 3 years and got a final amount of $390. What was the principal amount that he invested at the beginning?
(A) $340
(B) $300
(C) $280
(D) $260
(E) $240
Rationale: What shall be the rate of interest.? Does that is not required for the calculation?
Not really!
Keep in mind that the interest earned each year will be the same in Simple Interest.
At the end of 2 years, Amount = $300
At the end of 5 years, Amount = $390
This means she earned an interest of $90 in 3 years. Or $30 in each year.
We know that the interest earned each year will be the same.
Therefore she must have earned $60 in 2 years.
Hence Principal Amount = $300 - $60 = $240 Option E
Answer: (E) $240
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 166
(B) 178
(C) 342
(D) 199
(E) 112
Rationale: 400*(90/100)*(95/100)
= 342
Answer: C
Answer: (C) 342
Question: In a stack of boards at a lumber yard, the 13th board counting from the top of the stack is immediately below the 12th board counting from the bottom of the stack. how many boards are in the stack?
(A) 33
(B) 23
(C) 25
(D) 32
(E) 42
Rationale: 1 2 3 ....
..............13 12 ................. 1
So the number of boards = 13+10 =23.
Option: B
Answer: (B) 23
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 9
(C) 7
(D) 5
(E) 4
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer: A
Answer: (A) 8
Question: Pary spent 2⁄5 of her money on new clothes and then deposited 1⁄2 of what remained into her savings account. If she then had $21 left, how much did she have at the start?
(A) $30
(B) $35
(C) $70
(D) $105
(E) $210
Rationale: Pary spent 2⁄5 of her money on new clothes but if you see 21 is half of 3/5 money so 210 is too huge to be correct..
solution..
let the money be x..
2/5 is used...
1/2 of remaining 3/5 is put in savings account and remaining half is 21..
so 1/2 * 3/5 *x=21..
x=21*2*5/3=70..
C
Answer: (C) $70
Question: Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.” Every day Dave chooses an outfit consisting of one of each of the following garments: jacket, tie, shirt, pants, boxers, right sock, left sock, right shoe, left shoe. If Dave has more than one of each of the listed garments, and can make 21,870 different outfits, then for how many garments does Dave have exactly five choices?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 21,870 = 2187*10 = 2187*5*2
Dave has exactly 5 choices for one garment.
The answer is B.
Answer: (B) 1
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
(A) 7
(B) 6
(C) 4
(D) 3
(E) 2
Rationale: Explanation:
There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer: B
Answer: (B) 6
Question: A water tank is four-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely?
(A) 6
(B) 9
(C) 10
(D) 12
(E) 15
Rationale: The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15
Since the rate is negative, the tank will be emptied.
A full tank would take 15 minutes to empty.
Since the tank is only four-fifths full, the time is (4/5) * 15 = 12 minutes
The answer is D.
Answer: (D) 12
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 20 years. The present age of the husband is
(A) 35 years
(B) 40 years
(C) 50 years
(D) 55 years
(E) None
Rationale: Solution
Sum of the present ages of husband, wife and child	= (27x3+3x3) years
= 90 years.
Sum of the present ages of wife and child	= (20x2+5x2) years
= 50 years.
∴ Husband's present age	= (90 - 50) years
= 40 years.
Answer B
Answer: (B) 40 years
Question: The integer A has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of A and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let A be 67 and y be a8. Then the product of A and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.
So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9=66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.
So the answer is (C).
Answer: (C) 5
Question: A student has to obtain 30% of the total marks to pass. He got 150 marks and failed by 30 marks. The maximum marks are?
(A) 750
(B) 600
(C) 650
(D) 550
(E) 500
Rationale: Let the maximum marks be x
Then, 30% of x = 150+30
30x/100 = 180
30x= 180*100= 18000
x = 600
Answer is B
Answer: (B) 600
Question: A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 66000. What is the share of C?
(A) Rs. 15250
(B) Rs. 13375
(C) Rs. 16750
(D) Rs. 18000
(E) None of these
Rationale: Explanation:
Let the investment of C be Rs. x.
