mathewhe/aqua_rat huggingface dataset:
Question: If K is the sum of reciprocals of the consecutive integers from 13 to 18, inclusive, then K is closest in value to which of the following?
(A) 1/12
(B) 1/3
(C) 1/7
(D) 1/6
(E) 1/4
Rationale: 1/13 , 1/14 , 1/15 , 1/16 , 1/17 , 1/18
Hypothetically , assume all 6 Numbers to be 1/13
Hence sum of it would result in = 6/13 ( almost equals 1/2 , or slightly less than 1/2 - )
If all 6 nos were to be 1/8 ... Sum of which would result in 6/18 = 1/3 .
Hence answer should lie between 1/2 and 1/3
------------ 1/2 ------------1/3 .
The only option that satisfies this criteria is option B i.e 1/3
Answer: (B) 1/3
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 287
(B) 23
(C) 72
(D) 27
(E) 26
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer:C
Answer: (C) 72
Question: (18.6 x 17.2 ÷ 0.6) x 27.5 = ?
(A) 12132
(B) 14678
(C) 12708
(D) 14663
(E) 15688
Rationale: Explanation :
(319.92 ÷ 0.6) x 27.5 = 533.2 x 27.5 = 14663
Answer : Option D
Answer: (D) 14663
Question: Pradeep has to obtain 35% of the total marks to pass. He got 185 marks and failed by 25 marks. The maximum marks are
(A) 300
(B) 600
(C) 800
(D) 1000
(E) 900
Rationale: Explanation :
Let their maximum marks be x.
Then, 35% of x = 185 + 25
=>35/100x= 210
x = (210100/35)
x= 600.
Answer : B
Answer: (B) 600
Question: 20 women can do a work in 9 days. After they have worked for 6 days. 6 more men join them. How many days will they take to complete the remaining work?
(A) 4:3
(B) 4:8
(C) 4:5
(D) 4:1
(E) 4:4
Rationale: (20 * 16) women can complete the work in 1 day.
1 woman's 1 day work = 1/320
(16 * 15) men can complete the work in 1 day
1 man's 1 day work = 1/240
So, required ratio = 1/240 : 1/320 = 4:3.
Answer: A
Answer: (A) 4:3
Question: The average weight of a class is x pounds. When a new student weighing 70 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?
(A) 26
(B) 86
(C) 88
(D) 90
(E) 92
Rationale: When the student weighs 80 pounds the average weight is x - 1 pounds;
When the student weighs 110 pounds the average weight is x + 4 pounds.
So, the increase in total weight of 110 - 70 = 40 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 40/5 = 8 students (including the new one). So, initially there were 5 student.
Total weight = 5x + 70 = 8(x-1) --> x = 26 pounds.
Answer: A.
Answer: (A) 26
Question: Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 20 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered?
(A) 36
(B) 72
(C) 132
(D) 144
(E) 180
Rationale: 1st part: - In 1hr, Bus A covers 30 miles.
Relative speed of bus ABus B is (80-30) = 50mph.
So time required for Bus B to cover the exact distance as A is
50*t = 30
t=3/5 = 36min
2nd part
80*t=2d - B has to cover twice the distance
30*(t+1) = d - A traveled 1hr more and has to travel only only d
so
d/30 - 2d/80 = 1
D=120
T= 3hrs = 180 min
Question asks for +ve difference between part 1 and part 2 in minutes
= 180-36 = 132min
C
Answer: (C) 132
Question: John can complete a given task in 18 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 6 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?
(A) 11
(B) 34/5
(C) 44/5
(D) 54/5
(E) 12
Rationale: In such questions, you need to start from the end. Last 4 days John works alone and completes 6 * (1/18) = 1/3 of the work.
So 2/3 of the work should have been completed by the two of them together before Jane left.
Their combined rate of work is 1/18 + 1/12 = 5/36
Time taken to complete 2/3 of the work = (2/3)/(5/36) = 24/5 days.
So total number of days taken to complete the work =24/5 + 6 = 54/5 days.
D
Answer: (D) 54/5
Question: A rower can row upstream at 15 kph and downstream at 30 kph. What is the speed of the rower in still water?
(A) 20.9
(B) 21.3
(C) 21.7
(D) 22.1
(E) 22.5
Rationale: Let V be the rower's speed in still water.
Let S be the speed of the current in the stream
V-S = 15
V+S = 30
When we add the two equations, we get: 2V = 45
Then V = 22.5 kph.
The answer is E.
