mathewhe/aqua_rat huggingface dataset:
Question: Two pipes P and Q can fill a cistern in 10 and 15 minutes respectively. Both are opened together, but at the end of 2 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Let x be the total time it takes for the cistern to fill.
2/10 + x/15 = 1
x/15 = 4/5
x = 12
After the first pipe is turned off, it takes 10 more minutes to fill the cistern.
The answer is E.
Answer: (E) 10
Question: An employee may claim Rs. 7.00 for each km when he travels by taxi and Rs. 6.00 for each km if he drives his own car. If in one week he claimed Rs. 595 for traveling 90 km. How many kms did he travel by taxi ?
(A) 55 kms
(B) 85 kms
(C) 65 kms
(D) 15 kms
(E) 25 kms
Rationale: Explanation:
Let x and y be the respective km's travelled by man via taxi and by his own car.
Given x + y = 90 => x = 90 - y
But according to the question,
7x + 6y = 595
7(90-y) + 6y = 595
=> 630 - 7y + 6y = 595
=> y = 630 - 595 = 35
=> x = 90 - 35 = 55
Therefore, the distance travelled by taxi is 55 kms.
Answer: A
Answer: (A) 55 kms
Question: Three runners Bob, Mary and James start running around a circular track of length 15m from the same point simultaneously in the same direction at speeds of 1.5 m/s, 2.5 m/s and 4.5 m/s respectively. When will they meet for the first time after they started moving?
(A) 90 seconds
(B) 120 seconds
(C) 30 seconds
(D) 15 seconds
(E) 35 seconds
Rationale: If they all meet after T seconds, it means they covered the distances 1.5T, 2.5T, and 4.5T respectively.
Since they all arrive to the same spot, it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track, which is 15m. So, 1T, 2T, and 3T must all be multiples of 15. 1T multiple of 15 means T multiple of 15. The smallest T with this property is 15 and is on the list of answers.
Answer D.
Answer: (D) 15 seconds
Question: A man can row a boat at 24 kmph in still water. If the speed of the stream is 16 kmph, what is the time taken to row a distance of 70 km downstream?
(A) 7/4 hours
(B) 3/4 hours
(C) 8/13 hours
(D) 4/13 hours
(E) 10/13 hours
Rationale: Speed downstream = 24 + 16 = 40 kmph.
Time required to cover 70 km downstream = d/s = 70/40 = 7/4 hours.Answer:A
Answer: (A) 7/4 hours
Question: Which of the following is non-negative number?
(A) (a-0.9)(a-1)
(B) (a+1)(a-1)
(C) (a+0.9)(a+1)
(D) (a-0.6)(a-0.6)
(E) a(a+1)
Rationale: 5-sec approach:
D. (a-0.6)(a-0.6) = (a-0.6)^2. The square of a number is always non-negative.
Answer: D.
Answer: (D) (a-0.6)(a-0.6)
Question: Assume that f(1)=0 and f(m+n)=f(m)+f(n)+4(9mn-1). For all natural numbers (Integers>0)m and n. What is the value of f(17)?
(A) 4832
(B) 4855
(C) 4825
(D) 4895
(E) 4862
Rationale: Explanation:
f(1) = 0
f(2) = f(1+1) = f(1)+f(1)+4(9×1×1 – 1) = 0+0+4×8 = 32
f(4) = f(2+2) = f(2)+f(2)+4(9×2×2 – 1) = 32+32+4×35 = 204
f(8) = f(4+4) = f(4)+f(4)+4(9×4×4 – 1) = 204+204+4×143 = 980
f(16) = f(8+8) = f(8)+f(8)+4(9×8×8 – 1) = 980+980+4×575 = 4260
f(17) = f(1+16) = f(16)+f(1)+4(9×16×1 –1) = 4260+0+ 4×143 = 4832
Answer:A
Answer: (A) 4832
Question: If |y + 7| = 12, what is the sum of all the possible values of y?
(A) -14
(B) -12
(C) -8
(D) 8
(E) 12
Rationale: There will be two cases
y+7 = 12 or y+7 = -12
=> y = 5 or y = -19
sum of both the values will be -19 + 5 = -14
Answer: A
Answer: (A) -14
Question: What is the probability of getting a number less than 4 when a die is rolled?
