mathewhe/aqua_rat huggingface dataset:
Question: If f(x) = 12 - x^2/2 and f(2k) = 6k, what is one possible value for k?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: First of all, see thisGMAT blog postand check the related lesson linked below for some background on function notation.
We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be 12 - 4/2 = 10.
So the notation f(2k) means that we are going to plug a 2k in for x everywhere in the formula for f(x). That would be:
f(2k) = 12 - (2k)^2/2 = 12 - 2k^2.
Remember that we have to square both the 2 and the k, to get 4k2. Now, this expression, the output, we will set equal to 2k.
12 - 2k^2 = 2k --> k = -3 or k = 6.
All the answers are positive, so we choose k = 2.
Answer = D
Answer: (D) 6
Question: Two sides of triangle are ln(50) and ln(8), third side is ln(n). Find out the number of possible values of n?
(A) 392
(B) 398
(C) 393
(D) 395
(E) 399
Rationale: Explanation :
Sum of two sides of a triange is always greater than the third side
case 1:
So, ln(50) + ln(8) > ln(n)
=> ln(50x8) > ln(n) ( ∵ log (a) + log(b) = log(ab) )
=> 400 > n
i.e. n < 400
logax is defined for x > 0. So, n will be greater than 0
So, 0 < n < 400
case 2:
So, ln(50) + ln(n) > ln(8)
=> ln(50n) > ln(8) ( ∵ log (a) + log(b) = log(ab) )
=> 50n > 8
i.e. n > 4/25
case 3:
So, ln(8) + ln(n) > ln(50)
=> ln(8n) > ln(50) ( ∵ log (a) + log(b) = log(ab) )
=> 8n > 50
i.e. n > 25/4
Combining results from case 1, case 2 and case 3 we get:
25/4 < n < 400
So, range of integral values of n satisfying the above condition is: 7 ≦ n ≦ 400
Hence no of integral values of n are: 393
Answer : C
Answer: (C) 393
Question: If two different numbers are randomly selected from set { 1, 2, 3, 4, 5} what is the probability that the sum of the two numbers is greater than 4?
(A) 2/5
(B) 3/5
(C) 4/5
(D) 6/5
(E) 7/5
Rationale: First problem is 5C2 = 10 .. Not 20..
Point 2, you sum should be greater than 4, so these are the following possibilities you have
({1,4},{1,5},{2,3},{2,4},{2,5},{3,4},{3,5},{4,5}) which leads to 8 pairs
So the probability is 8 on 10 or 4/5..
ANSWER:C
Answer: (C) 4/5
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
(A) 143600 m
(B) 144600 m
(C) 153600 m
(D) 162600 m
(E) 165600 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: (C) 153600 m
Question: If Jane takes 12 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
(A) xy/12
(B) 12x/(60y)
(C) 60xy/12
(D) xy/720
(E) 720x/y
Rationale: The answer is B.
She runs x yards in 12x/y seconds =12x/60y minutes.
Answer: (B) 12x/(60y)
Question: List K consists of 10 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K?
(A) 5
(B) 6
(C) 7
(D) 11
(E) 4
Rationale: Answer = E = 4
If least = -4, then largest = 5
Range = 5 - 1 = 4
Answer: (E) 4
Question: The cash realised on selling a 14% stock is Rs.101.25, brokerage being 1/4% is
(A) 123
(B) 106
(C) 100
(D) 101
(E) 240
Rationale: Explanation:
Cash realised= Rs. (101.25 - 0.25)
= Rs. 101.
Answer: D
Answer: (D) 101
Question: A boat can travel with a speed of 5km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 100km downstream.
(A) 1 hr
(B) 2 hrs
(C) 3 hrs
(D) 4 hrs
(E) 10 hrs
Rationale: Speed downstream = (5 + 5) km/hr = 10 km/hr.
Time taken to travel 100 km downstream = 100/10 hrs = 10 hrs.
