mathewhe/aqua_rat huggingface dataset:
Question: A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?
(A) 189/13 days
(B) 188/13 days
(C) 180/13 days
(D) 180/17 days
(E) 280/13 days
Rationale: One day work of A and B = 1/12
One day work of B and C = 1/30
One day work of C and A = 1/36
2(A + B + C) = 1/12 + 1/30 + 1/36
2(A + B + C) = 13/90
(A + B + C) = 13/180
Number of days required = 180/13 days.
Answer:C
Answer: (C) 180/13 days
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
(A) 11
(B) 27
(C) 36
(D) 99
(E) 27
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: C
Answer: (C) 36
Question: If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 (512)
(A) 3.876
(B) 2.967
(C) 2.87
(D) 3.912
(E) 1.9
Rationale: log5 (512)
=	log (512)/log 5
=	log 2^9/log (10/2)
=	9 log 2/(log 10 - log 2)
=	(9 x 0.3010)/(1 - 0.3010)
=	2.709/0.699
=	2709/699
= 3.876
Answer is A.
Answer: (A) 3.876
Question: A man rows his boat 75 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 1 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 7 kmph
Rationale: Speed downstream = d/t = 75/(2 1/2) = 30 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (30 - 18)/2 = 6 kmph
Answer:B
Answer: (B) 6 kmph
Question: Find the L.C.M of 72,108,2100
(A) 37800
(B) 45836
(C) 52416
(D) 25874
(E) 36985
Rationale: 72=2^3*3^2 108=3^3*2^2 2100=2^2*5^2*3*7
L.C.M=2^3*3^2*5^2*7=37800
Answer=(A)
Answer: (A) 37800
Question: 1.5, 2.3, 3.1, 3.9, ..?
(A) 0.6
(B) 0.8
(C) 0.4
(D) 0.24
(E) 0.15
Rationale: 1.5+0.8=2.3
2.3+0.8=3.1
3.1+0.8=3.9
3.9+0.8=4.7
ANSWER:B
Answer: (B) 0.8
Question: The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Amount = (30000 + 4347) = Rs. 34347
Let the time be n years. Then,
30000(1 + 7/100)n = 34347
= (107/100)n = 34347/30000 = (107/100)2
n = 2 years.
Answer: A
Answer: (A) 2
Question: Pipes A and B can fill a tank in 11 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in
(A) 1 13/17 hours
(B) 2 8/11 hours
(C) 3 9/17 hours
(D) 5 17/23 hours
(E) None
Rationale: Solution
Net part filled in 1 hour	= (1/11 + 1/6 -1/12)
= 23/132.
Therefore, the tank will be full in 132/23 hrs.	â€¹=â€º 5 17/23 hrs.
Answer D
Answer: (D) 5 17/23 hours
Question: Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 9 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If one minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?
(A) 12
(B) 24
(C) 48
(D) 60
(E) 72
Rationale: the difference of the speed is 4m per second so in one minute Sacha will be 240 m ahead of Bruno..
Bruno will cover this in 240/5=48 secs..
C
Answer: (C) 48
Question: a man brought some watermelons to town and sold them. he sold 1/2 more than 1/2 of what he brought and he was left with one melon. how many melons did he bring to town?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: He sold 1/2 more than 1/2 of what he brought
thus he sold (1/2)+(x/2) and he was left with 1 water melon
so equation will be (1/2)+(x/2)+1 = x
or x/2 = 3/2 so x = 3
ANSWER:C
Answer: (C) 3
Question: At what rate percent on simple interest will a sum of money double itself in 20 years?
(A) 5%
(B) 3 1/9%
(C) 3 9/3%
(D) 3 2/3%
(E) 3 6/3%
Rationale: P = (P*20*R)/100
R = 5%
Answer: A
Answer: (A) 5%
Question: 287 x 287 + 269 x 269 - 2 x 287 x 269 = ?
(A) 534
(B) 446
(C) 354
(D) 324
(E) None of them
Rationale: =a^2+b^2-2ab
where a=287 and b=269
=(a-b)^2 = (287-269)^2
=(18)^2
=324
Answer is D
Answer: (D) 324
Question: Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 240 pounds of the seed mixture?
(A) 6
(B) 12
(C) 20
(D) 24
(E) 120
Rationale: Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 240 pounds of the seed mixture?
Amount of timothy needed for one acre is 2 pounds.
So the amount of grass seed needed for one acre is
= 2 (100/5) = 40 pounds
So the no.of acres that can be planted with 240 pounds is
= 240/40 = 6
The answer is A.
