mathewhe/aqua_rat huggingface dataset:
Question: A can do a work in 6 days. B can do the same work in 8 days. Both A&B together will finish the work and they got $1000 from that work. Find their shares?
(A) 600,800
(B) 500,500
(C) 300,700
(D) 800,200
(E) 550,450
Rationale: Ratio of their works A:B = 6:8
Ratio of their wages A:B = 3:4
A's share = (3/5)1000 = 600
B's share = (4/5)1000 = 800
correct option is A
Answer: (A) 600,800
Question: Randy'sbar serves customers every weeknight from 5 pm to 1 am. In Randy's bar,Silvermoonbeer is sold at a constant rate except during happy hour, from 6:30 to 9:30 pm, when the rate triples.
If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty?
(A) Monday, 7:30 pm
(B) Monday, 9 pm
(C) Monday, 7 pm
(D) Monday, 6:45 pm
(E) Monday, 9:30 pm
Rationale: Let the keg be a 150 Litre keg
At 5 pm.. There are 75 litres
At 6:30 pm there are 50 litres.
So, consumption rate is 25 litres per 1.5 hours.
So it will take 3 hours to finish 50 litres at this rate.
During happy hour it sells 3 times faster. So, rate = 1 hour per 50 litres.
So, keg becomes empty at 6:30 + 1 hour = 9:30 pm
Answer is E.
Answer: (E) Monday, 9:30 pm
Question: 196, 144, 100, 64, 36, ?
(A) 16
(B) 8
(C) 18
(D) 12
(E) 6
Rationale: Explanation :
The pattern is 14^2, 12^2, 10^2, 8^2, 6^2, ...
So next number is 4^2 = 16
Answer : Option A
Answer: (A) 16
Question: A person covered one-fourth of the total distance at 20 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
(A) 21 (1/8)
(B) 21 (1/7)
(C) 22 (6/7)
(D) 29 (1/7)
(E) 21 (4/3)
Rationale: Let the total distance be x km
total time taken = (x/4)/20 + (3x/4)/24 = 7x/160
Average speed = x/(7x/160) = 22 (6/7)kmph.
Answer: C
Answer: (C) 22 (6/7)
Question: The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 10800 sq. m, the cost of fencing the field @ 25 paise per metre is
(A) Rs. 55.50
(B) Rs. 67.50
(C) Rs. 86.50
(D) Rs. 105.00
(E) None of these
Rationale: Solution
Let length = (3x) metres and breadth = (4x) metres.
Then, 3x × 4x = 10800 ⇔ 12x2 = 10800 ⇔ x2 =900 ⇔ x = 30.
So, length = 90 m and breadth = 120 m.
Perimeter = [2(90 + 120)] m = 420 m.
∴ Cost of fencing = Rs. (0.25 × 420) = Rs. 105.00. Answer D
Answer: (D) Rs. 105.00
Question: Find the fourth proportion to 12,3,6
(A) 1.8
(B) 1.2
(C) 2.5
(D) 1.5
(E) 4
Rationale: Explanation:
12:3 :: 6:x
=> 12/3 = 6/x
=> x = 18/12
=> x = 3/2=1.5
Option D
Answer: (D) 1.5
Question: In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
(A) 8008
(B) 8000
(C) 8022
(D) 8021
(E) 8022
Rationale: x*110/100 * 90/100 = 7920
X*0.99=7920
X=7920/0.99
=> 8000
Answer:B
Answer: (B) 8000
Question: In Town X, 64 percent of the population are employed, and 49 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 20%
(C) 32%
(D) 40%
(E) 52%
Rationale: answer b
male-employed - 64%
female-employed-15%
Total employed 64%
means total unemployed = 36%
therefore d and e are not correct because female unemployed has to be less than 36%
female-unemployed = 32% male unemployed = 4%
48% + 4% = 52%
16% + 32% = 48%
plug in a and b in place of 32% and the sum is not 100%
15/64 =20 B
Answer: (B) 20%
Question: How many numbers can be formed with the digits 1, 6, 7, 8, 6, 1 so that the odd digits always occupy the odd places
(A) 15
(B) 12
(C) 18
(D) 20
(E) 22
Rationale: Solution
The digits are 1, 6, 7, 8, 7, 6, 1. In this seven-digit no.there are four odd places and three even places OEOEOEO. The four odd digits 1, 7, 7, 1 can be arranged in four odd places in [4!/2!×2] = 6 ways [as 1 and 7 are both occurring twice].