Answer: (E) 22.5
Question: A man counted his animals, 80 heads and 230 legs (ducks and goats). how many goats are there?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=230 and divide 2d+4g=230 by 2 we get d+2g=115 -----------> eq2
subtract eq1 from eq2
we get no of goats=30
ANSWER:A
Answer: (A) 30
Question: In how many ways, a committee of 5 members can be selected from 5 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 75
(B) 152
(C) 100
(D) 200
(E) 212
Rationale: (3 men out 5) and (2 ladies out of 5) are to be chosen
Required number of ways = (5C3 * 5C2) = 100
Answer is C
Answer: (C) 100
Question: if a no. is divided by 342 then remainder is 47.then if that no. is divided by 18 then what will be the remainder?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: let quotient be k if that no. is divided by 342 and remainder 47.
that no.= 342k+47 = (18*19k)+(18*2)+11
=18*(19k+2)+11
so remainder when divided by 18=11
answer A
Answer: (A) 11
Question: P is three times as fast as Q and working together, they can complete a work in 19 days. In how many days can Q alone complete the work?
(A) 16 1/4 days
(B) 27 1/4 days
(C) 25 1/4 days
(D) 14 days
(E) 10 days
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 19 days, which means Q can do the work in 76 days.
Hence, P can do the work in 25 1/4 days.
Answer:C
Answer: (C) 25 1/4 days
Question: Pipe A can fill a tank in 5 hours. Due to a leak at the bottom, it takes 10 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 67
(B) 10
(C) 18
(D) 26
(E) 12
Rationale: Let the leak can empty the full tank in x hours 1/5 - 1/x = 1/10
=> 1/x = 1/5 - 1/10 = 1/10
=> x = 10. Answer:B
Answer: (B) 10
Question: A and B walk around a circular track. A and B walk at a speed of 4 rounds per hour and 4 rounds per hour respectively. If they start at 6 a.m. from the same point in opposite directions, how many times shall they cross each other before 7.00 a.m.?
(A) 6
(B) 5
(C) 4
(D) 8
(E) 10
Rationale: Relative speed = Speed of A + Speed of B (âˆ´ they walk in opposite directions)
= 4 + 4 = 8 rounds per hour
=> They cross each other 8 times in 1 hour.
Time duration from 6.00 am to 7.00 am = 1 HOUR
Hence they cross each other 8 times before 7.00 am
Answer : D
Answer: (D) 8
Question: James is stacking piles of bricks. He has 2 in the first row and then one more in each row after that. If there are 20 rows all together, how many bricks are in the pile?
(A) 22
(B) 243
(C) 255
(D) 242
(E) 2200
Rationale: =2 + 3 + 4 + ... + 22
=1 + 2 +... + 22 - 1
=(22)(23)/2 - 1
=(11)(23)-1
=243 - 1
=242
Option D
Answer: (D) 242
Question: A multiple choice test consists of 4 questions, and each question has 5 answer choices. In how many W ways can the test be completed if every question is unanswered?
(A) 24
(B) 120
(C) 625
(D) 720
(E) 1024
Rationale: 5 choices for each of the 4 questions, thus total W of 5*5*5*5 = 5^4 = 625 ways to answer all of them.
Answer: C.
Answer: (C) 625
Question: The average age of a husband and a wife is 23 years when they were married FOUR years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
(A) 7 years
(B) 9 years
(C) 6 years
(D) 4 years
(E) 5 years
Rationale: 27 * 2 = 54
20 * 3 = 60
-----------
6 years
Answer: C
Answer: (C) 6 years
Question: Amy's sells kale at x dollar per pound for the first 25 pounds and .8x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and .9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal?
(A) 24
(B) 25
(C) 36
(D) 27
(E) 28
Rationale: For Amy's deal to be better, the cost has to be less or equal to Lucia's
Assuming 'n' is the number of pounds of kale, the equation is
25x + (n-25) (0.8x) <= 14x + (n-14)(0.9x)
Resolve it:
==> 25x + 0.8nx - 20x <= 14x + 0.9nx - 12.6x
==> 3.6x <=0.1nx
==> 36x < =nx
==> x (n-36) > = 0
as x cannot be 0,
==> n - 36 >=0
==> n > = 36
so the minimum value is 36
'C' would be the correct answer
Answer: (C) 36
Question: 4 brothers and 3 sisters is to be arranged in a row for a photograph. In how many ways can they be seated if all the sisters sit together?