Answer : E
Answer: (E) 10 hrs
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 126
(B) 217
(C) 150
(D) 277
(E) 212
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m. Answer:D
Answer: (D) 277
Question: A can have a piece of work done in 15 days, B can work three times faster than the A, C can work two times faster than A. How many days will they take to do the work together ?
(A) 3 days
(B) 8/9 days
(C) 10/3 days
(D) can't say
(E) none
Rationale: A's 1 day work is 1/20
B's 1 day work is 3/20
C's 1 day work is 2/20
(A+B+C)'s 1 day work(1/20+3/20+2/20) is 3/10
so, they can finish the work in 10/3 days
ANSWER:C
Answer: (C) 10/3 days
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 887
(B) 267
(C) 342
(D) 276
(E) 277
Rationale: 400*(90/100)*(95/100)
= 342
Answer: C
Answer: (C) 342
Question: A certain company consists of 8 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)
(A) 84
(B) 108
(C) 135
(D) 270
(E) 448
Rationale: Total # of teams of 3 possible is 16C3=560
# of teams with only managers or only non-managers is: 8C3+8C3=56+56=112;
# of teams of 3 with at least one manager or at least one non-manager is: 560-112=448.
ANSWER:E
Answer: (E) 448
Question: The length of a rectangle is four times its width. If the area is 100 m2 what is the length of the rectangle?
(A) 60 m
(B) 50 m
(C) 40 m
(D) 30 m
(E) 20 m
Rationale: Let L be the length and W be the width of the rectangle. Hence
L = 4 W
We now use the area to write
100 = L * W
Substitute L by 4 W in the equation above
100 = 4 W * W = 4 W2
Solve for W and find L
4 W2 = 100
W2 = 25 , W = 5 and L = 4 W = 20 m
correct answer E
Answer: (E) 20 m
Question: The average weight of A, B and C is 46 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 28 kg
(B) 32 kg
(C) 33 kg
(D) 34 kg
(E) None of these
Rationale: Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (46 x 3) = 138 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (43 x 2) = 86 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)
Subtracting (i) from (iv), we get : B = 28.
B’s weight = 28 kg.
Answer: A
Answer: (A) 28 kg
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2415?
(A) s.800
(B) s.810
(C) s.805
(D) s.900
(E) s.920
Rationale: 2415 * 1/3 = 805
Option C
Answer: (C) s.805
Question: A sum of money at simple interest amounts to $ 980 in 3 years and to $1024 in 4 years. The sum is:
(A) $153
(B) $848
(C) $398
(D) $549
(E) $675
Rationale: B
$848
S.I. for 1 year = $(1024 - 980) = $44.
S.I. for 3 years = $(44 x 3) = $132.
Principal = $(980 - 132) = $848.
Answer: (B) $848
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 299 m
(B) 982 m
(C) 399 m
(D) 150 m
(E) 354 m
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: D
Answer: (D) 150 m
Question: A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train?
(A) 150
(B) 872
(C) 250
(D) 288
(E) 212
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 15 = 250 meter
Answer:C
Answer: (C) 250
Question: (469 + 174)2 - (469 - 174)2	/(469 x 174)=?
(A) 2
(B) 4
(C) 295
(D) 643
(E) 123
Rationale: Explanation:
Given exp. =	(a + b)2 - (a - b)2/ab
=	4ab/ab
= 4 (where a = 469, b = 174.)
ANSWER IS B
Answer: (B) 4
Question: What is the sum of all the composite numbers up to 20?
(A) 228
(B) 277
(C) 198
(D) 132
(E) 281
Rationale: Explanation:
4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 132
Answer: D
Answer: (D) 132
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 10/7 sec
(B) 12/7 sec
(C) 20/7 sec
(D) 17/7 sec
(E) 19/7 sec
Rationale: Explanation:
They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.