The even digits 6, 8, 6 can be arranged in three even places in 3!/2! = 3 ways.
Total no. of ways = 6 × 3 = 18
Answer C
Answer: (C) 18
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of C?
(A) 2250
(B) 3000
(C) 3018
(D) 3019
(E) 3012
Rationale: 60*5:36*6:75*3
100: 72: 75
75/247 * 7410 = 2250
Answer: A
Answer: (A) 2250
Question: A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many R acres were used for corn?
(A)  188
(B)  258
(C)  376
(D)  470
(E)  517
Rationale: consider 5x acres of land used for bean
consider 2x acres of land used for wheat
consider 4x acres of land used for corn
Total given is 1034 acres
11x =1034
x = 94
land used for corn R= 4 * 94 = 376
correct option - C
Answer: (C)  376
Question: 2, 4, 6, 8, 10, ?
(A) 10
(B) 14
(C) 16
(D) 12
(E) 24
Rationale: The sequence is a series of even numbers, 2, 4, 6, 8, 10, 12....
Answer : D.
Answer: (D) 12
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3% loss
(B) 100/3% loss
(C) 50/3% profit
(D) 100/3% loss
(E) 200/3% loss
Rationale: Explanation:
15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
ANSWER IS A
Answer: (A) 16 2/3% loss
Question: If it is 5:27 in the evening on a certain day, what time in the morning was it exactly 2,880,717 minutes earlier? (Assume standard time in one location.)
(A) 5:22
(B) 5:24
(C) 5:27
(D) 5:30
(E) 5:32
Rationale: 5:27minus 2,880,717in any way must end with 0, the only answer choice which ends with 0 is D.
Answer: D.
Answer: (D) 5:30
Question: If (1 – 1.25)N = 4, then N =
(A)  −400
(B)  −16
(C)  −4
(D)  4
(E)  400
Rationale: (1 – 1.25)N = 4
Simplify to get: -0.25N = 4
Rewrite as (-1/4)N = 4
Multiply both sides by -4 to get: N = -16
Answer: B
Answer: (B)  −16
Question: Three pieces of timber 24 m, 28 m and 36 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
(A) 7 m
(B) 4 m
(C) 42 m
(D) 63 m
(E) None of these
Rationale: Answer
Greatest possible length of each plank = H.C.F of 24, 28, 36 = 4 m
Correct Option: B
Answer: (B) 4 m
Question: Line Q has the equation 5y – 3x = 15. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.)
(A) 9
(B) 11
(C) 13
(D) 15
(E) 17
Rationale: 5y - 3x = 15 and so y = 3x/5 + 3
When x = 0, then y = 3.
When y = 0, then x = -5
The slope is 3/5, so the slope of line S is -5/3.
Through the point (-5, 0), 0 = -5(-5)/3 + c
The y-intercept is c = -25/3 < -8.
Thus the perpendicular line S can have y-intercepts from -8 up to 2.
The number of possible lines is 8 + 2 + 1 = 11
The answer is B.
Answer: (B) 11
Question: Today is Saturday. After 72 days, it will be:
(A) Sunday
(B) Saturday
(C) Monday
(D) Thursday
(E) Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 70 days, it will be Saturday.
After 72 days, it will be Monday.
Answer :C
Answer: (C) Monday
Question: In western Europe, G bicycles were sold in each of the years 1990 and 1993. The bicycle producers of Western Europe had a 42 percent share of this market in 1990 and a 33 percent share in 1993. Which of the following represents the decrease in the annual number of bicycles produced and sold in Western Europe from 1990 to 1993?
