mathewhe/aqua_rat huggingface dataset:
Question: The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 8
(B) 9
(C) 7
(D) 62
(E) 2
Rationale: 2x * x = 162 => x= 9
Answer: B
Answer: (B) 9
Question: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 135 mangoes.
(A) 360
(B) 380
(C) 400
(D) 450
(E) 412
Rationale: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.
Method 1:
Let price per mango = x. Let number of mangoes be n. Then, nx = 360.
Now price = 0.9x; number of mangoes = n + 12. Total amount = 0.9x*(n+12) = 360.
nx = 0.9nx + 10.8x => 0.1nx = 10.8x => n = 108 => x = 360/108 = 3.33
Original price of 135 mangoes = 135*3.33 = 450.
Answer D
Answer: (D) 450
Question: A train running at the speed of 45 km/hr crosses a pole in 16 seconds. Find the length of the train.
(A) 200
(B) 188
(C) 204
(D) 288
(E) 500
Rationale: Speed = 45*(5/18) m/sec =25/2 m/sec
Length of Train (Distance) = Speed * Time
(25/2) * 16 = 200 meter
Answer: A
Answer: (A) 200
Question: If (a-5)(b+2) = 0 which of the following must be true?
(A)  a = b
(B)  a > b
(C)  a < b
(D)  ab = -10
(E)  None of the above
Rationale: (a-5)(b+2) = 0 means that EITHER a=5 OR b=-2. For example, if a=5, then y can be any number. The same way, if b=-2, then a can be any number.
Bunuel, although your solution is perfect, I would just point out arewordingsuggestion on your last comment. (a-5)(b+2) =0 means that a = 5 OR b =-2 (without the EITHER). Obviously both equalities COULD happen simultaneously, but they don't HAVE TO happen simultaneously in order for the equation in stem to be valid
Answer is E
Answer: (E)  None of the above
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
(A) 70
(B) 25
(C) 60
(D) 80
(E) 55
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
ANSWER A
Answer: (A) 70
Question: If r = 199,999 and s = 991,999, which of the following is the units digit of r^3 + s^3?
(A) 0
(B) 1
(C) 2
(D) 8
(E) 9
Rationale: The exponents of 9 cycle between 9 (odd exponents) and 1 (even exponents).
Then the sum of r^3+s^3 will have the units digit of 9+9 = 18 as a units digit.
The answer is D.
Answer: (D) 8
Question: Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 10 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?
(A) 1 hour
(B) 1 hour 10 minutes
(C) 2 hours 30 minutes
(D) 50 minutes
(E) 2 hours 10 minutes
Rationale: Both cars leave at the same time
Both cars travel at constant speed
Stealing a useful piece of information from Paragkan:
If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
ratio of speed: (a/b) = sq. rt(b/a)
sq. rt(b/a)
sq. rt(90/10)
sq. rt(3/2)
So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.
90*(2/3)where 2/3 represents the lesser amount of time it took A to travel the distance B did in 90 minutes.
= 60 minutes.
Therefore, A took 10 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (10+60)=50 minutes on the road.
D. 50 minutes
Answer: (D) 50 minutes
Question: 10^185 - 10^30 =
Which of the following best approximates the value of the expression above?
(A) 10^180
(B) 10^179
(C) 10^170
(D) 10^160
(E) 10^185
Rationale: 10^185 - 10^30 =
Which of the following best approximates the value of the expression above?
Yes, answer 10^185 is correct. Note that we need approximate value of the given expression and as 10^(185) is much larger number than 10^(30) then 10^(30) is pretty much negligible in this case: 10^(185)-10^(30)=~10^(185).
Answer : E
Answer: (E) 10^185
Question: A bag contains 21 toys numbered 1 to 21. A toy is drawn and then another toy is drawn without replacement. Find the probability that both toys will show even numbers.
(A) 5/21
(B) 9/42
(C) 6/22
(D) 4/21
(E) 3/21
Rationale: Since there are 10 even numbers in the given range, the probability that the first toy shows an even number = 10/21
Since the toy is not replaced, there are now 9 even numbered toys and total 20 toys left.
Hence, probability that the second toy shows an even number = 9/20.
Required probability = 10/21 x 9/20 = 9/42.