Answer: (A) 6
Question: A,B,C can complete a piece of work in 18,6,12 days. Working together, they complete the same work in how many days?
(A) 2
(B) 4/5
(C) 7/9
(D) 36/11
(E) 24/7
Rationale: A+B+C 1day work = 1/18 + 1/6 + 1/12 = 11/36
A,B,C together will complete the job in 36/11 days
Answer is D
Answer: (D) 36/11
Question: The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member?
(A) 23
(B) 27
(C) 40
(D) 28
(E) 271
Rationale: Explanation:
Let the average of all 10 members 4 years ago was x. After 4 years, 10 members age increases by 10 × 4 = 40. But there is no change in the average as a person is replaced by an younger one. Which means, the younger one age is 40 years less than the old one.
Answer: C
Answer: (C) 40
Question: In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 3 and a y-intercept of -3. If the two lines intersect at the point (a,b), what is the sum a+b?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The equation of Line A is y = -x + 1
The equation of Line B is y = 3x - 3
3x - 3 = -x + 1
x = 1
y = 0
The point of intersection is (1,0) and then a+b = 1.
The answer is B.
Answer: (B) 1
Question: From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 40 percent. What percent of the stockâ€™s 2007 starting price was the price of the stock at the end of 2009?
(A) 80
(B) 126
(C) 95
(D) 100
(E) 108
Rationale: Assume a value at the beginning of 2007. As this is a % question, assume P=100.
At the end of 2007 it becmae = 1.2*100=120
At the end of 2008 it decreased by 25% = 120*.75 = 90
At the end of 2009 it increased by 40% = 90*1.2 = 126
Thus ratio = 126/100 = 1.26 (in % terms = 126%). Thus B is the correct answer.
Answer: (B) 126
Question: Analyze the number square carefully and find out what number fits in place of question mark.
1	2	3
4	5 6
7	8	?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: 20 fits in place of question mark.
This is because (number in first column) / (number in second column) * 8 = number in third column.
Here (left number / middle number) * 8 = right number
(7 / 8) * 8 = (7 / 1) = 7
A
Answer: (A) 7
Question: A river boat leaves Silver Town and travels upstream to Gold Town at an average speed of 3 kilometers per hour. It returns by the same route at an average speed of 7 kilometers per hour. What is the average speed for the round-trip in kilometers per hour?
(A) 4.2
(B) 7.1
(C) 7.2
(D) 7.5
(E) 8.0
Rationale: Pick a number which is LCM of 7 and 3 = 21.
Upstream time = 21/3 =7 hrs
Downstream time = 21/7 = 3 hrs
Total time = 10 hrs
Total distance = 42
Average Speed = 42/10 = 4.2 km/hr
Answer: (A) 4.2
Question: A began business with 12000 and is joined afterwards by B with 48000. When did B join, if the profits at the end of the year are divided equally?
(A) 8 months
(B) 3 months
(C) 10 months
(D) 7 months
(E) None of these
Rationale: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 12000 : (12 – x) × 48000
or 12 : 4(12 – x)
Since profit is equally divided so
12 = 4(12 – x) or x = 3. Thus B joined after 8 months.
Answer B
Answer: (B) 3 months
Question: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $300. Find the original price of petrol?
(A) $11
(B) $5
(C) $45
(D) $400
(E) $6.6
Rationale: Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 300/45=$6.6
Answer: E.
Answer: (E) $6.6
Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?
(A) 87
(B) 16
(C) 10
(D) 76
(E) 17
Rationale: Average after 11 innings = 36
Required number of runs
= (36 * 11) - (32 * 10) = 396 - 320
= 76.
Answer: D
Answer: (D) 76
Question: (422 + 404)2 − (4 × 422 × 404) = ?
(A) None of these
(B) 342
(C) 324
(D) 312
(E) Cannot be determined
Rationale: Explanation :
Given Equation is in the form (a + b)2 − 4ab where a = 422 and b = 404
Hence answer = (a + b)2 − 4ab = (a − b)2 =(422 − 404)2 = 182 = 324, Answer : Option C
Answer: (C) 324
Question: A chair is bought for Rs.600/- and sold at a loss of 40% find its selling price
(A) s.360/-
(B) s.550/-
(C) s.560/-
(D) s.590/-
(E) s.580/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
60 % ------> 540 (60 * 6 = 360)
Selling price = Rs.360/-
A)
Answer: (A) s.360/-
Question: A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 m?