(A) 1/2
(B) 4/7
(C) 1/6
(D) 4/7
(E) 5/12
Rationale: Total number of outcomes possible when a die is rolled=6
Any one face out of the 6 face n(s)=6
e=getting a number less than 4={1,2,3}
Hence,n(e)=3
p(e)=n(e)/n(s)
=3/6
=1/2
Option A
Answer: (A) 1/2
Question: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 4?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Counting the different combinations possible is the easiest method as the options tell you that the correct number is a relatively small number.
The total cases possible are:
12
16
24
32
36
44 (not counted as we need distinct digits)
52
56
64
72
76
Edit: Total: 10
D is the correct answer.
Answer: (D) 10
Question: A courtyard is 25 meter long and 15 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?
(A) 22877
(B) 27778
(C) 18750
(D) 27999
(E) 17799
Rationale: Number of bricks =Courtyard area/1 brick area
=(2500×1500/20×10)=18750
Answer: C
Answer: (C) 18750
Question: The cost of Type 1 rice is Rs.15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is
(A) Rs.19.50
(B) Rs.19
(C) Rs.18
(D) Rs.18.50
(E) None
Rationale: Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have :
(20-x)/(x-15) = 2/3 =› 60 - 3x = 2x - 30
=› 5x = 90 =› x = 18.
so, price of the mixture is Rs. 18 per kg.
Answer C
Answer: (C) Rs.18
Question: How many factors does 49^2 have?
(A) 2
(B) 8
(C) 24
(D) 25
(E) 36
Rationale: 36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 6*6 = 36
Answer E.
Answer: (E) 36
Question: A code is to be made by arranging 9 letters. five of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?
(A) 42
(B) 210
(C) 46820
(D) 84002
(E) 90720
Rationale: we have 9 letters out of which 2 are of one kind, 2 are of another kind..
so total ways = 9!/2!2!=90720
ans E
Answer: (E) 90720
Question: In a race, A beats B by 15 metres and C by 29 metres. If B and C run over the course together, B wins by 15 metres. What is the length of the course?
(A) 225m
(B) 229m
(C) 222m
(D) 221m
(E) 226m
Rationale: Explanation:
Let X be the length of the course
according to the question,
A beats B by 15 metres and C by 29 metres
Applying this,
If A runs X metres, B runs (X-15) and C runs ( X-29) metres.
B and C together run, B runs X metres and C runs (X-15)
=> If B runs 1 metre, C runs X-15/X
=> B runs X-15 m, C runs (X-15/x) * (X-15)
APPLYING THIS,
X-29 = (X-15)(X-15) / X
Solving,
X2 -29X= X2 – 30 X + 225
X = 225
Thus, length of the course is 225 metres.
ANSWER: A
Answer: (A) 225m
Question: Find the value of x from the equation:
x^2−7x+10=0
(A) 5 or 2
(B) 4 or 1
(C) 4 or 2
(D) 6 or 1
(E) 7 or 4
Rationale: Here we need to find out a and b such that a + b = -7 and ab = +10
a = -5 and b = -2 satisfies the above condition.
Hence
x
2
−
7
x
+
10
=
(
x
−
5
)
(
x
−
2
)
x2−7x+10=(x−5)(x−2)
x
2
−
7
x
+
10
=
0
⇒
(
x
−
5
)
(
x
−
2
)
=
0
x2−7x+10=0⇒(x−5)(x−2)=0
Step 3: Equate each factor to 0 and solve the equations
(
x
−
5
)
(
x
−
2
)
=
0
⇒
(
x
−
5
)
=
0
or
(
x
−
2
)
=
0
⇒
x
= 5 or 2
A
Answer: (A) 5 or 2
Question: If a company allocates 10 percent of its budget to advertising, 10 percent to capital improvements, and 72 percent to salaries, what fraction of its budget remains for other allocations?
