mathewhe/aqua_rat huggingface dataset:
Question: What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
(A) 2000
(B) 2300
(C) 3000
(D) 3300
(E) 3400
Rationale: A.P.=(200X12900)/[4(200+5X3)]=3000 Ans
Alternative
100+105+110+115=12900
430=12900
100=12900/(430)X100=3000
C
Answer: (C) 3000
Question: Insert the missing number.
3, 6, 6, 12, 9, 18, 12, 24, 15, (....)
(A) 30
(B) 36
(C) 42
(D) 40
(E) 38
Rationale: Explanation:
There are two series, beginning respectively with 3 and 6. In one 3 is added and in another 6 is added.
The next number is 24+ 6 = 30.
Answer: A) 30
Answer: (A) 30
Question: If 3a – 2b – 2c = 30 and √3a-√(2b+2c)=4, what is the value of a + b + c?
(A) 3
(B) 9
(C) 10
(D) 12
(E) 14
Rationale: when we look at the two equations, we can relize some similarity, so lets work on it..
3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32
{√3a-√(2b+2c)}{√3a+√(2b+2c)}=32..
or 4*√3a+√(2b+2c)=32..
or √3a+√(2b+2c)=8..
now lets work on these two equations
1)√3a-√(2b+2c)=4..
2)√3a+√(2b+2c)=8..
A) add the two eq..
√3a+√(2b+2c)+√3a-√(2b+2c)=12..
2√3a=12..
or √3a=6..
3a=36..
a=12.
B) subtract 1 from 2..
√3a+√(2b+2c)-√3a+√(2b+2c)=4..
2√(2b+2c)=4..
√(2b+2c)=2..
2b+2c=4..
or b+c=2..
from A and B a+b+c=12+2=14..
C
Answer: (C) 10
Question: If Henry were to add 7 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?
(A) 25
(B) 40
(C) 64
(D) 80
(E) 56
Rationale: 7/8x-3/4x=7galls
1/8*x=7gallons
x=56 gallons
ANswer E
Answer: (E) 56
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is:
(A) 11
(B) 14
(C) 15
(D) 13
(E) 18
Rationale: Age of the 15th student=
[15 * 15 - (14 * 5 + 16 * 9)] = (225 - 214) = 11 years.
ANSWER A
Answer: (A) 11
Question: A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed?
(A) 56m
(B) 52m
(C) 27m
(D) 28m
(E) 19m
Rationale: Length of the wire fencing = perimeter = 2(90 + 50) = 280 metres
Two poles will be kept 5 metres apart. Also remember that the poles will be placed
along the perimeter of the rectangular plot, not in a single straight line which is
very important.
Hence number of poles required = 280 / 5 = 56
Answer: A
Answer: (A) 56m
Question: The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 23 years. What is the age of the new member ?
(A) 20 years
(B) 21 years
(C) 22 years
(D) 23 years
(E) 28 years
Rationale: The average age of the 5 members is 20 years
=> The sum of the ages of the 5 members is 20*5 = 100 years
Once the new member joins, the average age becomes 23 years.
Let the age of the new member be x.
Then (110+x)/6 = 23
=> x = 28 years
Answer E
Answer: (E) 28 years
Question: How long will a boy take to run round a square field of side 35 meters, if he runs at the rate of 9km/hr?
(A) 56sec
(B) 45sec
(C) 1min
(D) 32sec
(E) 25sec
Rationale: Speed = 9 km/hr = 9*5/18 = 5/2 m/sec
Distance = 35*4 = 140m
Time taken = 140*2/5 = 56sec
Answer is A
Answer: (A) 56sec
Question: Find the compound interest on $ 46,000 at 20% per annum for 9 months, compounded quarterly
(A) 2532.05
(B) 2552.32
(C) 2524.34
(D) 7250.75
(E) 9012.55
Rationale: Principal = $ 46000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = $ [46000 x (1+(5/100))^3] = $ 53250.75
CI. = $ (53250.75 - 46000) = $ 7250.75
Answer D.
Answer: (D) 7250.75
Question: If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?
(A) 26
(B) 39
(C) 42
(D) 65
(E) 156
Rationale: Here 156 has three two's
two three's
and one 13
rest of them must be in w
so w= 13*3*4 = 156
Answer: E
Answer: (E) 156
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
(A) 345
(B) 350
(C) 364
(D) 370
(E) 354
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: (C) 364
Question: A rectangle having length 150 cm and width 40 cm. If the length of the rectangle is increased by fifteen percent then how much percent the breadth should be decreased so as to maintain the same area.