The inverstment of B = Rs.(2x/3)
The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)
Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3
C's share = Rs. [(3/11) × 66000] = Rs. 18000
Answer: Option D
Answer: (D) Rs. 18000
Question: John makes $55 a week from his job. He earns a raise andnow makes $60 a week. What is the % increase?
(A) 16%
(B) 9.66%
(C) 9.09%
(D) 9.98%
(E) 17%
Rationale: Increase = (5/55)*100 = (1/11)*100 = 9.09%.
C
Answer: (C) 9.09%
Question: The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from r to s, inclusive, where 0<r<s?
(A) s(s+1)/2 - (r+1)(r+2)/2
(B) s(s+1)/2 - r(r+1)/2
(C) s(s+1)/2 - (r-1)r/2
(D) (s-1)s/2 - (r+1)(r+2)/2
(E) (s-1)s/2 - r(r+1)/2
Rationale: Or try plug-in method: let s=4 and r=3 --> then s+r=7. Let see which option yields 7.
A. s(s+1)/2 - (r+1)(r+2)/2 = 10-10=0;
B. s(s+1)/2 - r(r+1)/2 = 10-6=4;
C. s(s+1)/2 - (r-1)r/2 = 10-3=7 --> OK;
D. (s-1)s/2 - (r+1)(r+2)/2 = 6-10=-4;
E. (s-1)s/2 - r(r+1)/2 = 6-6=0.
Answer: C.
Answer: (C) s(s+1)/2 - (r-1)r/2
Question: A shopkeeper sells 200 metres of cloth for Rs. 12000 at a loss of Rs.12 per metre. Find his cost price for one metre of cloth?
(A) s.59
(B) s.72
(C) s.62
(D) s.50
(E) s.13
Rationale: SP per metre = 12000/200
= Rs. 60 Loss per metre
= Rs. 12 CP per metre = 60 + 12
= Rs.72
Answer: B
Answer: (B) s.72
Question: What was the day of the week on, 20th July, 1776?
(A) Tuesday
(B) Wednesday
(C) Monday
(D) Saturday
(E) SUNDAY
Rationale: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 6 days)
Total number of odd days = (0 + 6) = 6.
Required day was 'Saturday'.
Answer:D
Answer: (D) Saturday
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?
(A) 6
(B) 5
(C) 8
(D) 6
(E) 3
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle
= 2∏s = 12∏ cm.
Answer: C
Answer: (C) 8
Question: Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 4,700 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 700 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip?
(A) 14.0
(B) 13.0
(C) 12.0
(D) 11.0
(E) 10.0
Rationale: Solution:H stopped 700 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 5hrs.
this means she reached there at 11:00.
speed difference between them is 800-500=300 ft/hr
so by the time H stops they have 1500 ft of distance
so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11:00
means 12:00 is the answer.
C
Answer: (C) 12.0
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio S of men to women?
(A)  5:2
(B)  5:1
(C)  4:3
(D)  4:1
(E)  3:1
Rationale: (A) S=184 x 5 + 170 x 2 = 1260.A
Answer: (A)  5:2
Question: If a and b are the roots of the equation x2 - 5x + 5 = 0, then the value of a2 + b2 is:
(A) 36
(B) 24
(C) 15
(D) 6
(E) 5
Rationale: Sol.(b) The sum of roots = a+ b = 5
Product of roots = ab = 5
Now, a2 + b2 = (a + b)2 - 2ab = 25 - 10 = 15
Answer C
Answer: (C) 15
Question: In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1300 employees, then the no. of female employees who are computer literate ?
(A) 546
(B) 674
(C) 672
(D) 960
(E) None
Rationale: Solution: Total employees,
= 1300
Female employees, 60% of 1300.
= (60 *1300) /100 = 780.
Then male employees,
= 520
50 % of male are computer literate,
= 260 male computer literate.
62 % of total employees are computer literate,
= (62 *1300) /100 = 806 computer literate.
Thus, Female computer literate = 806 - 260
= 546.
Answer: Option A
Answer: (A) 546