mathewhe/aqua_rat huggingface dataset:
Question: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 330 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
(A) 330 * sqrt 2
(B) 330 * sqrt (2^7)
(C) 330 * sqrt (2^12)
(D) 330 * the twelfth root of (2^7)
(E) 330 * the seventh root of (2^12)
Rationale: Let the constant be k.
F1 = 330
F2 = 330k
F3 = 330 k * k = 330 * k^2
F13= 330 * k^12
we know F13 = 2 *F1 = 2 * 330 = 660
660/330 = k^12
k = twelfth root of 2
for F7...
F7 = 330 * k^6 ( as we wrote for F2 and F3)
F7 = 330 * (twelfth root of 2) ^ 6
F7 = 330 * sqrt (2)
The answer is A.
Answer: (A) 330 * sqrt 2
Question: A sells a bicycle to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays Rs. 225 for it, the cost price of the bicycle for A is?
(A) 277
(B) 268
(C) 270
(D) 150
(E) 282
Rationale: 125% of 120% of A = 225
125/100 * 120/100 * A = 225
A = 225 * 2/3 = 150.
Answer: D
Answer: (D) 150
Question: Find the average of first 50 natural numbers.
(A) A)25.5
(B) B)20.5
(C) C)24.5
(D) D)19.9
(E) E)25
Rationale: Sum of first n natural numbers = n(n+1)/2
sum of first 50 natural numbers = 50*51/2 =1275
average = 1275/50 = 25.5
Answer is A
Answer: (A) A)25.5
Question: If x dollars is invested at 9 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 9 percent investment will exceed the annual income from the 8 percent investment by $48. If $2,000 is the total amount invested, how much is invested at 9 percent?
(A) 300
(B) 250
(C) 1223.53
(D) 1133.24
(E) 776.47
Rationale: 2 equations with 2 unknowns
9x / 100 - 8y / 100 = 48
and
x + y = 2000
Solving these 2 equations, x = 1223.53 and y = 776.47
Answer -C
Answer: (C) 1223.53
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
(A) 288
(B) 270
(C) 289
(D) 480
(E) 211
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: D
Answer: (D) 480
Question: An urn contains 5 red, 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that the drawn ball are blue?
(A) 20/969
(B) 20/875
(C) 21/876
(D) 3/512
(E) 2/9
Rationale: Sample space = no. of ways 3 balls were drawn from urn = 19C3 = 969
No. ways 3 blue balls were drawn from bag = 6C3 = 20
Probability = 20 / 969
Ans - A
Answer: (A) 20/969
Question: A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 970gm. for a kg.His gain is …%.
(A) 3.09%
(B) 5.36%
(C) 4.26%
(D) 6.26%
(E) 7.26%
Rationale: His percentage gain is 100*30/970 as he is gaining 30 units for his purchase of 970 units.
so 3.09%.
ANSWER:A
Answer: (A) 3.09%
Question: Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 30 days.
(A) 16 days.
(B) 17 days.
(C) 18 days.
(D) 19 days.
(E) 20 days.
Rationale: They together completed 4/10 work in 4 days.
balance 6/10 work will be completed by Arun alone in 30*6/10 = 18 days.
ANSWER:C
Answer: (C) 18 days.
Question: During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies. The store still makes a profit of 10% on this sale. What is the mark up percentage on each candy?
(A)  100%
(B)  80%
(C)  75%
(D)  66+2/3%
(E)  55%
Rationale: Hi Akhil, I can share the way I solved it..
Let's say Marked price = M
So, there's a discount of 20% on M So, new S.P. = 80% of M
Now, the child convinces the owner to sell 20 candies for the price of 14 candies .
Let's say each candy after discount is 1$. So, S.P. of 20 candies = 20$. THe child bought it for 14 $ So, he got a discount of 6/20 *100 = 30%
So, the latest S.P. = 70% of 80% of M = 0.7* 0.8 M
Now, we are given that the shopkeeper still makes a profit of 12%. So we have ,
0.7 * 0.8 * M = 1.12 C.P
So, we get, M= 2 C.P.
i.e. Marked price was kept 100% above C.P.
C
Answer: (C)  75%
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 4 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.
4/12 + x/15 = 1
x/15 = 2/3
x = 10
After the first pipe is turned off, it takes 6 more minutes to fill the cistern.
The answer is A.