(A) 25%
(B) 9.09%
(C) 40%
(D) 75%
(E) None of these
Rationale: Explanation :
Solution: (15/(150+15) * 100)% = 9.09%
Answer : B
Answer: (B) 9.09%
Question: Johnny makes $7.35 per hour at his work. If he works 6 hours, how much money will he earn?
(A) $30
(B) $54
(C) $48.32
(D) $44.10
(E) $9.60
Rationale: 4.75*6=28.50. Answer is C.
Answer: (C) $48.32
Question: A bag contains 3 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.
(A) 19/20
(B) 17/20
(C) 21/40
(D) 7/10
(E) 9/40
Rationale: Let A be the event that ball selected from the first bag is red and ball selected from second bag is green.
Let B be the event that ball selected from the first bag is green and ball selected from second bag is red.
P(A) = (1/2) x (6/10) = 3/10.
P(B) = (1/2) x (4/10) = 1/5.
Hence, the required probability is P(A) + P(B) which is nothing but 7/10
ANSWER:D
Answer: (D) 7/10
Question: The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 275, then the mean profit for the last 15 days would be
(A) Rs. 200
(B) Rs. 350
(C) Rs. 275
(D) Rs. 425
(E) None of these
Rationale: Average would be : 350 = (275 + x)/2
On solving, x = 425.
Answer: D
Answer: (D) Rs. 425
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 5.6
(B) 8.9
(C) 7.2
(D) 2.5
(E) 7.4
Rationale: Explanation:
Speed = Distance/Time
Speed =(600/(5*60))m/sec
Converting m/sec to km/hr
=(2*18/5)km/hr=7.2 km/hr
Answer C
Answer: (C) 7.2
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
(A) 200
(B) 210
(C) 230
(D) 250
(E) 270
Rationale: 7p3 = 7 × 6 × 5 = 210
B)
Answer: (B) 210
Question: 11 speakers gathered to deliver speeches on two topics. Even though 11 speeches were initially planned to be delivered, due to lack of time only 2 speeches were finally decided to be delivered. Topics are to be spoken in a specific order and the speeches differ with respect to speaker or topic. How many such two speeches are possible?
(A) 2
(B) 121
(C) 50
(D) 100
(E) 1024
Rationale: 1)there are 11 speeches in ONE topic and 11 in OTHER..
2)there is a specific order for topics, so
a) both the topics are to be spoken on- so ONE from each
b) the order does not matter since there is ONLY one specific order..
so 11C1∗11C1=11∗11=121
ANSWER:B
Answer: (B) 121
Question: 1!+2!+3!+4!+5!+..100! is divided by 24. Find the remainder?
(A) 2
(B) 5
(C) 9
(D) 10
(E) 12
Rationale: By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24.
So the remainder = 1 + 2 + 6 + 0 + 0....... =
C
Answer: (C) 9
Question: The simple interest on Rs. 20 for 6 months at the rate of 5 paise per rupeeper month is
(A) 1.2
(B) 1.4
(C) 6
(D) 7
(E) None
Rationale: Sol.
S.I. = Rs. [20 * 5/100 * 6] = Rs. 6
Answer C
Answer: (C) 6
Question: C and D started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 10 : 3
(B) 12 : 3
(C) 17 : 3
(D) 20 : 15
(E) None
Rationale: Sol.
C : D = 85000 : 15000 = 85 : 15 = 17 : 3.
Answer C
Answer: (C) 17 : 3
Question: Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 4 times his original investment. What is the value of n
(A) 55/2
(B) 65/2
(C) 75/2
(D) 85/2
(E) 95/2
Rationale: PA=p
t=n
r=8%
According to question
p+(pnr/100)=4p
p[1+n8/100]=4p
n8/100=3
n=300/8
n=75/2
ANSWER:C
Answer: (C) 75/2
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
(A) 38008
(B) 38000
(C) 38029
(D) 380219
(E) 38012
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer:B
Answer: (B) 38000
Question: In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th, 15th, 16 and 17th terms in sequence S?
