mathewhe/aqua_rat huggingface dataset:
Question: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number T and the smallest possible number of students that could have taken both geometry and biology?
(A) 144
(B) 119
(C) 113
(D) 88
(E) 31
Rationale: OFFICIAL SOLUTION:
First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
The greatest possible number T of students that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
Answer: (D) 88
Question: Consider a quarter of a circle of radius 81. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
(A) 86*(sqr2 -1)
(B) 88*(sqr3 -1)
(C) 4*(sqr7 - 1)
(D) 81* (sqr2 -1)
(E) None of these
Rationale: I got 81/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer is D
Answer: (D) 81* (sqr2 -1)
Question: Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 6 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 6 minute mark.)
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: 6 minutes is 360 seconds.
Lamp A and Lamp B will flash together every 24 seconds.
360/24=15.
In the time period, Lamp A and Lamp B will flash together 15 times.
Lamp A and Lamp C will flash together every 30 seconds.
360/30=12.
In the time period, Lamp A and Lamp C will flash together 12 times.
Lamp B and Lamp C will flash together every 40 seconds.
360/40=9.
In the time period, Lamp B and Lamp C will flash together 9 times.
All three lights will flash together every 2*2*2*3*5=120 seconds.
360/120=3.
We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.
The number of times that exactly two lights flash together is 15+12+9-9=27 times.
The answer is D.
Answer: (D) 27
Question: The price of a jacket is reduced by 20%. During a special sale the price of the jacket is reduced another 25%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
(A) 32.5
(B) 35
(C) 48.1
(D) 65
(E) 66.67
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 20% , therefore bringing down the price to $80.
3) Again it is further discounted by 25%, therefore bringing down the price to $60.
4) Now 60 has to be added byX %in order to equal the original price.
60 + ( X% ) 60 = 100.
Solving this eq for X, we get X = 66.67
Ans is E.
Answer: (E) 66.67
Question: If Rs.3250 be divided among Ram, Shyam and Mohan in the ratio of 1/2:1/3:1/4 then the share of each are?
(A) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
(B) Ram = Rs.7500, Shyam = Rs.1000, Mohan = Rs.750
(C) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.250
(D) Ram = Rs.1500, Shyam = Rs.1080, Mohan = Rs.750
(E) Ram = Rs.1500, Shyam = Rs.1002, Mohan = Rs.750
Rationale: 1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
Answer:A
Answer: (A) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
Question: If S = {50, 72, 108, 120, 205}, how much less is the mean of the numbers in S than the median of the numbers in S?
(A) 2
(B) 3
(C) 5
(D) 8
(E) 9
Rationale: Mean = (50 + 72 + 108 + 120 + 205)/5 = 111
Median = 108
Difference = 111-108 = 3
Option B
Answer: (B) 3
Question: A man can row 8 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man?
(A) 7.82 km
(B) 6 km
(C) 5.76 km
(D) 5.66 km
(E) 10 km
Rationale: M = 8
S = 1.2
DS = 9.2
US = 6.8
x/9.2 + x/6.8 = 1
x = 3.91
D = 3.91 * 2 = 7.82
ANSWER:A
Answer: (A) 7.82 km
Question: If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 16 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers?
(A) 6
(B) 16
(C) 22
(D) 30
(E) 174
Rationale: The number of integers that belong to set X ONLY is 16-6=10;
The number of integers that belong to set Y ONLY is 18-6=12;
The number of integers that belong to set X or set Y, but not both is 10+12=22.
Answer: C
Answer: (C) 22
Question: The area of a rectangle is x2 + 4x -12. What are the dimensions of the rectangle (length and width)?