(A) 4/5
(B) 2/25
(C) 3/10
(D) 1/5
(E) 1/10
Rationale: 10 + 10 + 72 = 92% 100 - 92 = 8% to all others
B
Answer: (B) 2/25
Question: The sum of ages of 5 children born 3 years different each is 70 yrs. What is the age of the Elder child?
(A) 17
(B) 19
(C) 16
(D) 18
(E) 20
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 70
5x = 40
x = 8.
x+12= 8+12= 20
E
Answer: (E) 20
Question: A person can swim in still water at 12 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 10km?
(A) 1
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: M = 12
S = 2
US = 12 - 2 = 10
D = 10
T = 10/10 = 1 Answer:A
Answer: (A) 1
Question: Murali travelled from city A to city B at a speed of 20 kmph and from city B to city C at 80 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/20 + (3x)/80
= (8x + 3x)/80 = 11x/80
= (2x + 3x)/(11x/80) = 36.4 kmph.
Answer: B
Answer: (B) kmph
Question: If log 27 = 1.431, then the value of log 9 is:
(A) 0.954
(B) 2.35
(C) 3.68
(D) 9.87
(E) 4.25
Rationale: Explanation:
log 27 = 1.431
log (33 ) = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
answer A
Answer: (A) 0.954
Question: By selling 50 meters of cloth. I gain the selling price of 16 meters. Find the gain percent?
(A) 44 1/17%
(B) 42 5/8%
(C) 42 6/4%
(D) 42 6/8%
(E) 42 1/7%
Rationale: SP = CP + g
50 SP = 50 CP + 16 SP
34 SP = 50 CP
34 --- 16 CP gain
100 --- ? => 47 1/17%
Answer: A
Answer: (A) 44 1/17%
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
(A) 13 1/7 days
(B) 13 1/3 days
(C) 13 1/8 days
(D) 13 8/3 days
(E) 12 1/3 days
Rationale: 5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Answer:B
Answer: (B) 13 1/3 days
Question: Vicky's salary is 75% more than Ashu's. Vicky got a raise of 40% on his salary while Ashu got a raise of 25% on his salary. By what percent is Vicky's salary more than Ashu's?
(A) 96%
(B) 51.1%
(C) 90%
(D) 52.1%
(E) None of these
Rationale: Solution: Let Ashu's salary = 100; Ashu's salary after rise = 125.
Then Vicky's salary = 175.
Vicky's salary after rise of 40% = 245.
[As 10% of Vicky's salary is 17.5 then 40% = 17.5*4 = 70] .
Difference between Vicky's salary and Ashu's salary = 245-125 = 120; .
% more Vicky's salary than Ashu's = 120*100/125 = 96%.
Answer: Option A
Answer: (A) 96%
Question: 25% of all students in a class commute by public transportation. If 10% of the students aspire to be scientists, which of the following can be the percentage of students who do not commute by public transportation and do not aspire to be scientists?
I.	10%
II.	70%
III.	90%
(A) I ONLY
(B) II ONLY
(C) III ONLY
(D) I AND II
(E) I AND III
Rationale: 25% Students use public transportation. This means 75% students do not use public transportation. 10% students aspire to be scientists means even if all these students use public transportation, minimum 75% - 10% = 65% students do not use public transportation and do not aspire to be scientists.This means correct answer is between 65% and 75%
Answer : B.
Answer: (B) II ONLY
Question: If the average marks of three batches of 50, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is
(A) 53.33
(B) 54.83
(C) 55
(D) 57
(E) None
Rationale: Sol.
Required average = [50x50 + 60x55 + 45x60 / 50 + 60 + 45]
= [2500 + 3300 + 2700 / 155]
= 8500 / 155 = 54.83.
Answer B
Answer: (B) 54.83
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 120 meters long is?
(A) 29
(B) 44
(C) 54
(D) 99
(E) 11
Rationale: D = 540 + 120= 660
S = 54 * 5/18 = 15 mps
T = 660/15 = 44 sec
Answer: B
Answer: (B) 44
Question: Amal borrowed a sum of money with simple interest as per the following rate structure:
(a) 6 p.c. p.a. for the first three years
(b) 8 p.c. p.a. for the next five years
(c) 12 p.c. p.a. for the next eight years
If he paid a total of 5,040 as interest at the end of twelve years, how much money did he borrow?