ANSWER:B
Answer: (B) 9/42
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 25%?
(A) 2
(B) 9
(C) 6
(D) 3
(E) 5
Rationale: C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 150% of Re. 1 = Rs. 3/2
For Rs. 3/2 , toffees sold = 6.
For Re. 1, toffees sold = 6 x3/2 = 9.
Answer B
Answer: (B) 9
Question: A hostel had provisions for 250 men for 40 days. If 50 men left the hostel, how long will the food last at the same rate?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 65
Rationale: A hostel had provisions for 250 men for 40 days
If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.
Let the required number of days = x days
More men, Less days (Indirect Proportion)
(men) 250 : 200 :: x : 40
250×40=200x
5×40=4x
x=5×10=50
ANSWER C
Answer: (C) 50
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 28%
(B) 25%
(C) 85%
(D) 24%
(E) 22%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: B
Answer: (B) 25%
Question: What least fraction should be added to
1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ....... + 1/(21 × 22)
so that the result is unity?
(A) 5/11
(B) 6/11
(C) 4/11
(D) 7/11
(E) 8/11
Rationale: Explanation:
Given expression
= 1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ...... + 1/(21 × 22)
= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ..........
= (1/21 - 1/22) = 1/2 - 1/22 = 10/22 = 5/11
Thus, least fraction to be added = 1 - 5/11 = 6/11
Answer: Option B
Answer: (B) 6/11
Question: In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability Q that the worker is under 25 years old?
(A)  0.30
(B)  0.25
(C)  0.45
(D)  0.70
(E)  0.90
Rationale: Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old Q= .7
Answer D
Answer: (D)  0.70
Question: How many 4-digit numbers can be formed by using the digits 0-9, so that the numbers contains exactly 3 distinct digits?
(A) 1944
(B) 3240
(C) 3850
(D) 3888
(E) 4216
Rationale: Case I:
The repeated digit is the unit's digit.
So, the 1st, 2nd and 3rd digits can be selected in 9 x 9 x 8 ways, respectively.
Now the 4th digit (unit's digit) can be either equal to the 1st, 2nd or 3rd digit.
Thus, in all we have:
9x9x8x3
Case II:
The repeated digit is the ten's digit.
So, the 1st, 2nd and 4th digits can be selected in 9 x 9 x 8 ways, respectively.
Now the 3rd digit (ten's digit) can be either equal to the 1st or 2nd digit.
Thus, in all we have:
9x9x2x8
Case III:
The repeated digit is the hundred's digit.
So, the 1st, 3rd and 4th digits can be selected in 9 x 9 x 8 ways, respectively.
Now the 2nd digit (hundred's digit) is equal to the 1st digit.
Thus, in all we have:
9x1x9x8
In totality, we have 9x9x8(3+2+1) = 9x9x8x6 = 3888
ANS:D
Answer: (D) 3888
Question: If the sides of a triangle are 31 cm, 29 cm and 15 cm, what is its area?
(A) 220.75 cm2
(B) 258 cm2
(C) 225.50 cm2
(D) 222.25 cm2
(E) 217.5 cm2
Rationale: The triangle with sides 31 cm, 29 cm and 15 cm is right angled, where the hypotenuse is 31 cm.
Area of the triangle
= 1/2 * 29 * 15
= 217.5 cm2
Answer: E
Answer: (E) 217.5 cm2
Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
(A) Rs. 18.20
(B) Rs. 70
(C) Rs. 72
(D) Rs. 88.25
(E) None of these
Rationale: Explanation :
Let the C.P. of items sold in a week be Rs. x
So, Rs. 392 = x + 22.5% of x
=> (122.5/100)*x = 392
=> x = 392∗100/122.5 = 320
So, the profit = Rs. (392-320) = Rs. 72
Answer : C
Answer: (C) Rs. 72
Question: Employees of a certain company are each to receive a unique 9-digit identification code consisting of the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?
(A) 14,720
(B) 16,240
(C) 18,320
(D) 20,160
(E) 22,480
Rationale: There are 7! ways to make codes starting with 12.
There are 7! ways to make codes starting with 24.
There are 7! ways to make codes starting with 36.
There are 7! ways to make codes starting with 48.