(A) 3(2^16)
(B) 9(2^15)
(C) 21(2^14)
(D) 9(2^14)
(E) 45(2^13)
Rationale: The terms in the sequence can be shown as
a(n) = 2^(n-1)* a
So, the sequence will look like: 3, 2*3, (2^2) *3,...
And the nth term will be given as 2^(n-1) *3
Therefore, a(14) = (2^13)*3, a(15) = (2^14) *3, a(16) = (2^15) *3 and a(17) = (2^16) *3
So, a(14) + a(15) + a(16)+a(17)= (2^13) *3 + (2^14) *3 + (2^15) *3+ (2^16) *3
= 3* (2^13) *(1+2+4+8) = 3* (2^13) *15
= 45 * (2^13)
Answer : E
Answer: (E) 45(2^13)
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 188
(B) 280
(C) 166
(D) 199
(E) 121
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer:B
Answer: (B) 280
Question: Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 20 miles apart. One and a half hours later, they are again 20 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?
(A) a) 80-x
(B) b) 40-x
(C) c) 26.67-x
(D) d) 120-x
(E) e) 40-x/2
Rationale: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.
Here, the two cars approach a distance 20 mi, then move away from each other another distance of 20 miles. That's a total distance of 40 miles in 1.5 hr, which gives a rate of:
R = (40 mi)/(1.5) = 26.67 mph
That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.
One of the speeds is x, and let's call the other y. We want y.
x + y = 26.67
y = 26.67 - x
Answer =(C)
Answer: (C) c) 26.67-x
Question: Ann invested a certain sum of money in a bank that paid simple interest. The amount grew to $240 at the end of 2 years. She waited for another 3 years and got a final amount of $300. What was the principal amount that she invested at the beginning?
(A) $150
(B) $175
(C) $200
(D) $210
(E) $220
Rationale: Amount at end of 2 years = 240$
Amount at end of 5 years = 300$
Difference in amount for time period of 3 years = 60$
Annual Interest earned = 60/3 = 20$
Principal amount invested at the beginning = 240 - 2*20 = 200$
Answer C
Answer: (C) $200
Question: A shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
(A) Rs.55
(B) Rs.57
(C) Rs.54
(D) Rs.50
(E) Rs.87
Rationale: SP per metre = 18000/400
= Rs. 45 Loss per metre
= Rs. 5 CP per metre = 45 + 5
= Rs.50
Answer: D
Answer: (D) Rs.50
Question: A shipment of 9 television sets contains 2 black-and-white sets and 6 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?
(A) 1/7
(B) 1/4
(C) 5/14
(D) 11/28
(E) 7/12
Rationale: I get 7/12, which is not in the answer choices.
the probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)
1-C(6,2)/C(9/2)=21/36=7/12
E
Answer: (E) 7/12
Question: Sandy invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Sandy got back 5 times the original investment. What is the value of n?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: n* 0.08 * principal + principal = 5 * principal
n * 0.08 = 4
n = 50 years
The answer is E.
Answer: (E) 50
Question: Find large number from below question The difference of two numbers is 1335. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1254
(B) 1376
(C) 1456
(D) 1599
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1335).
x + 1335 = 6x + 15
5x = 1320
x = 264
Large number = 264+1335 = 1599
D
Answer: (D) 1599
Question: ((7.3)*(10^2))-((7)*(10^2))=?
(A) 300
(B) 30
(C) 730
(D) 7300
(E) 3000
Rationale: 10^2 is nothing but a 100.
7.3*(10^2)=7.3*100=730.
7*(10^2)=7*100=700
=730-700=30
The answer is option B
Answer: (B) 30
Question: Jadeja has x dollars more than Sharma has, and together they have a total of y dollars. Which of the following represents the number of dollars that Sharma has?
(A) 3(y – x)/2
(B) 5(y – x)/2
(C) (y – x)/5
(D) (y – x)/2
(E) (y – x)/6
Rationale: To solve, we will set up two equations. Let's start by defining two variables.
A = number of dollars Sharma has
B= number of dollars Jadeja has
We are given that Jadeja has x dollars more than Sharma. We set up an equation:
B= x + A
We are next given that together they have a total of y dollars. We can set up our second equation:
A + B = y
Since we know that B = x + A, we can substitute x + A for B into the second equation A+ B = y.
Notice that, after the substitution, we will only have variables of A, x, and y. Thus, we have:
A + x + A = y
2A + x = y
2A = y – x
A = (y – x)/2
Answer : D
Answer: (D) (y – x)/2
Question: The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people Z who purchased only book A?