(A) 9% of (x/100)
(B) 14% of (x/100)
(C) 75% of (x/100)
(D) 9% of G
(E) 14% of x
Rationale: Moreover is't question actually asking the the difference between the {(Quantity Produced + Quantity Sold )G in 1990 - (Quantity Produced + Quantity Sold ) in 1993}
Though the Quantity sold in both the years is same it actually boils down to (Quantity Produced in 1990 ) in (Quantity Produced in 1993)=D
Answer: (D) 9% of G
Question: Rectangular Floors X and Y have equal area. If Floor X is 16 feet by 18 feet and Floor Y is 9 feet wide, what is the length of Floor Y, in feet?
(A)  13 1/2
(B)  18
(C)  18 3/4
(D)  21
(E)  32
Rationale: The area of a rectangle is: Area = length x width
We are given that floor X is 16 feet by 18 feet and that floor Y is 9 feet wide. So we can say:
length of X = 16
width of X = 18
width of Y = 9
length of Y = n
We also can say:
Area of Floor X = Area of Floor Y
(length of X)(width of X) = (length of Y)(width of Y)
(16)(18) = 9n
(16)(2) = n
32 = n
Answer E.
Answer: (E)  32
Question: When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
(A) 349
(B) 300
(C) 500
(D) 450
(E) 250
Rationale: x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q - 13p = 2
q =	2 + 13p/17
Least value of p which q = 2+13p/17 => 26
x= (13*26+11) = 349
ANSWER A
Answer: (A) 349
Question: Two pipes A and B can fill a tank in 4 and 12 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 12
(B) 3
(C) 6
(D) 9
(E) 10
Rationale: Part filled by A in 1 min. = 14
Part filled by B in 1 min. = 1/12
part filled by (A + B) in 1 min. = 1/4+ 1/12 = 1/3.
Both the pipes can fill the tank in 3 minutes.
Answer: B
Answer: (B) 3
Question: John can hit a target 3times in 6shots, Karan can hit the target 2 times in 6 shots & Ashwini can hit 4 times in 4 shots. What is the probability that at least 2 shots hit the target ?
(A) 1/3
(B) 2/5
(C) 2/3
(D) 3/5
(E) 3/7
Rationale: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Karan hits tha target and Raja not hit the target.
or
Karan does not hit the target and Raja hits the target.
or.
Karan hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3
C
Answer: (C) 2/3
Question: A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of w square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)
(A) (5,280 mt) / 12 w
(B) (5,280 pt) / 12m
(C) (5,280 pmt) /12
(D) (5,280)(12m) / pt
(E) (5,280)(12p) / mt
Rationale: Given that: 1 gallon of paint covers an area ofwsquare feet. Question:how many gallonsof paint will be needed ...
In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/w, so w must be in the denominator: eliminate all but A and D.
Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.
Answer: A.
Answer: (A) (5,280 mt) / 12 w
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 297
(B) 879
(C) 342
(D) 762
(E) 269
Rationale: 400*(90/100)*(95/100)
= 342
Answer: C
Answer: (C) 342
Question: The banker's discount on Rs.1250 due a certain time hence is Rs.125. Find the true discount and the banker's gain.
(A) 11
(B) 15
(C) 18
(D) 21
(E) None
Rationale: Solution
Sum	=B.D x T.D/ B.D - T.D
= B.D x T.D/ B.G
T.D / B. G	=Sum / B.D
= 1250 / 125
= 10 / 1
If B.D is Rs. 11,T.D= Rs.10.
If B.D is Rs.125,
T.D	= Rs.(10 / 11 x 125)
= Rs.114.
And, B.G	= Rs(125 - 114)
= Rs.11.
Answer A
Answer: (A) 11
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1200, find the loss %?