The number of codes is 4*7! = 20,160.
The answer is D.
Answer: (D) 20,160
Question: The food in a camp lasts for 40 men for 20 days. If 10 more men join, how many days will the food last?
(A) 22 days
(B) 30 days
(C) 23 days
(D) 16 days
(E) 17 days
Rationale: one man can consume the same food in 40*20 = 800 days.
10 more men join, the total number of men = 50
The number of days the food will last = 800/50 = 16 days.
Answer:D
Answer: (D) 16 days
Question: If A's height is 25% less than that of B, how much percent B's height is more than that of A?
(A) 66.66%
(B) 66.68%
(C) 66.766%
(D) 33.33%
(E) 66.65%
Rationale: Excess of B's height over A's = [(25/(100 - 25)] x 100%
= 33.33%
Answer: D)
Answer: (D) 33.33%
Question: The radius of a cylinder is 10 m, height 14 m. The volume of the cylinder is:
(A) 2200
(B) 5500
(C) 3300
(D) 1100
(E) 4400
Rationale: Cylinder volume = πr(power2)h
= 22/7 × 10 × 10 × 14
= 4400 m(power3)
Answer is E.
Answer: (E) 4400
Question: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money T did Bob receive?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 52
Rationale: Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.
So, we getK - Bob's $ = 32
Bob received 4 dollars plus one-third of what remained
Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.
1/3 of K-4 is (K-4)/3
So ALTOGETHER, Bob receives4 + (K-4)/3
So, our equation becomes:K -[4 + (K-4)/3 ]= 32
Simplify to get: K - 4 - (K-4)/3 = 32
Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96
Simplify: 2K - 8 = 96
Solve: K = 52
Plug this K-value intoK - Bob's $ = 32to get: 52 - Bob's $ = 32
So, Bob's $ T= 20
Answer:
B
Answer: (B) 22
Question: A certain car dealership offers its newest model in ten exterior and ten interior colors. If the eight interior colors are identical to the eight exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
(A) 45
(B) 72
(C) 90
(D) 10!/2!
(E) 10!
Rationale: I lined up the 9 different colours for Exterion and Interior like this:
E: A B C D E F G H I
I: A B C D E F G H I
I calculated the number of combinations: 9*9= 81 combinations.
But, from these 100 we need to delete sth: the same colours.
There are 9 possible pairs of coulours that will be the same. So, I deleted these 9 pairs from 81, resulting in 72.
Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).
B
Answer: (B) 72
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?
(A) 17
(B) 19
(C) 12
(D) 28
(E) 32
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12
Answer:C
Answer: (C) 12
Question: The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
(A) 5.29 min
(B) 5.28 min
(C) 5.08 min
(D) 9.28 min
(E) 5.988 min
Rationale: Clearly, the two will meet when they are 726 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 726 m apart, they take (100/825 * 726/1000) hrs = (242/2750 * 60) min = 5.28 min.
Answer: B
Answer: (B) 5.28 min
Question: What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y = 3/4*x - 3?
(A) 1.4
(B) sqrt (2)
(C) 1.7
(D) sqrt (3)
(E) 2.0
Rationale: (A) 1.4
eqn of circle = x^2 + y^2 = 1, center = (0,0) radius = 1
min dist of line from circle = dist of line from the center - radius
Make the distance of the line from the circle to be 0 and we see that it becomes a tangent to the circle.
Now we know if we draw a line from the center to the point where the tangent touches the circle the line and the tangent are perpendicular to each other.
So we need to find the equation of this line first.
We can take the line back where it was now
Since the lines are perpendicular m1 x m2 = -1
m of line = 3/4
so slope of the new line = -4/3
Since the line passes through the origin (center of circle) its eqn => y=-4/3x
now we need to get the point of intersection of our two lines, which comes out to be (36/25,-48/25)
now get the distance of this point from the origin and subtract the radius from it.
Comes to 1.4 (may have made calculation errors )
So A.
Answer: (A) 1.4
Question: If a is a positive integer, and if the units digit of a^2 is 4 and the units digit of (a+1)^2 is 1, what is the units digit of (a+2)^2?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: If the units digit of a^2 is 4, then the units digit of a is either 2 or 8.
