mathewhe/aqua_rat huggingface dataset:
Question: 15 + sqrt(- 6 + 8Ã—5Ã·4) =?
(A) 31
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: According to order of operations, inner brackets first where 8x5Ã·4 is first calculated since it has a multiplication and a division.
8x5Ã·4 = 40Ã·4 = 10
Hence
15 + sqrt(- 6 + 8Ã—5Ã·4) = 15+ sqrt(- 6 + 10)
= 15 + sqrt(4) = 15 + 16 = 31
correct answer A)31
Answer: (A) 31
Question: How many of the positive factors of 63 , 84 and how many common factors are there in numbers?
(A) 2
(B) 4
(C) 3
(D) 5
(E) 1
Rationale: factors of 63 - 1,3,7,9,21,63
factors of 84 - 1,2,3,4,6,7,12,14,21,28,42,84
Comparing both, we have three common factors of 63 and 84- 1,3,7,21
Answer(B)
Answer: (B) 4
Question: A numberais squared and then multiplied by negative 3. The result of this operation R is equal to three times the sum of three timesaand two. What is one possible value ofa?
(A) -3
(B) -2
(C) 1
(D) 2
(E) 3
Rationale: R=-3*a^2=3(3a+2)
a= -2 or -1
a=-2=B
Answer: (B) -2
Question: Let the number which when multiplied by 13 is increased by 180.
(A) 14
(B) 20
(C) 15
(D) 28
(E) 30
Rationale: Solution
Let the number be x .
Then, 13x - x = 180
‹=›12x = 180
x ‹=› 15.
Answer C
Answer: (C) 15
Question: 5 persons a, b, c, d, e are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?
(A) 24
(B) 36
(C) 48
(D) 72
(E) 144
Rationale: firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..
total 5 are there..
take a,b, and c as one,so total =3..
these 3 can be arranged in 3! ways..
a,b, and c can be arranged within themselves in 3! ways ..
TOTAL = 3!*3!=36
B
Answer: (B) 36
Question: A rower whose speed is 4 km/hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 2 km/hr. What is the rower's average speed (in km/hr) for the total journey?
(A) 6
(B) 4
(C) 9
(D) 3
(E) 2
Rationale: time upstream = d / 2
time downstream = d / 6
total time = d/2 + d/6 = 2d/3
average speed = 2d / (2d/3) = 3 km/hr
The answer is D.
Answer: (D) 3
Question: What is the probability of getting exactly 2 heads in a single throw of four fair coins?
(A) 1/2
(B) 3/4
(C) 3/8
(D) 3/16
(E) 5/16
Rationale: One possible case is HHTT.
P(HHTT) = 1/2*1/2*1/2*1/2 = 1/16
There are 4C2 = 6 possible cases.
P(2 heads) = 6*1/16 = 3/8
The answer is C.
Answer: (C) 3/8
Question: The sale price sarees listed for Rs.750 after successive discount is 20% and 15% is?
(A) 227
(B) 570
(C) 342
(D) 680
(E) 230
Rationale: 750*(80/100)*(85/100)
= 570
Answer: B
Answer: (B) 570
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
(A) 49
(B) 88
(C) 25
(D) 18
(E) 11
Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
Answer: A
Answer: (A) 49
Question: How many odd factors does 520 have?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  8
Rationale: Start with the prime factorization: 520 = 2*5*13
For odd factors, we put aside the factor of two, and look at the other prime factors.
set of exponents = {1, 1}
plus 1 to each = {2, 2}
product = 2*2 = 4
Therefore, there are 4 odd factors of 520.
Answer: B.
Answer: (B)  4
Question: Population of a city in 20004 was 1300000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
(A) 354354
(B) 545454
(C) 465785
(D) 456573
(E) 2818075/2
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 2818075/2
E
Answer: (E) 2818075/2
Question: Find the area of a parallelogram with base 32 cm and height 14 cm?
(A) 498 cm2
(B) 384 cm2
(C) 430 cm2
(D) 128 cm2
(E) 448 cm2
Rationale: Area of a parallelogram
= base * height
= 32 * 14 = 448 cm2
Answer:E
Answer: (E) 448 cm2
Question: The probability of Sam passing the exam is 1/5. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test?
(A) 1/24.
(B) 1/2.
(C) 5/6.
(D) 2/3.