ANSWER IS C
Answer: (C) 20/7 sec
Question: A boy has five trousers and 14 shirts. In how many different ways can he select a trouser and a shirt?
(A) 60
(B) 278
(C) 70
(D) 108
(E) 271
Rationale: The boy can select one trouser in five ways.
The boy can select one shirt in 14 ways.
The number of ways in which he can select one trouser and one shirt is 5 * 14
= 70 ways.
Answer: C
Answer: (C) 70
Question: If the cost of 8 erasers and 5 sharpeners is Rs.31/-, what will be the cost of 24 erasers and 10 sharpeners?
(A) Rs.62/-
(B) Rs.84/-
(C) Rs.78/-
(D) Rs.150
(E) None of these
Rationale: Explanation:
By analysis, we get 8x2 = 16 (erasers)
5x3 = 15 (sharpeners)
:.1 Eraser costs Rs.2/- and 1 sharpener costs Rs.3/-
Hence, the cost of 24 erasers + 10 sharpeners = 24x2 + 10x3 = 48+30 = Rs.78/-
Answer: Option C
Answer: (C) Rs.78/-
Question: In how many ways can the letters of word DEVELOP be arranged such that all the vowels as well as all the Consonants always appear together?
(A) 9!
(B) 3!*4!*2!
(C) 5!*5!
(D) 5!*4!*2!
(E) 6!*4!
Rationale: Since all the vowels and consonants have to be together there can only be there are 3! way to order the vowels and 4! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.
So 3!4!2! (B)
Answer: (B) 3!*4!*2!
Question: Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 6 hours, how many minutes did it take Cole to drive to work?
(A) 84
(B) 136
(C) 172
(D) 210
(E) 478
Rationale: First round distance travelled (say) = d
Speed = 75 k/h
Time taken, T2 = d/75 hr
Second round distance traveled = d (same distance)
Speed = 105 k/h
Time taken, T2 = d/105 hr
Total time taken = 6 hrs
Therefore , 6 = d/75 + d/105
LCM of 75 and 105 = 525
6= d/75 + d/105
=> 6 = 7d/525 + 5d/525
=> d = 525 / 2 Km
Therefore, T1= d/75
=> T1 = 525 / (2 x 75)
=> T1 = (7 x 60) / 2 -- in minutes
=> T1 = 210 minutes.
D
Answer: (D) 210
Question: A dice has one of the first 4 prime number on each its six sides ,with no two sides having the same number .the dice is rolled 10 times and the results added.the addition is most likely to be closet to
(A) 41
(B) 43
(C) 60
(D) 68
(E) 70
Rationale: if die is rolled then avg score = (2+3+5+7 )/4 = 41/4
so, most likely sum for 10 times = 41/4 * 10 = 43
ANSWER:B
Answer: (B) 43
Question: Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 350 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 3 of the days were hot, then what was the price of 1 cup on a hot day?
(A) $ 1.50
(B) $ 1.88
(C) $ 2.14
(D) $ 2.50
(E) $ 3.25
Rationale: 7 regular days --> sales = 7*32*x = 224x;
3 hot days --> sales = 3*32*(1.25x) = 120x;
Total sales = 224x+120x = 344x.
Total cost = 10*32*0.75 = 240.
Profit = 344x - 240 = 350 --> x=1.715.
1.25x=~2.14.
Answer:C.
Answer: (C) $ 2.14
Question: Akhil borrowed a certain sum of money at the rate of 6%, 9% and 14% for a period of first two years, next three years and beyond the period of five years respectively. If at the end of nine years, he paid Rs. 8550 as interest, then find the sum of money he had borrowed.
(A) Rs. 9,000
(B) Rs.14,000
(C) Rs.15,000
(D) Rs.18,000
(E) None of these
Rationale: Explanation:
Let Rs.P be the money borrowed by Akhil.