(A) x + 6 , x + -2
(B) x + 7 , x + -2
(C) x + 8 , x + -2
(D) x + 9 , x + -2
(E) none
Rationale: Solution
The main idea is to factor x2 + 4x -12
Since -12 = -2 × 6 and -2 + 6 = 4
x2 + 4x -12 = ( x + -2) × ( x + 6)
Since the length is usually longer, lenth = x + 6 and width = x + -2
Answer A
Answer: (A) x + 6 , x + -2
Question: Pipes A and B can fill a tank in 8 and 24 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
(A) 12 hr
(B) 28 hr
(C) 23 hr
(D) 24 hr
(E) 24 hr
Rationale: Explanation :
Part filled by pipe A in 1 minute = 1/8
Part filled by pipe B in 1 minute = 1/24
Part emptied by pipe C in 1 minute = 1/12
Net part filled by pipe A, pipe B and pipe C in 1 minute = 1/8+1/24−1/12=2/24=1/12
i.e, the tank will be filled in 12 minutes
Answer is A
Answer: (A) 12 hr
Question: A straight pipe 3 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?
(A)  1/6 and 1/4 only
(B)  1/4 and 1/3 only
(C)  1/6, 1/4, and 1/3
(D)  1/12, 1/6 and 1/4
(E)  1/12, 1/6, and 1/3
Rationale: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.
In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).
Distinct lengths would be: 3=3/12=1/4, 4-3=1=1/3and 6-4=2=2/12=1/6meters long pieces.
Answer: C.
Answer: (C)  1/6, 1/4, and 1/3
Question: 4211.01 + 22.261 - ? = 2645.759
(A) 1587.512
(B) 1586.532
(C) 1588.021
(D) 1586.422
(E) None of these
Rationale: Explanation :
Required Value = 4211.01 + 22.261 - 2645.759 = 1587.512. Answer : Option A
Answer: (A) 1587.512
Question: A number when divided by 243 gives a remainder 26, what remainder will be obtained by dividing the same number 14?
(A) 7
(B) 6
(C) 9
(D) 2
(E) 3
Rationale: Explanation:
243 + 26 = 269/14 = 3 (Remainder)
Answer: E
Answer: (E) 3
Question: What percent of a day is 4 hours?
(A) 12%
(B) 12.5%
(C) 13%
(D) 11.3%
(E) None of these
Rationale: Explanation :
Solution: required percentage = (4/100 * 24) = 12.5%
Answer : B
Answer: (B) 12.5%
Question: A can do a piece of work n 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: A can complete the work in (7*9) = 63 days
B can complete the work in (6*7) = 42 days
--> A’s one hour’s work = 1/63 and B’s one hour work = 1/42.
(A+B)’s one hour work = 1/63+1/42 = 5/126
Therefore, Both can finish the work in 126/5 hours.
Number of days of 8 2/5 hours each = (126*5/(5*42)) = 3 day
Answer : A.
Answer: (A) 3
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 76 km
(B) 26 km
(C) 20 km
(D) 56 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2
=> x = 20 km.
Answer:E
Answer: (E) 20 km
Question: A no.when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
(A) 3
(B) 6
(C) 9
(D) 10
(E) 12
Rationale: 221 + 43 = 264/17 = 9 (Remainder)
C
Answer: (C) 9
Question: A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 90
(B) 94
(C) 96
(D) 97
(E) 102
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 544
16x = 544
x = 34.
Hence, total number of notes = 3x = 102.
E
Answer: (E) 102
Question: A and B started a business. A invests rs.6000 and b invests rs.8000 after 6 months c joined them with rs.6000 but b left with the capital.after one year they get a profit of rs.2600.the share of A is?
(A) 900
(B) 1100
(C) 1200
(D) 1000
(E) 1300
Rationale: 6000x12 : 8000x:6 : 6000x6 = 6:4:3
so A work 2600x6/13 =1200
so ans is 1200
ANSWER:C
Answer: (C) 1200
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
(A) 8
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer: A
Answer: (A) 8
Question: In Country Q, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
(A)  50% decrease
(B)  30% decrease
(C)  15% decrease
(D)  30% increase
(E)  55% increase
Rationale: Country Q 1992 1996
No of construction workers 100 120
Unemployment Rate 16% 9%
Unemployed workers 16 11
% change in unemployed workers=(16-11)=5/16=~33% decrease
Closest ans=30% decrease
Ans=B
Answer: (B)  30% decrease
Question: A certain college's enrollment at the beginning of 1992 was 30 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
(A) 43%
(B) 45%
(C) 50%
(D) 35%
(E) 38%
Rationale: Suppose enrollment in 1991 was 100
Then enrollment in 1992 will be 130
And enrollment in 1993 will be 130*1.1=143
Increase in 1993 from 1991 = 143-100= 43
Answer : A
Answer: (A) 43%
Question: Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors yellow, purple, orange, silver, blue and red. How many different ice-cream products have at least one stripe out of the following colors: yellow, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?