Answer: (A) 6
Question: Gaurav spends 30% of his monthly income on food articles, 40% of the remaining on conveyance and clothes and saves 50% of the remaining. If his monthly salary is Rs. 18,400, how much money does he save every month ?
(A) 3864
(B) 2338
(C) 3799
(D) 1267
(E) 2991
Rationale: Explanation:
Saving = 50% of (100 - 40)% of (100 - 30)% of Rs. 18,400
= Rs. (50/100 * 60/100 * 70/100 * 18400) = Rs. 3864.
Answer: A) 3864
Answer: (A) 3864
Question: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how
many days will 10 women working together finish it ?
(A) 30 days
(B) 40 days
(C) 50 days
(D) 60 days
(E) None of these
Rationale: Explanation:
Let 1 man's 1 day work = x
and 1 woman's 1 days work = y.
Then, 4x + 6y = 1/8
and 3x+7y = 1/10
solving, we get y = 1/400 [means work done by a woman in 1 day]
10 women 1 day work = 10/400 = 1/40
10 women will finish the work in 40 days
Answer: B
Answer: (B) 40 days
Question: In a company of 15 employees, 6 employees earn $37,000, 5 employees earn $42,000, and the 4 highest-paid employees earn the same amount. If the average annual salary for the 15 employees is $45,000, what is the annual salary for each of the highest-paid employees?
(A) $56,250
(B) $57,750
(C) $59,250
(D) $60,750
(E) $62,250
Rationale: 6*37,000+5*42,000+4x=15*45,000
4x=675,000-222,000-210,000
4x=243,000
x=60,750
The answer is D.
Answer: (D) $60,750
Question: $500 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
(A) $100
(B) $150
(C) $125
(D) $200
(E) $250
Rationale: A:(B+C) = 2:3
A's share = 500*2/5 = $200
Answer is D
Answer: (D) $200
Question: Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
(A) A)35
(B) B)28
(C) C)45
(D) D)25
(E) E)26
Rationale: Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Eight years ago, P was half of Q in age
=> 2(3x – 8) = (4x – 8)
=> 6x – 16 = 4x – 8
=> 2x = 8
=> x = 4
7x=7*4=28
Answer: Option B
Answer: (B) B)28
Question: 28 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 13.25
(B) 38.25
(C) 33.25
(D) 12.25
(E) 31.25
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 28 = 12.25
ANSWER:D
Answer: (D) 12.25
Question: If the number is divided by 3, it reduced by 24. The number is
(A) A)51
(B) B)50
(C) C)45
(D) D)40
(E) E)36
Rationale: Explanation:
Let the number be x. Then,
x - (x/3) = 24 => 2x/3 = 24
=> x = 36
Answer: Option E
Answer: (E) E)36
Question: A grocer has a sale of Rs. 3435, Rs. 3927, Rs. 3855, Rs. 4230 and Rs. 3562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 3500?
(A) s. 1991
(B) s. 2991
(C) s. 3991
(D) s. 4991
(E) s. 5991
Rationale: Explanation:
Total sale for 5 months = Rs. (3435 + 3927 + 3855 + 4230 + 3562) = Rs. 19009.
Required sale = Rs. [ (3500 x 6) â€“ 19009 ]
= Rs. (21000 â€“ 19009)
= Rs. 1991.
Answer A
Answer: (A) s. 1991
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.74 less, he could have gained 25%. What is the cost price?
(A) s.370
(B) s.375
(C) s.375
(D) s.350
(E) s.300
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
74 ----- ? => 370
ANSWER:A
Answer: (A) s.370
Question: Ian is paid an hourly wage, totaling $400 for h hours of work in a week, where h >0. If Ian's hourly wage increases by 25% and Ian decides to work 25% fewer hours each week, how much will Ian be paid in a week?
(A) $200
(B) $375
(C) $400
(D) $425
(E) $600
Rationale: let No of hours ian worked = h
and wage per hour = w
therefore w*h = 400
if he decides to work 25% fewer hours = 0.75 * h
and 25% more age is paid = 1.25 * w
therefore 1.25*w*0.75*h = 1.25*0.75*400 = 375
ANSWER:B
Answer: (B) $375
Question: A and B go around a circular track of length 400 m on a cycle at speeds of 36 kmph and 36 kmph. After how much time will they meet for the first time at the starting point?