I) R = 6%, T = 2 years
Simple Interest of 2 years = PRT/100
= P * 6 * 2/100 = 12P/100
II) R = 9%, T = 3 years
Simple Interest of 3 years = P * 9 * 3/100 = 27P/100
III) R = 14%, T = 4 years
Simple Interest of 3 years= P * 14 * 4/100 = 56P/100
Therefore, total Simple Interest of 9 years
= 12P/100 + 27P/100 + 56P/100
= 95P/100
The total interest paid after nine years = Rs.8550
95P/100 = 8550
Therefore, 95P = 855,000
P = 855,000/95 = Rs. 9,000
Amount of money borrowed by Akhil = Rs. 9,000
ANSWER A
Answer: (A) Rs. 9,000
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 70
(B) 71
(C) 72
(D) 73
(E) 74
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: Option C
Answer: (C) 72
Question: An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 3/2M + 15, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold
(A) a.	A - 40
(B) b.	B - 15
(C) c.	C – 22.5
(D) d.	D – 30
(E) e.	E – 67.5
Rationale: A --- 120/2 + 15 = 75 --- CORRECT
B --- 45/2 + 15 = not an integer --- wrong
C --- 22.5(3/2) + 15 = not an integer --- wrong
D --- 90/2+15 = 60 --- wrong
This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method.
A
Answer: (A) a.	A - 40
Question: Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number
(A) 17
(B) 15
(C) 8
(D) 3
(E) 2
Rationale: Explanation:
If the number is x,
Then, x + 17 =	60/x
x2 + 17x - 60 = 0
(x + 20)(x - 3) = 0
x = 3, -20, so x = 3 (as 3 is positive)
Answer: Option D
Answer: (D) 3
Question: In a class, the average age of 45 boys is 18 years and the average of 35 girls is 15 years. what is the average age of the whole class?
(A) 11 Years
(B) 12.6 Years
(C) 13 Years
(D) 16.6 Years
(E) 14 Years
Rationale: Total age of 80 students
(45X 18+35 X 15) = 1335
Average = 1335/80 = 16.6 Years
D)
Answer: (D) 16.6 Years
Question: 40, 45, 50, 50, 60, 75, 75, 100, 100, 100.
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.7, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The average of {40, 45, 50, 50, 60, 75, 75, 100, 100, 100} is 69.5.
1 standard deviation below the mean is 69.5 - 22.7 = 46.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean.
Answer B.
Answer: (B) 2
Question: I chose a number and divide it by 6. Then I subtracted 15 from the result and got 5. What was the number I chose?
(A) 600
(B) 700
(C) 120
(D) 900
(E) None
Rationale: Solution:
Let xx be the number I chose, then
x/6âˆ’15=5
x/6=20
x=120
Answer C
Answer: (C) 120
Question: A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, “How many gold coins do we have?” After pausing a moment, he replied, “Well! If I divide the coins into two unequal numbers, then 37 times the difference between the two numbers equals the difference between the squares of the two numbers.” The wife looked puzzled. Can you help the merchant’s wife by finding out how many gold are
(A) 36
(B) 37
(C) 38
(D) 39
(E) 40
Rationale: 37(x-y)=x^2-y^2. u no tht x^2-y^2=(x-y)(x+y).so (x-y) cancels on both sides to give x+y=37.so sum of unequal halves=37 which is the required answer.
Answer B
Answer: (B) 37
Question: How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
(A) 27
(B) 28
(C) 29
(D) 34
(E) 60
Rationale: The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = 5P3 = 60.
Answer:E
Answer: (E) 60
Question: If 145% of j is equal to 25% of k, 160% of k is equal to 50% of l, and 175% of l is equal to 75% of m, then 40% of m is equal to what percent of 200% of j ?
(A) 0.35
(B) 3.5
(C) 35
(D) 700
(E) 3500
Rationale: IMO answer should be 350...
consider j=10, then k=50, l=150 and m=350....
40% of 350, comes out to be 140....
200% of 10 is 20....