(A) 120 sec
(B) 99 sec
(C) 89 sec
(D) 80 sec
(E) 85 sec
Rationale: Explanation:
v = 240/24 (where v is the speed of the train) = 10 m/s
t = (240+650)/10 = 89 seconds
Answer: Option C
Answer: (C) 89 sec
Question: A and B together can do a work In 4 days. A alone can do it in 20 days.what time B will take to do the work alone?
(A) 6 days
(B) 8 days
(C) 12 days
(D) 10 days
(E) 5 days
Rationale: Explanation:
A and B 1day's work = 1/4
A alone can do 1day's work = 1/20
what time B will take to do the work alone?
B = (A+B) - A = (1/4) - (1/20) = 5 Days
Answer: Option E
Answer: (E) 5 days
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 7 kmph
(B) 9 kmph
(C) 4 kmph
(D) 8 kmph
(E) 2 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2
= 8 kmph
Answer:D
Answer: (D) 8 kmph
Question: There are 4 couples. If they will sit 8 chairs in a row such that each couple sits side by side, how many possible cases are there?
(A) 120
(B) 384
(C) 1,200
(D) 2,460
(E) 3,840
Rationale: Tie the couples. Then we have 4 persons that have to be arranged in 4 places. 4! ways.
Now the couples can change position with each other. 2! ways.
4! * (2!)^4 = 24 *16 = 384
Answer is B.
5! * 2! = 240 ways.
Answer: (B) 384
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
(A) 1/2
(B) 2/5
(C) 8/15
(D) 9/20
(E) 9/15
Rationale: Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) =	n(E)/n(S)	=	9/20	.
Answer :D
Answer: (D) 9/20
Question: A boy has to cover a total distance of 300 kms. in 6 hours. He travels at the rate of 60 kmph. for first 90 minutes and next 100 kms. at the rate of 50 kmph. At what average speed must he travel now in order to complete the journey in 6 hours?
(A) 24 kmph
(B) 84 kmph
(C) 48 kmph
(D) 44 kmph
(E) 14 kmph
Rationale: Explanation:
The boy travels 60 kmph for 90 min, this means he travels 90 km.
Next 100 km at the rate of 50 kmph, this means he travels 100 km.
Total distance traveled till now = 100 + 90 = 190 km
Time spent = 1.5 + 2 = 3.5 hr
Required speed = Remaining distance/ Time
= (300 – 190) /(6 – 3.5)
= 110/ 2.5 = 44 kmph\
ANSWER: D
Answer: (D) 44 kmph
Question: How many seconds will a 600 meter 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) 700
(B) 288
(C) 500
(D) 277
(E) 121
Rationale: Let length of tunnel is x meter
Distance = 600+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
600+x = (65/3) * 60
600+x = 20 * 65 = 1300
x = 1300 - 600 = 700 meters
Answer: A
Answer: (A) 700
Question: How many bricks, each measuring 25 cm x 11 cm x 6 cm, will be needed to build a wall of 8 m x 1 m x 5 cm?
(A) 5600
(B) 6000
(C) 242
(D) 7200
(E) 8600
Rationale: Number of bricks =Volume of the wall/Volume of 1 brick =	(800 x 100 x 5)/(25 x 11 x 6) = 242.
Answer: Option C
Answer: (C) 242
Question: If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability E that their product will be of the form of x^2-(by)^2, where b is an integer?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) E=1/6
Rationale: Only (X+y)(x-y) pair will give the form x^2-(by)^2
The probability of selecting these two pairs are 1/4 * 1/3 = 1/12, assuming x+y is picked first, then x-y, but x-y can be picked first followed by x+y. So the probability E= 1/12 * 2 = 1/6
Ans E
Answer: (E) E=1/6
Question: A certain sum of money doubles itself in 7 years in how much many years will it trible itself at the same rate?
(A) 20 years
(B) 14 years
(C) 88 years
(D) 44 years
(E) 11 years
Rationale: 100 ---- 100 --- 7
100 --- 7
--------------------
300 ---- 14 years
Answer: B
Answer: (B) 14 years
Question: How much time will it take for an amount of 450 to yield 81 as interest at 4.5% per annum of simple interest?
(A) 3.5 years
(B) 4 years
(C) 4.5 years
(D) 5 years
(E) None
Rationale: Explanation: Time = (100 x 81)/(450 x 4.5) years = 4 years.
Answer: Option B
Answer: (B) 4 years
Question: K and L start a business jointly. L invests Rs.16000 for 8 months and L remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B ?