(A) 40 sec
(B) 198 sec
(C) 178 sec
(D) 665 sec
(E) 276 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 400/ (36 * 5/18) , 400/ (36 * 5 /18) }
= LCM (40, 40) = 40 sec.
Answer:A
Answer: (A) 40 sec
Question: If 821562 is to be divisible by 5, what is the least whole number that should be added to it?
(A) 6
(B) 4
(C) 5
(D) 2
(E) 3
Rationale: A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
Here, 821562 =562,
the next multiple of 9 is 568.
6 must be added to 821562 to make it divisible by 8
A
Answer: (A) 6
Question: If a:b=2:3 and b:c=2:4 find a:b:c?
(A) 6:2:3
(B) 2:6:3
(C) 2:3:6
(D) 3:2:6
(E) 6:3:2
Rationale: a:b = 2:3, b:c = 2:4
2:3
2:4
(a = a × b, b = b × b and c = b × c)
a:b:c = 2:3:6
C
Answer: (C) 2:3:6
Question: If x = -2 and y = -4, what is the value of 5(x-y)^2 - xy ?
(A) 12
(B) 13
(C) 15
(D) 18
(E) 22
Rationale: x = -2 and y = -4
x-y = -2 - (-4) = -2+4 = 2
x*y = -2 * -4 = 8
Now we apply it in the equation 5(x-y)^2 - xy =5 (2)^2-8
==>5*4 -8 = 20-8 =12
Answer : A
Answer: (A) 12
Question: Country X taxes each of its citizens an amount equal to 11 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?
(A) $40,000
(B) $56,000
(C) $64,000
(D) $58,000
(E) $80,000
Rationale: Equation is correct, so math must be a problem.
0.11*40,000+0.2*(x-40,000)=8,000 --> 4,400+0.2x-8,000=8,000 --> 0.2x=11,600 --> x=58,000.
Answer: D.
Answer: (D) $58,000
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 8% p.a. in 5 years. What is the sum?
(A) Rs. 10060.625
(B) Rs. 10040.62
(C) Rs. 12040.62
(D) Rs. 20040.625
(E) Rs. 10030.625
Rationale: Principal = (100 * 4016.25) / (8 * 5) = Rs. 10040.625.
ANSWER:B
Answer: (B) Rs. 10040.62
Question: If any amount is distributed among A ,B and C so that the part of A is doubled that of the part of B and part of b is 3 time the part of C .Find the ratio among their parts.
(A) 1:2:4
(B) 1:4:1
(C) 8:4:1
(D) 2:4:1
(E) 6:3:1
Rationale: By the assumptions as mentioned we have A=2B and B=3C. So A=2(3C) and we get A=6C. We have, therefore, A:B:C = 6C:3C:C. By cancelling the ratio with C we have 6:3:1. The answer is, therefore, E.
Answer: (E) 6:3:1
Question: An antique shop has four different vases (vase 1, vase2, vase3, vase4) which are valued at different prices. If vase2 is 30% less in value than vase1, vase3 is 10% less than vase2, and vase4 is 5% less than vase3. what percent of vase1's cost is a vase3?
(A) 50.85%
(B) 59.85%
(C) 60.85%
(D) 40.5%
(E) 39.85%
Rationale: Let the cost of vase1 be $100
I) vase2 is 30% less in value than vase1--100-30=70
II) vase3 is 10% less than vase2--70-7=63
III) vase4 is 5% less than vase3--63-3.15=59.85
what percent of vase1's cost is a vase3=59.85*100/100
Answer is B
Answer: (B) 59.85%
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 962
(C) 267
(D) 258
(E) 268
Rationale: Profit on first article
= 20% of 1000
= 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer:A
Answer: (A) 200
Question: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 5/6 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
(A) 4/7
(B) 5/9
(C) 6/11
(D) 7/12
(E) 8/13
Rationale: Let x be the number of workers on the day crew.
Let y be the number of boxes loaded by each member of the day crew.
Then the number of boxes loaded by the day crew is xy.
The number of boxes loaded by the night crew is (5x/6)(3y/4) = 5xy/8
The total number of boxes is xy + 5xy/8 = 13xy/8
The fraction loaded by the day crew is xy / (13xy/8) = 8/13
The answer is E.
Answer: (E) 8/13
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 1.8
(B) 1.5
(C) 1.3
(D) 1.2
(E) 1.6
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: (B) 1.5
Question: The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x5x cents per day while the price of wheat is decreasing at a constant rate of 2√∗x−x2∗x−x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
(A) $4.50
(B) $5.10
(C) $5.30
(D) $5.50
(E) $5.60
Rationale: Let yy be the # of days when these two bushels will have the same price.