(140*100)/20=700....
Ans : D
Answer: (D) 700
Question: A sum fetched total simple interest of 4016.25 at the rate of 14 p.c.p.a. in 5 years. What is the sum?
(A) 5737.5
(B) 8032.5
(C) 4462.5
(D) 8900
(E) None of these
Rationale: Let the sums be P.
Now, 70% of P = 4016.25
or, P = 5737.5
Answer A
Answer: (A) 5737.5
Question: Average Age of residents of a colony is 38 years with Standard deviation of 5 years
If Mr.X's age lies within 2 SD from mean and Mr.Y's age lies within 1 SD from mean then find
maximum values of (X/Y) = ?
(A) 48/38
(B) 48/43
(C) 48/33
(D) 38/33
(E) 48/35
Rationale: Mean = 38
X = Mean + 2SD => 28 < x < 48
Y = Mean + 1SD => 33 < x < 43
So, Maximum Value of x/y = Maximum Value of x / Minimum Value of y = 48/33
Hence answer will be (C) 48/33
Answer: (C) 48/33
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9hours. If both the taps are opened simultaneously then after how much time will the cistern get filled?
(A) 6hr
(B) 5.6hr
(C) 9.5hr
(D) 7.2hr
(E) 4hr
Rationale: Net part filled in 1 hour 1/4 - 1/9 = 5/36
The cistern will be filled in 36/5 hr = 7.2hr
Answer is D
Answer: (D) 7.2hr
Question: Find the simple interest on Rs 7000 at 50/3 % for 9 months
(A) Rs. 1075
(B) Rs. 975
(C) Rs. 875
(D) Rs. 775
(E) None of these
Rationale: Explanation:
S.I. = P×R×T100
So, by puƫing the values in the above formula, our result will be.
Required result = 7000×50×93×12×100=875
[Please note that we have divided by 12 as we converted 9 months in a year format]
Answer: C
Answer: (C) Rs. 875
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 29
(B) 29
(C) 60
(D) 19
(E) 12
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5
= 60 km/hr.
Answer:C
Answer: (C) 60
Question: If the selling price is septuple,the profit is octupled,what is the percentage of profit??
(A) 50%
(B) 100%
(C) 150%
(D) 200%
(E) 250%
Rationale: we can make two equations from the given info..
let selling price be S and cost price be C..
so profit=P=S-C...
if S is doubled profit is tripled..
so 8P=7S-C..
or S=7P...
therefore C=P..
% of profit=P/P=100%
B
Answer: (B) 100%
Question: N is a positive integer. When N + 1 is divided by 3, the remainder is 2. What is the remainder when N is divided by 3?
(A) 1
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: N+1 = 3a+2
i.e. N+1 = 5, 8, 11, 14, ... etc.
i.e. N = 4, 7, 10, 13, ... etc.
When N is divided by 3 Remainder is always 1
Answer: A
Answer: (A) 1
Question: Find the odd man out. 1,8,27,60,125
(A) 216
(B) 125
(C) 185
(D) 64
(E) 14
Rationale: Explanation :
1^3=3
2^3=8
3^3=27
4^3=64
5^3=125
Hence, it is clear that 64 should have come instead of 60
Answer : Option D
Answer: (D) 64
Question: On dividing 161 by a number, the quotient is 10 and the remainder is 1. Find the divisor.
(A) A)12
(B) B)14
(C) C)16
(D) D)18
(E) E)22
Rationale: d = (D-R)/Q
= (161 - 1)/10
= 160/10 = 16
C)
Answer: (C) C)16
Question: A metallic sphere of radius 24 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
(A) 26 cm
(B) 45 cm
(C) 58 cm
(D) 63 cm
(E) 72 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)^2 * h = (4/3)π (24)^3 => h
= 72 cm
Answer:E
Answer: (E) 72 cm
Question: A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
(A) 70.24km/hr
(B) 74.24km/hr
(C) 71.11km/hr
(D) 72.21km/hr
(E) 75.32km/hr
Rationale: Explanation:
Average Speed =2x64x80 / 64+80
=71.11km/hr
Answer is C
Answer: (C) 71.11km/hr
Question: The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area?