If the units digit of (a+1)^2 is 1, then the units digit of a+1 is either 1 or 9.
To satisfy both conditions, the units digit of a must be 8.
Then a+2 has the units digit of 0, thus the units digit of (a+2)^2 will be 0.
The answer is A.
Answer: (A) 0
Question: A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?
(A) 2/33
(B) 5/66
(C) 5/33
(D) 5/11
(E) 1/2
Rationale: No of Loose blue socks = 6 (3 pairs)
No. of Loose white Socks = 6 (3 pairs)
total no. of blue and white socks = 12
Total no. of socks to be selected = 4
So we have C (12,4) = no of ways the socks can be selected = 495
No of ways One pair of blue socks is selected ( 2 blue socks) , C (6,2) , No of ways one pair of white socks can be selected C (6,2) ..Because we have to find a scenario where EXACTLY one pair of Blue socks and ONE pair of WHITE socks is selected we will multiply the two .. ie 15 x 15 ..
Filling the information in the Probability formula we get P (A) = (15 x 15) / 495 = 5 /11
ANSWER : (D)
Answer: (D) 5/11
Question: The sum of the squares of three numbers is 241, while the sum of their products taken two at a time is 100. Their sum is:
(A) 20
(B) 11
(C) 21
(D) 41
(E) None of these
Rationale: x^+y^2+z^2=241
xy+yz+zx=100
as we know.. (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
so (x+y+z)^2=241+(2*100)
(x+y+z)^2=441
so x+y+z=21
ANSWER:C
Answer: (C) 21
Question: The average of ten numbers is 8. If each number is multiplied by 11, then what is the average of the new set of numbers?
(A) 8
(B) 11
(C) 19
(D) 88
(E) 121
Rationale: The sum of the ten numbers is 8*10 = 80
If each number is multiplied by 11, the new sum is 11*(80).
The average is then 11*8 = 88
The answer is D.
Answer: (D) 88
Question: What percentage of numbers from 1 to 100 have cube that end in the digit 5?
(A) 1
(B) 10.5
(C) 25
(D) 20
(E) 22
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 95 are 5,15,25,35,45,55,65,75,85,95.
Number of such numbers = 95.
Required percentage = (10/95 * 100) = 10.5%
ANSWER:B
Answer: (B) 10.5
Question: Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and U. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of U if J is negative?
(A) -2
(B) U=0
(C) 1
(D) 2
(E) 5
Rationale: since j is negative, therefore median of the set will be 3. which is an odd number. also, we know that odd^n will always be odd. now since 34 is even, therefore 3^w will have only one factor with 34 for w=0.
mode of the set is a number which occurs maximum number of time in the set. now, since U is the mode of the set. therefore U=0. hence answer is B
Answer: (B) U=0
Question: If X, Y and Z are digits and 7XYZ is a 4-digit number that is divisible by 2, which of the following is a possible product of X, Y and Z?
(A) 17
(B) 42
(C) 13
(D) 27
(E) 51
Rationale: Key to this question is to remember the fact that a number divisible by 2 must end with 2 OR 0 (i.e Z).
If Z had to be 0, product should also be 0 regardless of X and Y.
The product is a multiple of 2. Only one answer choice meets the requirement.
Ans B.
Answer: (B) 42
Question: A sales executive gets 20% bonus of the total sales value and 10% commission besides the bonus on the net profit after charging such commission. If the total sales value be Rs. 10 lakh per annum and the total profit of the company be Rs. 1.32 lakh, then his total earning per annum will be, given that he is not entitled to receive any fixed salary from the company :
(A) 2.3 lakh
(B) 2.32 lakh
(C) 2.12 lakh
(D) 3.2 lakh
(E) None of these
Rationale: Solution: His bonus,
= (20 *1000000) /100 = 2lakh
Total profit = net profit + (10 *net profit) /100
1.32lakh = net profit *[1 + (10/100)]
Net profit = 132000 /1.1 = 120000.
Commission,
= (total profit - net profit)
= 132000 - 120000
= 12000.
Hence, his total earnings = 2lakh + 12000 = Rs. 212000.