(A) 520 ways
(B) 820 ways
(C) 620 ways
(D) 720 ways
(E) 420 ways
Rationale: Since all the sister sit together we can consider them as a single unit. this together and 4 brothers can be arranged in 5x4x3x2x1 ways. The three sisters themselves can be arranged in 3x2x1 ways. The total number arrangements required = 5x4x3x2x3x2 ways =720 Answer : D
Answer: (D) 720 ways
Question: The ratio of present ages of X and Y is 4:5. Which of the following cant be the ratio of ages of X and Y, 20 years ago?
(A) 2:4
(B) 9:10
(C) 2:3
(D) 3:5
(E) 3:6
Rationale: 9:10
as ratio of X:Y can not be more than 4:5 earlier.
ANSWER:B
Answer: (B) 9:10
Question: What is the greatest integer m for which the number 50!/14^m is an integer?
(A) 11
(B) 10
(C) 9
(D) 8
(E) 7
Rationale: 14^m = 2^m*7^m.
Let's figure out how many 7's are in the prime factorization of 50!
The multiples of 7 are: 7, 14, 21, 28, 35, 42, 7*7.
Thus 7^8 will divide 50! but 7^9 will not.
Clearly 2^8 will divide 50!
So m=8 is the largest possible integer.
The answer is D.
Answer: (D) 8
Question: How many seconds will a 500 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) 22
(B) 30
(C) 88
(D) 29
(E) 26
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 = 500 * 3/50 = 30 sec.
Answer: B
Answer: (B) 30
Question: The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:
(A) 0.04
(B) 0.004
(C) 0.4
(D) 0.0004
(E) None of them
Rationale: Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x.
For the given expression to be a perfect square, we must have
11.98 x (x) = 2 x 11.98 x 0.02 or
x = 0.04
Answer is A
Answer: (A) 0.04
Question: 2/5 of the fish in an aquarium are red and 1/4 of the fish are brown. 1/4 of the red fish and 2/5 of the brown fish are male. If the rest of the fish in the aquarium are female, what is the probability that a fish randomly picked from the aquarium is male?
(A) 1/4
(B) 1/5
(C) 1/10
(D) 1/12
(E) 1/20
Rationale: 1/4*2/5 + 2/5*1/4 = 1/5
The answer is B.
Answer: (B) 1/5
Question: If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 5.
II. x is an integer multiple of 3
III. x is an integer multiple of 6
(A) a) I only
(B) b) II only
(C) c) I and II only
(D) d) I and III only
(E) e)II and III only
Rationale: The answer should be D i.e. X will be an integer and multiple of 3 and 6.
Let us take example n, n+1, n+2 as 3 three consecutive positive integers.
In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12
Hence in a product of 3 consecutive integers, the product is always divisible by 3.
Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.
Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even
Answer E
Answer: (E) e)II and III only
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.300 and C's share is Rs.130, what is B's capital?
(A) 19878
(B) 12798
(C) 6166
(D) 11750
(E) 22073
Rationale: 300 + 130 = 430
800 - 430 = 370
300 ---- 5000
370 ---- ? => 6166
Answer: C
Answer: (C) 6166
Question: If 10/b + 20/b + 30/b is an integer, which of the following must also be an integer?
(A) 20/b
(B) b/16
(C) 60/b
(D) 4b
(E) 4+b
Rationale: If 10/b + 20/b + 30/b; then (10+20+30)/b is also integer.
i.e. 60/b is an integer.
Answer is C
Answer: (C) 60/b
Question: The president of a country and 2 other dignitaries are scheduled to sit in a row on the 3 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 3 people?
(A)  4
(B)  5
(C)  20
(D)  24
(E)  2
Rationale: IMO E
Given that one chair is taken, i think the remaining 2 dignitaries can be arranged 2!. That is 2*1=2.
Answer: (E)  2
Question: There are 7 people and 7 chairs. In how many different ways people can occupy the chairs?
(A) 5040
(B) 4500
(C) 3400
(D) 6766
(E) 120
Rationale: number of ways =7! = 5040
Answer is A
Answer: (A) 5040
Question: What is the next number in the sequence below?
1 4 9 16 25 36 __ ?
(A) 45
(B) 46
(C) 47
(D) 48
(E) 49
Rationale: as the series of numbers are squares of numbers
1^2=1
2^2=4
3^2=9
and so on
therefore 7^2=49
ANSWER:E
Answer: (E) 49
Question: The compound ratio of 1:2, 2:5 and 3:10?
(A) 1:2
(B) 1:5
(C) 3:5
(D) 1:50
(E) 3:50
Rationale: 1/2 * 2/5 * 3/10 = 3/503:50Answer: E
Answer: (E) 3:50
Question: A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. while machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?