First let's simplify the formula given for the rate of decrease of the price of wheat: 2√∗x−x=1.41x−x=0.41x2∗x−x=1.41x−x=0.41x, this means that the price of wheat decreases by 0.41x0.41x cents per day, in yy days it'll decrease by 0.41xy0.41xy cents;
As price of corn increases 5x5x cents per day, in yy days it'll will increase by 5xy5xy cents;
Set the equation: 320+5xy=580−0.41xy320+5xy=580−0.41xy, solve for xyxy --> xy=48xy=48;
The cost of a bushel of corn in yy days (the # of days when these two bushels will have the same price) will be 320+5xy=320+5∗48=560320+5xy=320+5∗48=560 or $5.6.
Answer: E.
Answer: (E) $5.60
Question: If C + D = 12 and C and D are positive integers, which of the following is a possible value for 5C + 8D?
(A) 111
(B) 121
(C) 150
(D) 171
(E) 180
Rationale: c + d = 11
5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 60 + 3d=D=30
D=30
c+d=12=C+30=9=C=12-30=-18
C=-18
5C + 8D=5(-18)+8(30)=-90+240=150
Hence, C is the right answer.
Answer: (C) 150
Question: Two years ago, Ram put $1,000 into a savings account. At the end of the first year, his account had accrued $200 in interest bringing his total balance to $1,200. The next year, his account balance increased by 20%. At the end of the two years, by what percent has Ram's account balance increased from his initial deposit of $1,000 ?
(A) 19%
(B) 30%
(C) 42%
(D) 45%
(E) 25%
Rationale: investment 1000 dollars
1 st year total gained = 200
total amount end of first year = 1200
second year account increased by 20 % = 1200*0.2 = 240
therefore total amount by second year end = 1420
so total percentage increase in money = (1420-1000)*100/1000 = 42 %
Correct Answer C=42%
Answer: (C) 42%
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
(A) 16 hours
(B) 28 hours
(C) 18 hours
(D) 19 hours
(E) 10 hours
Rationale: 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
Answer:B
Answer: (B) 28 hours
Question: How many positive integers P less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?
(A) 19
(B) 18
(C) 17
(D) 16
(E) 15
Rationale: We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?
The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?
1, 3, 5, 7
None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = E
Answer: (E) 15
Question: In Town X, 64 percent of the population are employed, and 38 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 25%
(C) 32%
(D) 40%
(E) 52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 38 are employed males,hence 26% are employed females.
(employed females)/(total employed people)=26/64=40%
Answer: D.
Answer: (D) 40%
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
(A) 1/3
(B) 2/3
(C) 2/5
(D) 3/7
(E) 3/11
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A
Answer: (A) 1/3
Question: The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 67 kmph
(C) 5 kmph
(D) 88 kmph
(E) 12 kmph
Rationale: Speed of the boat in still water
= (70+80)/2
= 75 kmph. Speed of the stream
= (80-70)/2
= 5 kmph.
Answer:C
Answer: (C) 5 kmph
Question: While driving from A-ville to B-town, Harriet drove at a constant speed of 100 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 150 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?
(A) 138
(B) 148
(C) 150
(D) 162
(E) 180
Rationale: 5hr = 300min.
If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.
Now let plug in ans. D or E and verify which one give same distance on each leg.
E. t= 180min
* leg A-B ---> d = 100.180/60 = 18000/60
* leg B-A ----> d = 150*120/60 = 18000/60
so the correct ans. isE
Answer: (E) 180
Question: If x, y, and z are positive integers, and 2x = 5y = 6z, then the least possible value of x + y + z is
(A) 15
(B) 26
(C) 37
(D) 42
(E) 60
Rationale: Take LCM of 2,5 and 6 = 30
Now 2x = 30 => x =15
5y = 30 => y = 6
6z = 30 => z =5
15+6+5 = 26.
Option B.
Answer: (B) 26
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 36 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 18.4 sec
(B) 77 sec
(C) 76 sec
(D) 20 sec
(E) 66 sec
Rationale: Relative speed = (42 + 36) * 5/18 = 21.7 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/21.7 = 18.4 sec.