(A) 12
(B) 14
(C) 18
(D) 19
(E) 20
Rationale: IMO: D - 19
There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, Red) will not contain at least one of the colors yellow, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors yellow, purple, or orange (YPO).
#1: Pick one out of YPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of YPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of YPO: 3C3 = 1
9 + 9 + 1 = 19
answer is D
Answer: (D) 19
Question: Four years ago, the ratio of ages of P and Q was 5:3. Ten years from now, the ratio of their ages will be 6:5. What is P's age at present?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 3(P-4)/5 = (Q-4). Then Q = 3(P-4)/5 + 4
5(P+10)/6 = Q+10
5(P+10)/6 = 3(P-4)/5 + 14
25P+250 = 18P + 348
7P = 98
P = 14
The answer is D.
Answer: (D) 14
Question: Complete the sequence:
C E I O ?
(A) M
(B) W
(C) S
(D) D
(E) Z
Rationale: C+2=E
E+4=I
I+6=O
O+8=W
B
Answer: (B) W
Question: Rose's grade was 70th percentile of the 60 grades for her class. Of the 40 grades from another class, 16 were higher than Rose's, and the rest were lower. If no other grade was the same as Rose's grade, then Rose's grade was what percentile of the grades of the two classes of two classes combined?
(A) 66th
(B) 70th
(C) 74th
(D) 82nd
(E) 85th
Rationale: 66th/70th/74th/82nd/85th
Correct option: A
Answer: (A) 66th
Question: The “a-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^a, where a is the a-number of the result of his die roll, and plots 3^a on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?
(A)  3/8
(B)  13/36
(C)  17/36
(D)  19/36
(E)  23/36
Rationale: If you calculate 3^a for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.
About distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.
On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:
probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9
probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9
probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36
All together: 1/9 + 1/9 + 5/36 = 13/36=B
Answer: (B)  13/36
Question: A present value of a machine is $800. Its value depletion rate is 10% per annum then find the machine value after 2 years?
(A) $900
(B) $810
(C) $915
(D) $715
(E) $648
Rationale: P= $800
R = 10%
T = 2 years
Machine value after 2 years = P[(1-R/100)^T]
=800*9/10 * 9/10
=$648
Answer is E
Answer: (E) $648
Question: If p and r are integers, and p^2 = 24r, then r must be divisible by which of the following?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 14
Rationale: Ans: D
Solution: for p to be an int 24 r must be whole square of a number.
28r= 3*2*2*2*r
to make it whole square we need 3
so r can must be divisible by 3y where y is itself a whole square.
so B is the ans
Answer: (B) 3
Question: A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 20 balls per box. If 76 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?
(A) 2
(B) 1
(C) 4
(D) 6
(E) 8
Rationale: We have to work with multiples of 20 and 25.
First, we must know the limits of this multiples, so:
76/25= 3....so the max is 3
76/20=3...so the max is 3
76-75 =1
Answer : B
Answer: (B) 1
Question: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 15 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?
(A) 40
(B) 48
(C) 43
(D) 45
(E) 41
Rationale: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion.
Ele = 3*Lyn
Usually, ages are integers so there is a good possibility that the age of Ele is 45 (the only option that is a multiple of 3).
Then age of Lyn would be 15. In 15 yrs, Ele would be 60 and Lyn would be 30 - so Lyn would be half as old as Ele.