(E) 2/5
Rationale: 1/5 *1/m= 1/6 , 1/m = 5/6
Answer C
Answer: (C) 5/6.
Question: A shipment of 8 television sets contains 2 black-and-white sets and 4 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) 11/14
(E) 13/28
Rationale: I get 11/14, 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(4,2)/C(8/2)=22/28=11/14
D
Answer: (D) 11/14
Question: An office supply store stocks three sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 3 notebooks of the same size and the same color or 3 notebooks of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
(A) 24
(B) 30
(C) 42
(D) 45
(E) 60
Rationale: First let's consider the small notebooks.
There are 5 ways to choose 3 notebooks of the same color.
The number of ways to choose 3 notebooks with different colors is 5C3=10.
There are 15 different packages we can make with the small notebooks.
We can use the same process to find 15 different packages with medium and large notebooks.
The total number of different packages is 45.
The answer is D.
Answer: (D) 45
Question: A train 175 m long pass a telegraph pole in 5 seconds. Find the speed of the train
(A) 66 km/hr
(B) 68.4 km/hr
(C) 72 km/hr
(D) 126 km/hr
(E) None
Rationale: Sol.
Speed = [175/6] m/sec = [352 * 18/5] km/hr = 126 km/hr.
Answer D
Answer: (D) 126 km/hr
Question: A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in?
(A) 20 years
(B) 1 years
(C) 15 years
(D) 39 years
(E) 39 years
Rationale: Explanation:
P(1 + R/100)5 = 2P => (1 + R/100)5 = 2
Let P(1 + R/100)n = 8P
=> (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3
=> (1 + R/100)n = (1 + R/100)15 => n = 15 Required time = 15 years.
Answer: Option C
Answer: (C) 15 years
Question: Set F consists of all the prime numbers between 10 and 25. What is the range of set F?
(A) 12
(B) 13
(C) 16.6
(D) 17
(E) 23
Rationale: Answer of set F is 12=A
Answer: (A) 12
Question: If a mixture is 5⁄9 alcohol by volume and 4⁄9 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
(A) 1/4
(B) 3/4
(C) 5/4
(D) 6/4
(E) 7/4
Rationale: Should be a sub-600 level Q..
volume= {5/9}/{4/9}=5/4
C
Answer: (C) 5/4
Question: when n divided by 3, the remainder is 2.
when n divided by 4, the remainder is 1
what is the the remainder when divided by 12
(A) 1
(B) 3
(C) 4
(D) 5
(E) 12
Rationale: when n divided by 3, the remainder is 2.
This statement can be written as
n=3k+2 (where k is the quotient) ----1
similarly
when n is divided by 4, the remainder is 1
can be written as
n=4p+1 (here p is the quotient) ------2
from eq 1 and 2
3k+2=4p+1
or,
k=(4p-1)/3
substitute p= 1 , the result will give ----> k=1
substitute back in the equations
in both the cases we have n=5
dividing n by 12 will give remainder 5 !!
ANSWER:D
Answer: (D) 5
Question: The mean of set L does not exceed mean of any subset of set L. Which of the following must be true about set L?
I. Set L contains only one element
II. All elements in set L are equal
III. The median of set L equals the mean of set L
(A) of the three qualities is necessary
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: The only necessary condition seems to be II.
If all nos are equal.... them mean of any subset is the same.
I is obviously ruled out ( e.g. L = {1,1,1} )
But III, what about 3?
It is not necessary in itself, rather, is automatically implied by II.
All sets that satsify II satisfy III=D
Answer: (D) II and III only
Question: The ratio of number of students studying Arts, Commerce and Science in a College is 7 : 5 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
(A) 18 : 35 : 50
(B) 3 : 10 : 10
(C) 4 : 8 : 5
(D) 21 : 35 : 50
(E) None of these
Rationale: Suppose the number of students studying Arts, Commerce and Science be 7x, 5x and 8x respectively.
When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes
7x × 120% : 5x × 140% :
8x × 125% = 42 : 70 : 100
= 21 : 35 : 50
Answer D
Answer: (D) 21 : 35 : 50
Question: xy=1 then what is (4^(x+y)^2) / (4^(x-y)^2)
(A) 2
(B) 4
(C) 8
(D) 256
(E) 32
Rationale: (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
4^4 = 256
Answer D
Answer: (D) 256
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:9
(C) 1:1
(D) 1:9
(E) 3:2
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer: A
Answer: (A) 1:2
Question: A researcher computed the mean, the median, and the standard deviation Q for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
(A) The mean only
(B) The median only
(C) The standard deviation only
(D) The mean and the median
(E) The mean and the standard deviation
Rationale: If we add or subtract a constant to each term in a set the standard deviation Q will not change..