Answer:A
Answer: (A) 18.4 sec
Question: P,Q and R enter into a partnership in the ratio 7/2 : 4/3 : 6/5. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs.21600, then B’s share in the profit is:
(A) Rs.2100
(B) Rs 2400
(C) Rs.3600
(D) Rs.4000
(E) Rs.3000
Rationale: Ratio of initial investments = 105 : 40 : 36.
Let the initial investments be 105x, 40x & 36x.
Therefore, P : Q : R = 105x * 4 + 150/100 x 105x * 8 : 40x * 12 : 36x * 12
= 1680x : 480x : 432x = 35 : 10 : 9.
Therefore, Q’s share = Rs. 21600 * 10/54
= Rs.4000.
ANSWER:D
Answer: (D) Rs.4000
Question: What will be the remainder when 8-3 + 3^5 + 2^10 is divided by 4?
(A) 12
(B) 3
(C) 16
(D) 0
(E) 9
Rationale: The multiplication(e.g. 2^10) is done first and then the sum(e.g. 15+20) and
subtraction (e.g. 8-3), and after all this expression it should be divided by 4 and the answer is 0, option D.
Answer: (D) 0
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 9:7
(B) 9:8
(C) 9:1
(D) 9:2
(E) 9:9
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer:B
Answer: (B) 9:8
Question: Find the numbers which are in the ratio 3:2:4 such that the sum of the first and the second added to the difference of the third and the second is 28?
(A) 4,3,22
(B) 4,4,22
(C) 12,6,16
(D) 9,6,12
(E) 9,2,23
Rationale: Let the numbers be a, b and c.
a:b:c = 3:2:4
Given, (a + b) + (c - b) = 21
=> a + c = 28
=> 3x + 4x = 28 => x = 4
a, b, c are 3x, 2x, 4x
a, b, c are 12, 8, 16.
Answer:C
Answer: (C) 12,6,16
Question: In a city the doors of buildings where numbered from 1 to 100. How many 3’s are there as the door number?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: We will have the 3’s as follows 3,13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93.
In 33 we have 2 3’s. So we get 20 3’s from 1 to 100.
Note: for any numbers from 1 to 9 we’ll get 20 as answer.
Answer B
Answer: (B) 20
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 225 m
(C) 245 m
(D) 250 m
(E) 300 m
Rationale: Explanation:
Speed =45 X 5/18 m/sec =25/2 m/sec
Time = 30 sec.
Let the length of bridge be x metres.
Then,	130 + x	/30=25/2
2(130 + x) = 750
x = 245 m.
ANSWER IS C
Answer: (C) 245 m
Question: If 0.75: x :: 5:8, then x is equal to:
(A) 1.12
(B) 1.16
(C) 1.20
(D) 1.3
(E) None of these
Rationale: Explanation:
(x * 5) = (0.75 *8)
X=6/5 = 1.20
Answer: C
Answer: (C) 1.20
Question: Find the number of different prime factors of 25650
(A) 4
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: Explanation:
L.C.M of 25650 = 2 x 3 x 3 x 3 x 5 x 5 x 19
3, 2, 5,19
Number of different prime factors is 4.
Answer: Option A
Answer: (A) 4
Question: If y = x^2 + ux + v, y is minimum when x is:
(A) u/u
(B) -u/u
(C) -u/2
(D) -v/2
(E) v/u
Rationale: We're given the equation Y = X^2 + uX + v.
IF.. we use a simple Classic Quadratic....
u = 2
v = 1
Y = X^2 + 2X + 1
We can then go about finding the answer that yields the MINIMUM result when X = ...
Answer A: u/v = 2/1 = 2 --> 4+4+1 = +9
Answer B: -u/v = -2/1 = -2 --> 4-4+1 = +1
Answer C: -u/2 = -2/2 = -1 --> 1-2+1 = 0
Answer D: -v/2 = -1/2 -->(1/4)-1+1 = +1/4
Answer E: v/u = 1/2 --> (1/4)+1+1 = +2 1/4
From these results, we can see the minimum result:
C
Answer: (C) -u/2
Question: 164 pencils are distributed to children with the same number. What can’t be the range including the number of children?
(A) 1~10
(B) 10~20
(C) 50~60
(D) 20~30
(E) 70~80
Rationale: In 164=1*164=2*82=4*41=6*24, you can come up with 4 cases. Amongst these cases, what is not included is C. 50~60. Therefore, the answer is C.
Answer: (C) 50~60