Answer (D)
Answer: (D) 45
Question: Without any stoppage, a person travels a certain distance at an average speed of 42 km/h, and with stoppages he covers the same distance at an average speed of 28 km/h. How many minutes per hour does he stop?
(A) 14 minutes
(B) 15 minutes
(C) 28 minutes
(D) 38 minutes
(E) None of these
Rationale: Let the total distance to be covered is 48 kms.
Time taken to cover the distance without stoppage = 48/42 hrs = 2 hrs
Time taken to cover the distance with stoppage = 48/28 = 3 hrs.
Thus, he takes 60 minutes to cover the same distance with stoppage.
Therefore, in 1 hour he stops for 20 minutes.
ANSWER:E
Answer: (E) None of these
Question: Two wheels are connected via a conveyor belt. The larger wheel has a 40cm diameter and the smaller wheel has a 24cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?
(A) 1280π
(B) 75r
(C) 100r
(D) 24r
(E) (64π)/3
Rationale: Interesting to note that the larger wheel has a diameter of 40 (8*5) while the smaller one has a diameter of 24 (8*3)...
If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 40pi and 28pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.66 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.66 = 16.6 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.66 = 1000 revolutions per hour.
If r = 10, then the answer choice must be b.
C. 100r
Answer: (C) 100r
Question: If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.150 then sum is
(A) s.15000
(B) s.15100
(C) s.15800
(D) s.16000
(E) s.16200
Rationale: p(r/100)^2=C.I-S.I
P(10/100)^2=150
15000
ANSWER:A
Answer: (A) s.15000
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 88
(B) 20
(C) 99
(D) 18
(E) 11
Rationale: Explanation:
C = 1/2 - 1/4 - 1/5 = 1/20 => 20 days
Answer:B
Answer: (B) 20
Question: Three people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
(A) 1/2
(B) 2/7
(C) 3/2
(D) 4/7
(E) None of them
Rationale: Original share of 1 person = 1/3
New share of 1 person = 1/2
Increase = (1/2 - 1/3	= 1/6)
Therefore, Required fraction = (1/6)/(1/3)	= (1/6)x (3/1)	= 1/2
Answer is A.
Answer: (A) 1/2
Question: 1200 men have provisions for 18 days. If 450 more men join them, for how many days will the provisions last now?
(A) 12.9
(B) 12.0
(C) 12.5
(D) 12.2
(E) 13.1
Rationale: 1200*18 = 1650*x
x = 13.1
Answer:E
Answer: (E) 13.1
Question: If a+b+c=13, a2+b2+c2=69, then find ab+bc+ca
(A) 50
(B) 30
(C) 20
(D) 94
(E) 25
Rationale: (a+b+c)2= a2+b2+c2+2(ab+bc+ca)
2(ab+bc+ca)= (a+b+c)2- a2+b2+c2
=169-69
=100
ab+bc+ca=50
ANSWER A 50
Answer: (A) 50
Question: The letters E,A,W,D,S and R are rearranged to form the word 'Rewads'. Find its probability.
(A) 1/120
(B) 1/720
(C) 1/680
(D) 1/760
(E) 1/53
Rationale: Explanation :
There are total 6 letters. The probability that E gets the first position is 1/6.
The probability that A is in the second position is 1/5.
Likewise, probability for W,D,R and S are 1/4, 1/3,1/2 and 1/1.
Hence, the required probability is:-
=> (1/6) x (1/5) x (1/4) x (1/3) x (1/2) x 1.
=> 1/720.
Answer : B
Answer: (B) 1/720
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but one contained 8 books and the last shelf contained 11 books, how many shelves does the bookcase have?
(A) 8
(B) 6
(C) 4
(D) 3
(E) 2
Rationale: Let x be the number of shelves.