(A) 11 : 30 am
(B) 12 noon
(C) 12 : 30 pm
(D) 1 pm
(E) None of these
Rationale: (P + Q + R)’s 1 hour’s work = (1⁄8 + 1⁄10 + 1⁄12) = 37⁄120
Work done by P, Q and R in 2 hours = (37⁄120 × 2) = 37⁄60
Remaining work = (1 - 37⁄60) = 23⁄60
(Q + R)’s 1 hour’s work = (1⁄10 + 1⁄12) = 11⁄60
Now, 11⁄60 work is done by Q and R in 1 hour.
So, 23⁄60 work will be done by Q and R in
(60⁄11 × 23⁄60) = 23⁄11 hours ≈ 2 hours.
So, the work will be finished approximately 2 hours after 11 a.m., i.e., around 1 p.m.
Answer D
Answer: (D) 1 pm
Question: Given the following equation 25% of 2475 + 20% of 2115 = x, Find the approximate value should come in place of the x.
(A) 1046
(B) 1048
(C) 1049
(D) 1047
(E) 1040
Rationale: x = 25% of 2475 + 20% of 2115
x = 25/100*2475 + 20/100*2115
x = 1041.75
≈ 1040
Answer E
Answer: (E) 1040
Question: A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle ?
(A) 88 cm2
(B) 154 cm2
(C) 1250 cm2
(D) 616 cm2
(E) None of these
Rationale: Perimeter of the circle = 2πr = 2(18 + 26)
⇒ 2 × 22⁄7 × r = 88 ⇒ r = 14
∴ Area of the circle
= πr2 = 22⁄7 × 14 × 14 = 616 cm2
Answer D
Answer: (D) 616 cm2
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) Rs. 650
(B) Rs. 690
(C) Rs. 698
(D) Rs. 700
(E) None of these
Rationale: Explanation :
S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer : C
Answer: (C) Rs. 698
Question: Find the number of factors R of 180 that are in the form (4*k + 2), where k is a non-negative integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) R=6
Rationale: As for the question, the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number). Number of factors of 180 R (=2^2*3^2*5) = 18. So listing the factors gives us:
1, 180
2, 90
3, 60
4, 45
5, 36
6, 30
9, 20
10, 18
12, 15
As the question asks us about the factors of the form 4k+2 ---> eliminate all ODD factors. You are now left with
2,4,6,10,12,18,20,30,36,60,90,180
For the form 4k+2, the first few values are 2, 6, 10, 14, 18, 22, 26, 30 ... already giving you 5 factors (=2,6,10,18,30). You can stop here and mark 6 (6th one = 90) as the correct answer as 5 is not given.
For checking any particular factor whether they conform to the form 4k+2---> do the following
4k+2 = 36 ---> 4k = 34 --> this will NOT give you an integer value for k ---> reject. Proceed with others until you find all the values asked.
E is thus the correct answer.
Answer: (E) R=6
Question: A bus leaves Santa Barbara at 8:00 a.m. traveling east at 80 miles per hour. At 3:00 p.m. a plane leaves Santa Barbara traveling east at 360 miles per hour. At what time will the plane overtake the bus?
(A) 5:00 p.m.
(B) 6:00 p.m.
(C) 4:00 p.m.
(D) 5:30 p.m.
(E) 4:30 p.m.
Rationale: At 3:00pm, the bus is 560 miles ahead of plane
The plane travels at 360 mph, which gains 250 mph on bus
560/280= 4/3 hours = 120 minutes
3:00 + 2:00 = 5:00
The plane will overtake bus at 5:00pm
Answer:A
Answer: (A) 5:00 p.m.
Question: Mary charges $8.50 per hour to clean a house. If she works 25 hours, how much
does she earn in one week?
(A) $612.50
(B) $112.50
(C) $212.50
(D) $412.50
(E) $312.50
Rationale: Multiply 25 hours x $8.50 =
Answer: $212.50
correct answer C
Answer: (C) $212.50
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 24 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 180
(B) 240
(C) 288
(D) 267
(E) 211
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 24)m = 360 m. Let the length of the platform be x meters. Then, (x + 360)/36 = 15 ==> x + 360 = 540 ==> x = 180 m.Answer: A
Answer: (A) 180
Question: There are 8 books in a shelf that consist of 3 paperback books and 5 hardback books. If 3 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
(A) 40
(B) 46
(C) 50
(D) 55
(E) 60
Rationale: 8C3 [Select any four] -5C3 [Select all hard backs] = 46
B
Answer: (B) 46
Question: The difference of the areas of two squares drawn on two line segments of different lengths is 32 sq	.cm. Find the length of the greater line segment if one is longer than the other by 2cm.