(A) 8,000
(B) 10,000
(C) 12,000
(D) 6,000
(E) None of these
Rationale: Let x be the amount Amal borrowed.
∴ 18% of x + 40% of x + 48% of x = 5040
or, 106% of x = 5040
∴ x = 5040⁄106 × 100 = 4754.71
Answer E
Answer: (E) None of these
Question: How many consonants are present between the first and second vowel in the sequence of English alphabet ?
(A) 3
(B) 13
(C) 11
(D) 10
(E) None of these
Rationale: Explanation:
Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The first and second vowels are A and E respectively. There are 3 letters between A and E; there are no vowels in between. Thus, there are 3 consonants between A and E.
ANSWER A
Answer: (A) 3
Question: If q > a and L < a, which of the following cannot be true?
(A)  d + L = 14
(B)  d - L = 7
(C)  d - L = 1
(D)  a - q = 9
(E)  a + d = 9
Rationale: Is the answer D?
If q>a, then q-a>0 (always positive). The converse would be a-q<0 (always negative). Option D states that a-q=9, which can never be true.
Answer: (D)  a - q = 9
Question: Which of the following best approximates the percent by which the distance from A to C along a diagonal of square ABCD reduces the distance from A to C around the edge of square ABCD?
(A) 30%
(B) 43%
(C) 45%
(D) 50%
(E) 70%
Rationale: let the sides be 2 units.
original distance=2+2=4 units
changed distance=2sq.root2
%change=change dist.-original dist./original dist.
=(2sq.root 2-4)/4==-.2955
reduced by ~30%
Ans A
Answer: (A) 30%
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 170 cookies, what percent of the cookies did Irin bake?
(A) 0.125%
(B) 1.25%
(C) 12.5%
(D) 53.5%
(E) 0.152%
Rationale: 9.18x+5.17x+2.05x = 16.4x = 170 cookies
x= 170/16.4 = 10 (approx)
So, Irin baked 10*9.18 cookies or 91 cookies (approx)
% share = 91/170= 53.5 approx
Hence, answer is D.
Answer: (D) 53.5%
Question: A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
(A) 27
(B) 36
(C) 72
(D) 112
(E) 422
Rationale: {1}{2}{greater than 6}{divisible by 3}{3x}{x}:
The third digit can take 3 values: 7, 8, or 9.
The fourth digit can take 3 values: 3, 6, or 9.
The fifth and sixth digits can take 3 values: 31, 62, or 93.
Total = 3*3*3 = 27.
Answer: A.
Answer: (A) 27
Question: The population of a village is 7800. It increases annually at the rate of 18% p.a. What will be its population after 2 years?
(A) 10000
(B) 12000
(C) 13000
(D) 10860
(E) 14400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
7800 × 118/100 × 118/100 = 10860
D
Answer: (D) 10860
Question: Find the fourth proportional to 2.7, 4.6 and 7.6?
(A) 12.95
(B) 13.95
(C) 15.23
(D) 15.95
(E) 16
Rationale: Formula = Fourth propotional = (b Ã— c)/a
A = 2.7 , B = 4.6 and C = 7.6
(4.6 Ã— 7.6)/2.7 = 12.95
A
Answer: (A) 12.95
Question: If x and y are integers such that |y + 3| ≤ 3 and 2y – 3x + 6 = 0, what is the least possible value Q of the product xy?
(A) 	-12
(B) 	-3
(C) 	0
(D) 	2
(E) 	None of the above
Rationale: How to deal with inequalities involving absolute values? First example shows us the so callednumber case
In this case we have |y + 3| ≤ 3 which is generalized |something| ≤ some number. First we solve as if there were no absolute value brackets:
y + 3 ≤ 3
y ≤ 0
So y is 0 or negative
Second scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:
y + 3 >= -3
y >= -6
Therefore we have a possible range for y: -6=<y<=0
Ok, so far so good, we're half way through. What about x?
Here's the formula: 2y – 3x + 6 = 0, rewrite it as 2y + 6 = 3x.