(A) 376
(B) 148
(C) 216
(D) 168
(E) 178
Rationale: 2(4*5 + 5*6 + 4*6)
= 148
Answer: B
Answer: (B) 148
Question: The EastBank Choir out sold the WestBank Choir by 40% of the 100 boxes of donuts they ordered. The EastBank Choir hustled and made all of the last sales closing the sale with an average of only 25%. How many more sales did the choir make to reach this average?
(A) 20
(B) 5
(C) 10
(D) 15
(E) 25
Rationale: Explanation: Identify the parts, set up equation, and solve.
Number of boxes of donuts initially sold by EastBank Choir:
40% * 100 = 40
Total boxes sold by the end of the sale leaving an average at 25%. (Let x represent the unknown number of additional boxes sold by the EastBank Choir.) Therefore, the total number of boxes sold is 100+x, and the total number of boxes sold by the EastBank Choir is 40+x. This gives the equation as:
25%*(100+x)=40+x
Solve: Let's get rid of the percent sign
25/100*(100+x)=40+x
1/4 *(100+x)=40+x
Get rid of the fraction:
4[1/4 * (100+x)]=4(40+x)
1 * (100+x) =160+4x
100+x =160+4x
(100-160)+x = (160-160)+4x
-60+x= 4x
-60=3x
20=x
Answer: A
Answer: (A) 20
Question: A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
(A) 20
(B) 30
(C) 15
(D) 10
(E) 25
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+5)=4/5 20x=4(3x+5)8x=20 x=2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
ANSWER D
Answer: (D) 10
Question: Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (127)?
(A) 2
(B) 4
(C) 5
(D) 12
(E) 25
Rationale: (21)(3^7) is divisible by 3 but 127 is not divisible by 3.
Therefore (21)(3^7) - 127 is not divisible by 3 and thus not divisible by 12.
The answer is D.
Answer: (D) 12
Question: The average of the two-digit numbers, which remain the same when the digits interchange their positions, is?
(A) 56
(B) 86
(C) 55
(D) 87
(E) 88
Rationale: Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99)/9
= [(11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55]/9
= [(4 * 110) + 55]/9 = 495/9 =55.
Answer:C
Answer: (C) 55
Question: A certain sum of money at simple interest amounted Rs.870 in 10 years at 3% per annum, find the sum?
(A) 665.23
(B) 666.23
(C) 667.23
(D) 668.23
(E) 669.23
Rationale: 870 = P [1 + (10*3)/100]
P = 669.23
Answer: E
Answer: (E) 669.23
Question: Find the compound ratio of (2:3), (6:11) and (11:6) is
(A) 3:2
(B) 2:1
(C) 1:2
(D) 4:5
(E) 2:3
Rationale: Required ratio = 2/3 * 6/11 * 11/6 = 2/1 = 2:3
Answer is E
Answer: (E) 2:3
Question: A three-person committee must be chosen from a group of 7 professors and 20 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?
(A) A)70
(B) B)1785
(C) C)630
(D) D)1,260
(E) E)1,980
Rationale: Total number of ways to select at least one professor = Number of ways to select 3 people from 20 students and 7 professors - Number of ways to select 3 people from 20 student (i.e. without including any professor)
= 27C3 - 20C3 = 2925 - 1140 = 1785
ANSWER:B
Answer: (B) B)1785
Question: When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country?
(A) 166 2/7
(B) 166 2/1
(C) 166 2/2
(D) 166 2/3
(E) 166 2/8
Rationale: 5% - 2% = 3%
3% ---- 5
100% ---- ?
=> 166 2/3
Answer:D
Answer: (D) 166 2/3