(A) 250
(B) 500
(C) 750
(D) 1000
(E) 1500
Rationale: This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both, Z=1000 purchased A only. (This is much simpler to solve using the Venn diagram).
Correct answer is D. 1000
Answer: (D) 1000
Question: What number has a 150:1 ratio to the number 2?
(A) 130
(B) 300
(C) 200
(D) 30
(E) 75
Rationale: 150:1 = x: 2
x = 150*2
x=300
ANSWER:B
Answer: (B) 300
Question: What is the greatest number of four digits which is divisible by 8, 16, 32 and 40 ?
(A) 9930
(B) 9940
(C) 9920
(D) 9950
(E) 9960
Rationale: Greatest number of four digits = 9999
LCM of 8, 16, 32 and 40 = 160
9999 ÷ 160 = 62, remainder = 79
Hence, greatest number of four digits which is divisible by 8, 16, 32 and 40
= 9999 - 79 = 9920
answer : C
Answer: (C) 9920
Question: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
(A) Rs.1185
(B) Rs.1285
(C) Rs.1385
(D) Rs.1485
(E) Rs.1495
Rationale: 22/7 * 14 * 3/2 * 3/2 = 99 m2
99 * 15 = 1485
ANSWER:D
Answer: (D) Rs.1485
Question: 5 men and 11 boys finish a job in 13 days, 11 men and 11 boys finish it in 10 days. 6 men and 6 boys shall finish it in how many days?
(A) 12
(B) 17
(C) 10
(D) 13
(E) 18
Rationale: 5 M + 11 B ----- 13 days
11 M + 11 B ------- 10 days
06 M + 06 B -------?
55 M + 121 B = 66 M +66 B
55 B = 11 M => 5 B = 1 M
25 B + 11 B = 36 B ---- 13 days
30 B + 6 B = 36 B -----? => 13 days
Answer: D
Answer: (D) 13
Question: If the price of a certain computer increased 30 percent from b dollars to 351 dollars, then 2b =
(A) 540
(B) 570
(C) 619
(D) 649
(E) 700
Rationale: Before Price increase Price = b
After 30% Price increase Price = b+(30/100)*b= 1.3b = 351 (Given)
i.e. b= 351/1.3 = $270
i.e. 2b = 2*270 = 540
Answer: option A
Answer: (A) 540
Question: A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 20% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
(A) 45%
(B) 40%
(C) 35%
(D) 30%
(E) 25%
Rationale: Anyway, in this question, there is no discount but the mark up is given as 40% of the selling price. So it is not 20% of $150 but instead, 20% of Selling price which is obtained by adding mark up to $150.
So if selling price is S,
150 + 20% of S = S
S = 150/0.8
Profit = 150/0.8-150= which is calculated on cost price in % terms. So 37.5/150 * 100 = 25% is profit.
E
Answer: (E) 25%
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 20 white marbles. How many red marbles could be in bag A?
(A) 1
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: 6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:4
Let W in bag B be 4k
W = 20 = 6K+4k
k=2
Total Red's in bag A will be 2K = 4
C
Answer: (C) 4
Question: On a scale that measures the intensity of a certain phenomenon, a reading of g+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of g. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?
(A)  5
(B)  50
(C)  10^5
(D)  5^10
(E)  8^10 - 3^10
Rationale: To solve this problem we need to examine the information in the first sentence. We are told that “a reading of g + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of g.”
Let’s practice this idea with some real numbers. Let’s say g is 2. This means that g + 1 = 3. With the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2.
Furthermore, we can say that a reading of 4 is actually 10 x 10 = 10^2 times as great as the intensity of a reading of 2.
Increasing one more unit, we can say that a reading of 5 is 10 x 10 x 10 = 10^3 times as great as the intensity of a reading of 2.
We have found a pattern, which can be applied to the problem presented in the stem:
3 is “one” unit away from 2, and thus a reading of 3 is 10^1 times as great as the intensity of a reading of 2.
4 is “two” units away from 2, and thus a reading of 4 is 10^2 times as great as the intensity of a reading of 2.
5 is “three” units away from 2, and thus a reading of 5 is 10^3 times as great as the intensity of a measure of 2.