You can say that 2y + 6 is a multiple of 3 (=3x). So all values which must be integer must also satisfy this constraint. I'm just saying that, so it's easier to evaluate all the possible numbers (-6, -3, 0). If you plug in y = 0, x will be 2 and xy = 0 as the lowest possible value Q.
Hence, Answer Choice C is the one to go.
Answer: (C) 	0
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 400 resolutions?
(A) 563.2 m
(B) 704 m
(C) 287 m
(D) 278 m
(E) 927 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 400 resolutions.
= 400 * 2 * 22/7 * 22.4 = 56320 cm
= 563.2 m
Answer:A
Answer: (A) 563.2 m
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
(A) 91.5 cm
(B) 23.9 cm
(C) 62.9 cm
(D) 27.8 cm
(E) 21.2 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42
= 91.5 cm
Answer:A
Answer: (A) 91.5 cm
Question: Find the area of a rhombus one side of which measures 20 cm and one diagonal is 25 cm.
(A) 700cm2
(B) 600cm2
(C) 500cm2
(D) 400cm2
(E) 100cm2
Rationale: Explanation: Let other diagonal = 2x cm.
Since diagonals of a rhombus bisect each other at right angles, we have:
(20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm. _I
So, other diagonal = 32 cm.
Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 25 x 32) cm2 = 400 cm2
Answer: Option D
Answer: (D) 400cm2
Question: Find the number of square tiles to cover the floor of a room measuring 6 m * 10 m leaving 0.50 m space around the room. A side of square tile is given to be 50 cms?
(A) 100
(B) 180
(C) 277
(D) 18
(E) 150
Rationale: 5*9= 1/2 * 1/2 * x => x =180
Answer: B
Answer: (B) 180
Question: Little Texas Drilling Company has three wells, each producing oil at a constant rate. Well A produces one barrel every two minutes. Well B produces one barrel every three minutes. Well C produces one barrel every four minutes. How many hours does it take Little Texas Drilling Company to produce 195 barrels of oil?
(A) 2
(B) 3
(C) 4
(D) 18
(E) 180
Rationale: Well A produces 1/2 a barrel per minute.
Wells B and C produce 1/3 + 1/4 = 7/12 (a little more than half) a barrel per minute.
So all three wells combined produce a little more than 1 barrel per minute.
So for 165 barrels they will take a bit less than 195 mins which will be more than 3 hrs but less than 4 hrs.
Answer (C)
Answer: (C) 4
Question: A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?
(A) 5
(B) 7
(C) 9
(D) 10
(E) 14
Rationale: Solution: The number should be multiple of 5. So, the last digit is 5 or 0. But 0 cant be a factor. So, Last digit is 5. The sum of all digits should be a multiple of 9. Now the sum is 22. So, 4th digit should be 5. Therefore, required sum = 10
Option D
Answer: (D) 10
Question: A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent Q of the list price is the lowest possible sale price?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50
Rationale: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 40
and 0.8x = 32
so lowest sale price is 32, which is Q =40% of 80
hence, D is the answer
Answer: (D) 40
Question: All votes cast in a recent presidential election were for either the incumbent or the challenger. The challenger received 5.4 million votes and the incumbent received 5 million. If after a recount of the votes and the addition of previously uncounted absentee ballots, the incumbent had 5.2 million votes while the challenger had 5.4million, then the percentage of the total number of votes that were for the challenger
(A) decreased by approximately 10 %
(B) decreased approximately 1%
(C) neither increased nor decreased
(D) increased approximately 1%
(E) increased approximately 2%
Rationale: I estimated the Challenger's share by 5.4/10.4*100. Here by approximation it would come to around 51%.
After the recalculation, Challenger's share 5.4/10.6*100. Here by approximation it would come to around 52%.
The numerator is the same but the denominator has changed so it will be decrease for sure. so C,D,E are ruled out.
out of A and B, in B 10% is too large.
A is most suitable as 1% is nearest to the actual answer.
Answer: (A) decreased by approximately 10 %
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 7967 for a computer table, then what was the cost price of the computer table?