No of books in the beginning =11*x
After taking out 21 books No of remaining books = 11x -21
when the remaining books are rearranged, each shelf except the last shelf has 8 books and the last shelf has 11 books. So No of remaining books is also equal to 8*(x-1)+11
11x-21=8(x-1)+11
3x=24
x=8. Answer A
Answer: (A) 8
Question: A square carpet with an area 169 m2 must have 2 metres cut-off one of its edges in order to be a perfect fit for a rectangular room. What is the area of rectangular room?
(A) 180 m2
(B) 164 m2
(C) 152 m2
(D) 143 m2
(E) None of these
Rationale: Side of square carpet = √Area=√169=13m
After cutting of one side,
Measure of one side = 13 – 2 = 11 m
and other side = 13 m (remain same)
∴ Area of rectangular room = 13 × 11 = 143 m2
Answer D
Answer: (D) 143 m2
Question: One-third less than 20% of 180 is equal to:
(A) 24
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: Lots of ways to tackle this.
20% of 180 =36
1/3 of 36= 12
So, 1/3,less than 36 is equal to 36- 12 = 24
Answer: A
Answer: (A) 24
Question: Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on $4000 for 2 years at 10% per annum. The sum placed on simple interest is:
(A) $1750
(B) $2250
(C) $1250
(D) $1500
(E) $2000
Rationale: Compound Interest = (4000 x (1 + 10/100)^2 - 4000)
= 4000 x 11/10 x 11/10 - 4000 = 840
Therefore the sum is 420 x 100/(3 x 8) = 1750.
Answer A) $1750
Answer: (A) $1750
Question: Average monthly income of a family of 4 earning members was Rs. 782. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?
(A) Rs. 1178
(B) Rs. 820
(C) Rs. 990
(D) Rs. 1385
(E) None
Rationale: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 782 x 4 - 650 x 3 Rs.
= 1178 Rs.
Correct Option: A
Answer: (A) Rs. 1178
Question: At the start of the fall shopping season, a pair of boots cost $700. By the end of the season, the price was reduced to $420. If you waited to purchase the boots at the lower price, what percentage of the original price will you have paid?
(A)  25%
(B)  33%
(C)  50%
(D)  60%
(E)  75%
Rationale: A certain percentage of questions in the Quant section of the GMAT are just 'math questions' - you'll use a formula, do some calculations and you'll have the answer. This is one of those types of questions. You still have to write everything down and stay organized, but the work involved is relatively straight-forward.
Here, we're told that the original price of the boots is $700 but that the purchase price is $420. We're asked what PERCENTAGE OF the original price is the purchase price.
Original Price = $700
Purchase Price = $420
The percentage of the original price of the boots:
$420/$700 = 3/5 = 60%
D
Answer: (D)  60%
Question: Factor: 5x2 – 15x – 20.
(A) 5(x-4)(x+1)
(B) -2(x-4)(x+5)
(C) -5(x+4)(x-1)
(D) 5(x+4)(x+1)
(E) 6(x+4)(x+1)
Rationale: Solution:
5x2 – 15x – 20.
= 5(x2 – 3x – 4).
= 5(x2 – 4x + x – 4).
= 5{x(x - 4) +1(x - 4)}.
= 5(x-4)(x+1).
Answer: (A).
Answer: (A) 5(x-4)(x+1)
Question: with the digits 1,2,3,4,5,6 make all 6 digit nos which r not divisible by 5. The no of such 6 digit no's is ?
(A) 37,880
(B) 38,880
(C) 39,880
(D) 38,890
(E) 38,980
Rationale: 6c1*6c1*6c1*6c1*6c1*5c1 = 6*6*6*6*6*5
= 38,880
ANSWER:B
Answer: (B) 38,880
Question: Find the area of circle whose radius is 21m?
(A) 2884
(B) 1544
(C) 7674
(D) 1684
(E) 1386
Rationale: 22/7 * 21 * 21
= 1386
Answer: E
Answer: (E) 1386
Question: Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all
(A) 15.5
(B) 15
(C) 16
(D) 17
(E) Cant be computed
Rationale: Explanation:
As number of girls and boys is not given so result cant be computed
Option D
Answer: (D) 17