If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.
Answer: D.
Answer: (D) The mean and the median
Question: If X = Y/Z+1, -1 < Z < 0 and 2 < Y, which of the following is correct?
(A) 1 < X <2
(B) 0 < X <-2.
(C) -4 < X < 0
(D) 0 < X <-4
(E) X < -20
Rationale: Y is +ve & Z is -ve
For min. value max. numerator and minimize denominator
take Y=2.1 & Z=-0.9
X=2.1/(-0.9+1) X=2.1/1.9
1 < X <2
Ans A
Answer: (A) 1 < X <2
Question: If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?
(A) 25/√π
(B) 30/√π
(C) 20
(D) twenty five (25)
(E) 30
Rationale: 60/360 = 1/6
1/6 of total area = 5
5/6 of total area = 5*5 = 25
ANSWER:D
Answer: (D) twenty five (25)
Question: Two assembly line inspectors, Lauren and Steven, inspect widgets as they come off the assembly line. If Lauren inspects every fourth widget, starting with the fourth, and Steven inspects every third, starting with the third, how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector?
(A) 50
(B) 52
(C) 53
(D) 55
(E) 56
Rationale: Widgets inspected by Lauren: ((96-4)/4)+1=23+1=24
Widgets inspected by Steven: ((96-3)/3)+1 =31+1 =32
Widgets inspected by both: ((96/12)+1 =9
Total : 24+32 -9=45
hence, widgets not inspected: 98-45=53
Option C
Answer: (C) 53
Question: How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 36 sec
(B) 30 sec
(C) 13 sec
(D) 19 sec
(E) 12 sec
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 600 * 3/50
= 36 sec.
Answer:A
Answer: (A) 36 sec
Question: In a series of football matches, the probability that Team P wins a match against Team Q is 1/3 and the probability that the match ends in a draw is 1/5. If the two teams play five matches, what is the probability that all five matches end in a draw?
(A) 1/1625
(B) 1/2225
(C) 1/3125
(D) 1/4225
(E) 1/5425
Rationale: P(5 draws)=(1/5)^5=1/3125
The answer is C.
Answer: (C) 1/3125
Question: A man gets a simple interest of Rs.600 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
(A) Rs.500
(B) Rs.250
(C) Rs.307.5
(D) Rs.5062.50
(E) None of these.
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.600
(P)(8)(5)/100 = 600
P = 1500
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=3000{ [1 + 5/100]2 - 1} = 3000{ 212 - 202 /202}
= 3000/400(441 - 400)
= Rs.307.5
ANSWER:C
Answer: (C) Rs.307.5
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 167 ways
(B) 828 ways
(C) 627 ways
(D) 108 ways
(E) 622 ways
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer:D
Answer: (D) 108 ways
Question: A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
(A) 1375 toys
(B) 2375 toys
(C) 3375 toys
(D) 4375 toys
(E) 5375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
5500 ? 4 = 1375 toys
correct answer A
Answer: (A) 1375 toys
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 20 kmph
(B) 40 kmph
(C) 27 kmph
(D) 28 kmph
(E) 22 kmph
Rationale: Speed downstream = 60 + 20
= 80 kmph
Speed upstream = 60 - 20
= 40 kmph
Answer:B
Answer: (B) 40 kmph
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) 87
(B) 98
(C) 12
(D) 27
(E) 28
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) 12
Question: The length and width of a rectangle are integer values. What is the area of the smallest such rectangle that can be inscribed in a circle whose radius is also an integer
(A)  12
(B)  24
(C)  46
(D)  48
(E)  60
Rationale: If we consider all pythagorean triplets with integral values, we have the following results:-
(3,4,5),(6,8,10)........
The diameter of the circle is 5 in the 1st case and 10 in the 2nd.
But the question says that radius of the circle is also an integer hence the 1st triplet will be ruled out.
We are left with the 2nd triplet where radius of the circle=5,
Hence the sides of the rectangle are 6 and 8 making the area =46.