Answer: Option C
Answer: (C) 2.12 lakh
Question: If a Ã— b = 2a - 3b + ab, then 3 Ã— 2 + 2 Ã— 3 is equal to :
(A) 7
(B) 8
(C) 9
(D) 25
(E) 26
Rationale: Explanation:
3 Ã— 2 + 2 Ã— 3 = (2 Ã— 3 - 3 Ã— 2 + 2 Ã— 3) + ( 2 Ã— 2 - 3 Ã— 3 + 2 Ã— 3)
= (6 + 4 - 9 + 6) = 7.
Answer: A
Answer: (A) 7
Question: A sum of money deposited at compound interest (compounded yearly) amounts to $600 in 2 years and to $624 in 3 years. What is the interest rate?
(A) 2%
(B) 4%
(C) 6%
(D) 7%
(E) 8%
Rationale: 624 - 600 = 24
24/600 = 0.04 = 4%
The answer is B.
Answer: (B) 4%
Question: In expressing a length 810472 km as nearly as possible with three significant digits , find the percentage error
(A) 0.34%
(B) 0.034%
(C) 0.0034%
(D) 0.00034%
(E) 3.4%
Rationale: Error = (81.5 – 81.472)km = 0.028.
Required percentage = [(0.028/81.472)*100]% = 0.034%.
Answer is B.
Answer: (B) 0.034%
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 60 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 10 sec
(B) 16 sec
(C) 12 sec
(D) 67 sec
(E) 13 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 60 * 100/18 = 1000/3
RS = 60 + 40 = 100 * 5/18
T = 1000/3 * 18/500 = 12 sec
Answer: C
Answer: (C) 12 sec
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
(A) 33 1/8%
(B) 33 8/3%
(C) 33 1/3%
(D) 37 1/3%
(E) 33 1/4%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
(A) 2288
(B) 2667
(C) 2799
(D) 6725
(E) 2771
Rationale: CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725.
Answer:D
Answer: (D) 6725
Question: 6x − 12 = 6y
5y + 5x = 10
Which of the following is the number of solutions to the system of equations shown above?
(A) More than three
(B) Exactly three
(C) Exactly two
(D) Exactly four
(E) None of these
Rationale: 6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1
5y + 5x = 15
=>x + y = 2 -- 2
From equation 1 and 2 , we get
2x = 4
=> x=2
y=0
Therefore , the given system will have Exactly one solution
Answer : E
Answer: (E) None of these
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 28% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
(A) 35.67%
(B) 64.75%
(C) 68.57%
(D) 70.20%
(E) none of these
Rationale: Girls = 900, Boys = 1100
Passed = ( 28% of 1100 ) + ( 32% of 900)
= 308 + 288 = 596
Failed = 2000 - 596 = 1404
Failed % = [(1404/2000) x 100]%
= 70.2%.
ANSWER:D
Answer: (D) 70.20%
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 5 per metre of cloth. What is the cost price of one metre of cloth?
(A) 21
(B) 28
(C) 90
(D) 100
(E) 11
Rationale: Explanation:
SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 5 = Rs. 100.
Answer: D
Answer: (D) 100
Question: 54671 - 10456 - 33466 = ?
(A) 2449
(B) 10449
(C) 10749
(D) 10449
(E) 6468
Rationale: C
If we calculate we will get 10749
Answer: (C) 10749
Question: If |4x+6| = 42, what is the sum of all the possible values of x?
(A) 2
(B) -3
(C) 4
(D) -5
(E) 6
Rationale: There will be two cases
4x+6= 42 or 4x+6 = -42
=> x =9 or x= -12
sum of both the values will be -12 +9 = -3
Answer is B
Answer: (B) -3
Question: Find the value of m 62519 x 9999 = m?
(A) 724533811
(B) 625127481
(C) 545463251
(D) 725117481
(E) 677899932
Rationale: 62519 x 9999 = 62519 x (10000 - 1)
= 62519 x 10000 - 62519 x 1
= 625190000 - 62519
= 625127481
B
Answer: (B) 625127481
Question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
(A) 6
(B) 2
(C) 8
(D) 9
(E) 3
Rationale: Work done by A in 2 days = 2/5
Remaining work = 3/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 3/5 * 10/3 = 2 days. Answer: B
Answer: (B) 2