(A) 7297
(B) 6425
(C) 2871
(D) 6725
(E) 2981
Rationale: Explanation:
CP = SP * (100/(100 + profit%))
= 7967(100/124) = Rs. 6425.
Answer: B
Answer: (B) 6425
Question: In assembling a Bluetooth device, a factory uses one of two kinds of modules. One module costs $8 and the other one, that is cheaper, costs $3. The factory holds a $100 worth stock of 25 modules. How many of the modules in the stock are of the cheaper kind?
(A) 21
(B) 20
(C) 22
(D) 23
(E) 24
Rationale: So the number of $3 modules must be 20 so that the leftover 5 modules are of $8 which will give a total value $100. 20*3+5*8 = 60+40=100.
Answer : B
Answer: (B) 20
Question: An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
(A) 23777
(B) 37500
(C) 29977
(D) 26777
(E) 19871
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 39/4 * 1/100)
(9x + 1100000 - 11x)/100 = 39000/4 = 9750
x = 62500
Sum invested at 9% = Rs. 62500
Sum invested at 11% = Rs. (100000 - 62500) = Rs. 37500.
Answer: B
Answer: (B) 37500
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
9 * 11 * 13 =?
(A) 89
(B) 152
(C) 68
(D) 38
(E) 55
Rationale: B
152
(13 * 11) + 9 = 152
Answer: (B) 152
Question: What percent is 150 of 90?
(A) 133 1/3%
(B) 163 2/3%
(C) 166 2/3%
(D) 166 3/3%
(E) None of these
Rationale: Explanation:
150/90 = 5/3
5/3 * 100 = 500/3 = 166 2/3%
Answer: Option C
Answer: (C) 166 2/3%
Question: Sarah is driving to the airport. After driving at 15 miles per hour for one hour, she realizes that if she continues at that same average rate she will be an hour late for her flight. She then travels 60 miles per hour for the rest of the trip, and arrives 30 minutes before her flight departs. How many miles did she drive in all?
(A) 45
(B) 175
(C) 210
(D) 245
(E) 280
Rationale: After driving at 15 miles per hourfor one hour, this distance left to cover is d-15. Say this distance is x miles.
Now, we know that the difference in time between covering this distance at 15 miles per hour and 60 miles per hour is 1+ 1/2 = 3/2 hours.
So, we have that x/15 - x/60 = 3/2 --> 4x/60 - x/60 = 3/2 --> 3x/60 = 3/2 --> x = 30.
Total distance = x + 15 = 45 miles.
Answer: A
Answer: (A) 45
Question: Six machines at a certain factory operate at the same constant rate. If five of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?
(A) 3
(B) 5
(C) 6
(D) 16
(E) 24
Rationale: The total work is 5*30 = 150 machine hours
The time required for six machines is 150/6 = 25 hours, thus 5 fewer hours.
The answer is B.
Answer: (B) 5
Question: If x ≠ 0 and (y^2 + xy)/x=y+x, which of the following expressions is equal to its opposite?
(A) x^2
(B) x^2 + y^2
(C) x^2 - y^2
(D) (y + x)^2
(E) (x – y)^2
Rationale: (y^2 + xy)/x=y+x
=> y^2 + xy = xy +x^2
=> x^2 - y^2 = 0
Answer C
Answer: (C) x^2 - y^2
Question: Convert 800 miles into meters?
(A) 1287472
(B) 845796
(C) 804670
(D) 784596
(E) 864520
Rationale: 1 mile = 1609.34 meters
800mile = 800*1609.34 = 1287472 meters
Answer is A
Answer: (A) 1287472
Question: Out of three consecutive odd numbers eight times the first number is equal to addition of thrice the third number and adding 5 to twice the second . What is the first number?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Description :
=> 8x=2(x+2)+5+3(x+4)
=> 3x=21,x=7
=> x+4=11
X=11-4=7
Answer C
Answer: (C) 7
Question: A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 70, how many coins of each type are there?
(A) 20 coins
(B) 30 coins
(C) 40 coins
(D) 25 coins
(E) None of these
Rationale: Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 70
⇒ 1.75x = 70 ⇒ x = 40 coins
Answer C
Answer: (C) 40 coins