C
Answer: (C)  46
Question: Solving a linear equation with several occurrences of the variable, solve for w. Simplify answer as much as possible.
(7w + 6)/6 + (9w +8)/2 = 22
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (7w + 6)/6 + (9w +8)/2 = 22
or, [7w + 6 + 3(9w + 8)]/6 = 22
or, 7w + 6 + 27w + 24 = 132
or, 34w + 30 = 132
or, 34w = 132 - 30
or, 34w = 102
or, w = 102/34
Therefore, w = 3
Answer: C
Answer: (C) 3
Question: What is the square root of 81, divided by 3?
(A) 9
(B) 36
(C) 122
(D) 3
(E) 1
Rationale: Square root is a number times itself
Square root of 81=6, 9/3=3
(D)3
Answer: (D) 3
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 56 more. What was his original selling price?
(A)  $770
(B)  $660
(C)  $700
(D)  $1100
(E)  $880
Rationale: Let the original purchase price be X
So original selling price at 10% profit = 1.1X
If product is purchased at 10% less of original = 0.9X
Profit of 30% on this price = 1.3(0.9X)
He would have received $56 more in second scenario => 1.3(0.9X) - 1.1X = 56
=> 0.07X = 56
=> X = $800
Original purchase price = $800
Hence, original selling price (at 10% of profit) = 1.1(800) = $880
Option E
Answer: (E)  $880
Question: Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 222 runs?
(A) 6
(B) 6.25
(C) 7.25
(D) 7.5
(E) 4.75
Rationale: Required run rate = 222 - (3.2 x 10) =	190 = 4.75
40	40
E
Answer: (E) 4.75
Question: Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 48 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
(A) 72 sec
(B) 132 sec
(C) 157.5 sec
(D) 252 sec
(E) None
Rationale: Solution
Relative Speed	= (48 - 40 ) Kmph
= 8 kmph
=(8 x 5 / 18)m/sec
= (40 / 18 ) m/sec
Time taken	= (350 x 18 / 40) sec
= 157.5 sec.
Answer C
Answer: (C) 157.5 sec
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
(A) 23277
(B) 20000
(C) 28778
(D) 28788
(E) 18881
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer: B
Answer: (B) 20000
Question: If a real number x is chosen at random in the interval [0,5] and a real number y is chosen at random in the interval [0,7], what is the probability that x < y?
(A) 5/7
(B) 2/3
(C) 9/14
(D) 4/5
(E) 7/8
Rationale: Since x is in [0,5] and y is in [0,7] we can draw a rectangle in the coordinate plane with vertices (0, 0), (5, 0), (0, 7), and (5, 7).
The points above the line y=x satisfy x < y.
The part of the rectangle below y=x has an area of 12.5
The whole rectangle has an area of 35.
P(x < y) = (35-12.5)/35 = 22.5/35 = 45/70 = 9/14
The answer is C.
Answer: (C) 9/14
Question: Three bottles whose capacities are as 5 : 3 : 2 are completely filled with milk mixed with water. The ratio of milk to water in the mixture of bottles are as 3 : 2, 2 : 1 and 3 : 1 respectively. Find the percentage of water in the new mixture obtained when 1/3rd of first, 1/2 of second and 2/3rd of the third bottle is taken out and mixed together
(A) 66.66%
(B) 50%
(C) 16.66%
(D) 33.33%
(E) 36.33%
Rationale: Let the percentage of water be X
The quantity of new mixture = (5X/3) + (3X/2 )+ (4X/3) = 27X/6 = 9X/2.
Percentage of milk = (5X/3) x (3/5) + (3X/2) x (2/3) + (4X/3) x (3/4) = 3X
Percentage of water = (5X/3) x (2/5) + (3X/2) x (1/3) + (X/2) x (2/3) = 3X/2
Percentage of water = (3X/2)/(9X/2) x 100
= 100/3
= 33 (1/3)%
ANSWER:D
Answer: (D) 33.33%
Question: The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?
(A) 5N
(B) 7N
(C) 10N
(D) 15N
(E) 20N
Rationale: In 1992, the company's assets were N.
In 1993, the company's assets were N + 4N = 5N.
In 1994, the company's assets were 5N + 5N = 10N.
The answer is C.