We can use this pattern to easily answer the question. Here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3. Because 8 is 5 units greater than 3, a reading of 8 is 10^5 times as great as the intensity corresponding to a reading of 3.
Answer C.
Answer: (C)  10^5
Question: 17 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
(A) 34
(B) 87
(C) 30
(D) 99
(E) 77
Rationale: 3W = 2M
17M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
17 * 21 * 8 = 14 * x * 6
x = 34
Answer: A
Answer: (A) 34
Question: If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 96?
(A) 20
(B) 22
(C) 24
(D) 12
(E) 36
Rationale: The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.
The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.
96=2*3*4*4 is divisible by 12. therefore the greatest common divisor is 12
D
Answer: (D) 12
Question: A is thrice efficient as B and C is twice as efficient as B. what is the ratio of number of days taken by A,B and C, when they work individually?
(A) 2:6:3
(B) 2:6:9
(C) 2:6:6
(D) 2:6:1
(E) 2:6:2
Rationale: Answer: A) 2:6:3
Answer: (A) 2:6:3
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. c-a=2
II. abc is an even integer
III. a-b is positive integer
(A) I
(B) II
(C) I and II
(D) II and III
(E) I, II and III
Rationale: If a, b, c are consequitive positive integers and a<b<c, which of the following must be true?
1. c-a=2
2. abc is an even integer
3. (a+b+c) is an integer
1.
a=a
b=a+1
c=a+2
c-a=a+2-a=2.
Correct
2. abc
a can be either even or odd
if a=even; abc=even;
if a=odd,b=even; abc=even
Rule:
multiple of any number of integers if atleast once multiplied by an even number will result in even.
even*even=even
even*odd=even
Correct
3. a-b = 1-2 = -1 => negative
Answer : C
Answer: (C) I and II
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 4900 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140 sq.units
(B) 280 sq.units
(C) 167sq.units
(D) 178sq.units
(E) 176sq.units
Rationale: Given that the area of the square = 4900 sq.units
=> Side of square = √4900 = 70 units
The radius of the circle = side of the square = 70 units Length of the rectangle = 2/5 * 70 = 28 units
Given that breadth = 10 units
Area of the rectangle = lb = 28 * 10 = 280 sq.units
Answer:B
Answer: (B) 280 sq.units
Question: In a Question paper there are 4 subjects. Each subject has has 5 question sets with each subject having one single question set that is the toughest of all. What is the total number of ways in which a candidate will not get all the four toughest question sets?
(A) 19
(B) 85
(C) 120
(D) 624
(E) 1024
Rationale: A candidate can get a question set in 5*5*5*5=5^4 number of ways (each aubject has 5 question sets and we have total of 4 subjects). Now, out of these cases there will be only one case when the candidate got all the four toughest question sets. Therefore the total number of ways in which a candidate will NOT get all the four toughest question set is is 5^4-1=624.
Answer: D.
Answer: (D) 624
Question: A card is randomly drawn from a deck of 52 cards. What is the probability getting an Ace or King or Queen?
(A) 7/13
(B) 9/13
(C) 3/13
(D) 4/13
(E) 5/13
Rationale: Total number of cards = 52
Total number of Ace cards = 4
P(Ace) = 4/52=1/13
P(King) = 4/52=1/13
P(Queen) = 4/52=1/13
P(Ace or King or Queen) = P (Ace) + P (King)+ P(Queen)
=1/13+1/13+1/13=3/13
Answer C
Answer: (C) 3/13
Question: Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If E is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?
(A)  0<y<4
(B)  4<y<10
(C)  10<y<20
(D)  20<y<30
(E)  y>30
Rationale: E Smallest prime factor is greater than 29. So answer is E
Answer: (E)  y>30
Question: In a certain population, there are 6 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is
(A)  1 to 2
(B)  1 to 3
(C)  1 to 4
(D)  2 to 3
(E)  6 to 7
Rationale: Consider the ratio of the under population of 21 to over the 21 as 6:1
therefore 6x:1X
Now the ratio of the under to the whole population becomes 6x/6x+1x
= 6/7
Answer is E
Answer: (E)  6 to 7
Question: What percent of 5.2 kg is 16 gms ?
(A) 30
(B) 66
(C) 58
(D) 29
(E) 17
Rationale: Explanation:
Required percentage = (16/5200 * 100)% = 3/10% = 0.30%
Answer: A) .30%
Answer: (A) 30