(A) 12,812
(B) 12,820
(C) 12,800
(D) 12,120
(E) 12,811
Rationale: 16x8 : Px4 = 5:2
P = 12.8 => Rs.12,800
Answer: C
Answer: (C) 12,800
Question: A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?
(A) 400
(B) 267
(C) 288
(D) 278
(E) 309
Rationale: 2000 ---- 50
2000 ---- 40
x ----- 50
x*50 = 2000*40
x=1600
2000
-------
400
Answer: A
Answer: (A) 400
Question: At a particular pizza shop, a pizza can be created from any combination of 8 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?
(A) 6
(B) 35
(C) 120
(D) 450
(E) 1200
Rationale: Number of possible ways to select 1 type of spice = 8c1 = 8
Number of possible ways to select 2 types of cheese = 4c2 = 6
Number of possible ways to select 4 types of meat but without pepperoni and anchovies together
= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together
= 7c4 - 5c2
=35 - 10
=25
Possible ways to garnish the pizza are available to the customer = 8*6 * 25
=1200
Answer E
Answer: (E) 1200
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 250
(B) 327
(C) 367
(D) 289
(E) 281
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer:A
Answer: (A) 250
Question: If the sum of 5 consecutive integers is 125, what is sum of the 5 consecutive integers preceding the former sequence?
(A) 35
(B) 25
(C) 100
(D) 105
(E) 103
Rationale: 1) least of each will have a difference of 5 and next least too will have a difference of 5 and so on...
Therefore all 5 terms will have a term LESS by 5..
Sum = 125-(5*5) = 100
2.) if sum is 125, the average = median = 125/5 = 25. The median of previous 5 will be 25-5 = 20.
And sum would be 20*5 = 100
Answer: C
Answer: (C) 100
Question: What is the range of all the roots of |x^2 - 4| = x ?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: we get 2 quadratic equations here ..
1) x^2-x-4=0 ....... roots 2 , -1
2) x^2+x-4=0 ........ roots -2, 1
Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations .
So value of x for given equation .... x=4 or x=1
I guess range is 4-1 =3
B
Answer: (B) 3
Question: (X+1) is an even number and (Y+1 )is a positive odd number. Which of the following expressions cannot be ODD?
(A) (Y+1)
(B) (Y+1)^2
(C) (X+1) (Y+1)
(D) (Y+1)^3
(E) (Y+1)^4
Rationale: (X+1) (Y+1) WILL BE EVEN
C
Answer: (C) (X+1) (Y+1)
Question: In the quadrilateral PQRS d=6 cm, h1=5 cm and
h2=2.5 cm. Find the area
(A) 21
(B) 22.5
(C) 23
(D) 24
(E) 25
Rationale: area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)
so 1/2*6*(5+2.5)=22.5
ANSWER:B
Answer: (B) 22.5
Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
(A) 229
(B) 108
(C) 278
(D) 126
(E) 112
Rationale: S = 180/6 * 18/5 = 108 kmph
Answer: B
Answer: (B) 108
Question: Richard's company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 30 hrs and a machine of type S does the same job in 15 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) 3
(B) 4
(C) 5
(D) 9
(E) 12
Rationale: Rate of machine R =1/30
Rate of machine S =1/15
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/30 +x/15 =1/2
3x/30=1/2
x=30/6=5
So no of machine R is 5
Answer C
Answer: (C) 5
Question: What is the sixth digit to the right of the decimal point, in the decimal expansion of (3/5)^6?
(A)  2
(B)  4
(C)  6
(D)  8
(E)  0
Rationale: Step 1 Convert fraction to decimal with two decimal places 3/5 = 0.60 then convert to scientific number = 6*10^-1
Step 2 Multiply 6^6 by 10^-6
Step 3 6 has the sequence 6, 36, 216
Answer is C
Answer: (C)  6
Question: There is a five digit code consist of letters and digit. the code can have one digit from 1,2,3 and any four letters from A,b,c,d,e. first and last code must be a letter and all letters can be repeated. How many combinations can be possible?
(A) 625
(B) 3840
(C) 5625
(D) 11520
(E) 12520
Rationale: since repetitions are allowed so there are 5 ways to choose the letters for the first slot, and five ways to choose for last slot
that can be like:- 5 x _ x _ x _ x 5
you still have to choose 1 digit and 2 letters between. For the letters, again, repetitions are allowed so each slot can be filled in 5 ways. For digit, it can only be filled in 3 ways. However, since the digit can be in any one of the 3 middle slots, so we multiply by 3 again:
5 x 3 x 5 x 5 x 5 or
5 x 5 x 3 x 5 x 5 or
5 x 5 x 5 x 3 x 5
so 5 x 5 x 5 x 5 x 3 x 3 = 5^4 x 3^2 = 5625.