Answer: (C) 10N
Question: If A and B get profits of Rs.5,000 and Rs.2,000 respectively at the end of year then ratio of their investments are
(A) 4:1
(B) 1:4
(C) 5:2
(D) 2:3
(E) 2:5
Rationale: Ratio = 5000/2000 = 5 : 2
Answer : C
Answer: (C) 5:2
Question: If the cost price of 44 chocolates is equal to the selling price of 24 chocolates, the gain percent is :
(A) 83.55%
(B) 83.33%
(C) 80%
(D) 83.39%
(E) 84.33%
Rationale: Explanation :
Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 24 chocolates = Rs. 24;
S.P. of 24 chocolates =Rs. 44.
.'. Gain% = 20*100/24 =83.33%
Answer : B
Answer: (B) 83.33%
Question: If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor A of 2x and 3y?
(A) A=1
(B) A=Cannot be determined
(C) 2
(D) 5
(E) 6
Rationale: My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.
and hence answer B
Answer: (B) A=Cannot be determined
Question: The original price of a certain TV set is discounted by d percent, and the reduced price is then discounted by 2d percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?
(A) P(1 - 0.03x + 0.02x^2)
(B) P(1 - 0.03d + 0.0002d^2)
(C) P(1 - 0.03x + 0.002x^2)
(D) P(1 - 2x^2)
(E) P(1 - 3x + 2x^2)
Rationale: Youcansolve this problem with number plugging.
Say the original price was $10 and d=50. Then after the first reduction the price would become $5 and after the second reduction of 2*50=100% the rprice would become $0.
Now, since P is not zero, then the expression in the brackets must be zero for d=50. Only answer choice B works.
Answer: B.
On this problem - number pluggin is not giving me the answer.. I initially used d = 10, then 2d = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.
100 (1-0.03(10) + 0.0002 (10)^2)
100 (1-0.3 + 0.0002 (100))
100 (0.7 + 0.02)
100 (0.68) = 68????
double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice B..
Answer: (B) P(1 - 0.03d + 0.0002d^2)
Question: Of 300 surveyed students, 20% of those who read book A also read book B and 50% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?
(A) 120
(B) 125
(C) 130
(D) 135
(E) 150
Rationale: Say the number of students who read book A is A and the number of students who read book B is B.
Given that 20% of those who read book A also read book B and 50% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.5B --> A=2.5B.
Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 300=2.5B+B-0.5B --> B=100, A=2.5B=250 and {Both}=0.5B=50.
The number of students who read only book A is {A}-{Both}=250-50=200;
The number of students who read only book B is {B}-{Both}=100-50=50;
The difference is 200-50=150.
Answer: E.
Answer: (E) 150
Question: John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?
(A) 50 ml
(B) 60 ml
(C) 70 ml
(D) 80 ml
(E) 90 ml
Rationale: concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)
concentration of water in pure water= 1 ...(2)
Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3
=> concentration of water in mixture2 =310
By rule of alligation,
concentration of water in mixture1 (29)
concentration of water in pure water (1)
Mean concentration
(310)
1−310=710
310−29=790
=> Quantity of mixture1 : Quantity of water
=710:790=110:190=1:19
Given that Quantity of mixture1 = 630 ml
=> 630 : Quantity of water =1:19
=> Quantity of water =630×19=70 ml
C
Answer: (C) 70 ml
Question: By investing Rs. 1620 in 8% stock,Michael earns Rs. 135.The stock is then quoted at :
(A) Rs. 80
(B) Rs. 96
(C) Rs. 106
(D) Rs. 108
(E) Rs. 109
Rationale: Solution
To earn Rs. 135, investment = Rs. 1620.
To earn Rs. 8, investment = Rs. (1620/135X8)= Rs. 96.
∴ Market value of Rs. 100 stock = Rs. 96.
Answer B
Answer: (B) Rs. 96
Question: The least number which must be subtracted from 509 to make it exactly divisible by 9 is:
(A) A)2
(B) B)3
(C) C)5
(D) D)5
(E) E)6
Rationale: On dividing 509 by 9, we get remainder= 5
Therefore, required number to be subtracted= 5
Answer: C
Answer: (C) C)5
Question: A watch was sold at a loss of 10%. If the watch was sold for $28 more, there would have been a gain of 4%. What is the cost price?
(A) $180
(B) $200
(C) $220
(D) $240
(E) $260
Rationale: 0.9x + 20 = 1.04x
0.14x = 28
x = 200
The answer is B.
Answer: (B) $200