(A) 6 cm
(B) 7 cm
(C) 9 cm
(D) 11 cm
(E) None
Rationale: Solution
Let the lengths of the line segments be x cm and (x + 2) cm.
Then (x+2)2 - x2 = 32
<=> x2+4x+4-x2 = 32
<=> 4x = 28
Therefore x = 7.
Length of longer line segment	= (7 + 2) cm
= 9 cm.
Answer C
Answer: (C) 9 cm
Question: John makes $50 a week from his job. He earns a raise andnow makes $90 a week. What is the % increase?
(A) 15%
(B) 16.66%
(C) 17.8%
(D) 80%
(E) 21%
Rationale: Increase = (40/50)*100 = (4/5)*100 = 80%.
D
Answer: (D) 80%
Question: You collect balls. Suppose you start out with 16. Mike gives you another 17 balls. How many balls do you have at the end?
(A) 33
(B) 34
(C) 35
(D) 36
(E) 37
Rationale: Solution
Start with 16 balls.
Mike gives you 17 balls: 16 + 17 = 33 balls.
So you have 33 at the end.
Correct answer: A
Answer: (A) 33
Question: In your classes you counted 120 hands. How many students were at the class?
(A) 60
(B) 61
(C) 85
(D) 86
(E) 88
Rationale: Total number of hands = 120
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 120 by 2
220 ÷ 2 = 60
Therefore, there were 60 students at the class.
ANSWER IS A
Answer: (A) 60
Question: In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 10% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?
(A) 22%
(B) 23%
(C) 24.4%
(D) 25%
(E) 34%
Rationale: Since 10% of the customers who sample the candyare notcaught, then 90% of the customers who sample the candyarecaught:
{% of customers who sample candy}*0.90 = 0.22;
{% of customers who sample candy} = 0.25.
Answer: C.
Answer: (C) 24.4%
Question: Find the area of the quadrilateral of one of its diagonals is 26 cm and its off sets 9 cm and 6 cm?
(A) 188 cm2
(B) 150 cm2
(C) 168 cm2
(D) 195 cm2
(E) 987 cm2
Rationale: 1/2 * 26(9 + 6)
= 195 cm2
Answer: D
Answer: (D) 195 cm2
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 2
(B) 3.5
(C) 3
(D) 4
(E) 5
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
C)
Answer: (C) 3
Question: A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 50 grams of protein daily, how many grams of food X are in the mixture?
(A) 120
(B) 140
(C) 150
(D) 160
(E) 200
Rationale: Let x be the number of grams of food X in the mixture.
0.1x + 0.15(400-x) = 50
0.05x = 10
x = 200
The answer is E.
Answer: (E) 200
Question: he number of sequences in which 5 players can throw a ball, so that the youngest player may not be the last is?
(A) 96
(B) 12
(C) 50
(D) 42
(E) 18
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 4 players. The first 4 players can throw the ball in 4P4 ways.
The required number of ways = 4(4!) = 4320
Answer:A
Answer: (A) 96
Question: The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is?
(A) 23
(B) 77
(C) 88
(D) 48
(E) 11
Rationale: Let the numbers be 3x and 4x.
Then their H.C.F = x. So, x = 4.
So, the numbers are 12 and 16.
L.C.M of 12 and 16 = 48.
Answer:D
Answer: (D) 48
Question: In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?
(A) 25%
(B) 27%
(C) 34%
(D) 43%
(E) 49%
Rationale: Let total votes in County A = 3x.
Let total votes in County B = x.
Hence total votes in Count A & B together = 4x
Given that, 0.52(4x) = 0.61(3x) + n(x)
So, 2.08x = 1.83x + nx
So, n = 0.25 = 25%
Hence option A
Answer: (A) 25%
Question: A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 34 inches and the width of the wall is 54 inches, what is the length of the wall, in inches?
(A)  22.8
(B)  33.8
(C)  42.8
(D)  63.8
(E)  56.8
Rationale: Since the mirror is 42 inches in all sides, it must be a square. Area of a square is A=a^2; 34^2=1156.Area of rectangle is double of that 2 *1156=2312.Now A=lw and we need find w so A/l=w ; 2312/54= 42.8 Answer!
Answer is C
Answer: (C)  42.8