ANSWER:C
Answer: (C) 5625
Question: Two trains 140 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 17.9 sec
(B) 11.88 sec
(C) 27.7 sec
(D) 10.8 sec
(E) 17.8 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 190 = 330 m.
Required time = 330 * 9/250 = 11.88 sec.
Answer: B
Answer: (B) 11.88 sec
Question: The average age of an adult class is 40 years. 12 new students with an avg age of 32 years join the class. Therefore decreasing the average by 6 year. Find what was the original average age of the class?
(A) 10
(B) 12
(C) 16
(D) 20
(E) 4
Rationale: Let original strength = y
Then , 40y + 12 x 32 = ( y + 12) x 34
â‡’ 40y + 384 = 34y + 408
â‡’ 6y = 24
âˆ´ y = 4
E
Answer: (E) 4
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $38. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) 180xy
(B) 180/(xy)
(C) 20xy
(D) 342/(xy)
(E) xy/180
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 38 / (xy/9) = 342/(xy).
The answer is D.
Answer: (D) 342/(xy)
Question: A store sells a certain product at a fixed price per unit. At the product's current price, f units cost a total of exactly $300. If the price were lowered by $5 from its current value, then f + 2n units would cost exactly $300; if the price were raised by $5, then f – n units would cost exactly $300. What is the value of f?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: It got too complicated when I used algebra. Using plugging in, it was quite fast.
Price Quantity total value
p f pf = 300
p-5 f+2n (p-5)(f+2n) = 300
p+5 f-n (p+5)(f-n) = 300
Solving three equations for three unknowns. Tough!!
Plugging in, I always start with C. C was the answer here, so saved calculation!
Putting values in above equations:
Price Quantity total value
15 20 300
10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5
20 15 300
So f = 20 satisfies all equations!!
Answer: (C) 20
Question: A toy train started on a 12-feet loop trail at a rate of 4 feet per minute. One minute afterwards, a toy scooter from the same starting point on the loop trail at 6 feet per minute. What is the shortest time that the scooter would take on the trail in order to catch up with the train?
(A) 4 minutes
(B) 3 minutes
(C) 2 minutes
(D) 1 minutes
(E) 0.8 minutes
Rationale: we don't need to assume here the direction.we need to find which will take less time
so there are 2 cases
1)both moving in same direction...then time would be 2 minutes
2)both moving in opp direction then time would be 0.8 minutes
as we need the shortest time it would be the second case
Answer:E
Answer: (E) 0.8 minutes
Question: If x-y=8, which of the following must be true?
I. If x is positive, y must be positive
II. If x is negative, y must be negative
III. Both x and y are positive
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: The best way to approach such questions is to plug in values for x and y
Given: x-y=8
III. Both x and y are positive:
Let x=10 and y=2
x-y=8
But,
Let x=6 and y=-2
x-y=8
Therefore, NOT TRUE
III. If x is positive, y must be positive
Let x=10 and y=2
x-y=8
But,
Let x = 6 and y=-2
x-y=8
Therefore, NOT TRUE
II. If x is negative, y must be negative
If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!
Therefore, TRUE
Ans: 'B'
Answer: (B) II only
Question: A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 17% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ?
(A) 1/3
(B) 2/3
(C) 2/5
(D) 3/5
(E) 4/5
Rationale: Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.
Let x ml be the amount removed ---> total alcohol left = 4-0.4x
New quantity of whiskey added = x ml out of which 0.19 is the alcohol.
Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml.
Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/5.
Hence, C is the correct answer.
Answer: (C) 2/5
Question: Find the number which when multiplied by 15 is increased by 196
(A) 10
(B) 12
(C) 14
(D) 16
(E) 17
Rationale: Explanation:
Let the number be x.
Then, 15x = x + 196
=› 14 x= 196
=› x = 14.
Answer: Option C
Answer: (C) 14
Question: The sum of two numbers is 75 and their difference is 20. Find the difference of their squares.
(A) 1400
(B) 1500
(C) 1600
(D) 1700
(E) 1800
Rationale: Solution:
If the sum of two numbers is x and their difference is y, then the difference of their squares is xy.
Here x= 75 and y = 20
75 × 20 = 1500
Answer B
Answer: (B) 1500