(A) 18
(B) 16
(C) 26
(D) 17
(E) 20
Rationale: Explanation:
1500 ---- 300
100 ---- ? => 20%
Answer:E
Answer: (E) 20
Question: Jancy decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Jancy s savings by the end of the year from these monthly savings were five times the amount she spent per month, what should be the fraction of her salary that she spent each month?
(A) 15/17
(B) 17/12
(C) 10/17
(D) 13/17
(E) 12/17
Rationale: Let Jancy's monthly savings = S
Jancy's monthly pay = P
Jancy's monthly expenditure = P-S
Jancy's savings by the end of the year from these monthly savings were Five times the amount she spent per month
12S = 5*(P-S)
=>12/5 S = P-S
=> P = 17/5 S
Jancy's monthly expenditure = P-S = 17/5S-S = 12/5S
fraction of her salary that Jancy spent each month = 12/5S / 17/5S=P-S/P = 12/17. Answer is E
Answer: (E) 12/17
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
(A) 287 cm2
(B) 887 cm2
(C) 384 cm2
(D) 268 cm2
(E) 668 cm2
Rationale: Area of a parallelogram = base * height
= 24 * 16
= 384 cm2
Answer: C
Answer: (C) 384 cm2
Question: A departmental store has 7 managers and 30 associates. The 7 managers have an average salary of $4200. The 30 associates have an average salary of $6,000. What is the average salary for the departmental store?
(A) $5659.46
(B) $5888.56
(C) $5200.26
(D) $5929.25
(E) $5126.98
Rationale: Number of managers is 7
Their average salary is $4200
Number of associates is 30
Their average salary is $6000
Total salary of managers is 7*4200=$29,400
Total salary of associates is 30*6000=$180,000
Total salary for the departmental store is 180,000+29,400=209400
Average salary for the departmental store is 209400/7+30=5659.46
Answer is A
Answer: (A) $5659.46
Question: If x > y and y > z, which of the following represents the greatest number Q?
(A)  x − z
(B)  x − y
(C)  y − x
(D)  z − y
(E)  z − x
Rationale: Because x>y>z
thus Q= x- z wil lbe greatest
Ans: A
Answer: (A)  x − z
Question: If W persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
(A) z
(B) x
(C) x/y
(D) z/x
(E) y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
W person can do z jobs in y days..
so W person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: (E) y/z
Question: The tax on a commodity is diminished by 17% and its consumption increased by 15%. The effect on revenue is?
(A) 2%
(B) 8%
(C) 4.5%
(D) 6.5%
(E) 1.5%
Rationale: 100 * 100 = 10000
83 * 115 = 9545
-----------
10000-----------455
100-----------? => 4.55% decrease
Answer: C
Answer: (C) 4.5%
Question: What is the sum Q of all 3 digit numbers that leave a remainder of '2' when divided by 3?
(A) 897
(B) 164,850
(C) 164,749
(D) 149,700
(E) 156,720
Rationale: The series is => 101+...998
Number of terms => 300
sum Q=> 300/2 * [101+998]
hence sum => 164850 i.e. option B
Answer: (B) 164,850
Question: Hari purchased 6 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)910
(B) B)1065
(C) C)1070
(D) D)1075
(E) E)1080
Rationale: Cost of 6 kg grapes = 70 × 6 = 420.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 420 + 490 = 910
A
Answer: (A) A)910
Question: 4, 12, 48, 240, 1440,10080,80640, 725760(...)
(A) 7257600
(B) 10080
(C) 6200
(D) 10020
(E) 12500
Rationale: Explanation :
Go on multiplying the given numbers by 3, 4, 5, 6, 7,8,9,10
Answer : Option A
Answer: (A) 7257600
Question: In a lottery, there are 12 prizes and 30 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/3
(B) 1/5
(C) 2/5
(D) 1/7
(E) 2/7
Rationale: P(winning a prize) = 12 / (12+30) = 12/42 = 2/7
The answer is E.
Answer: (E) 2/7
Question: From a group of 3 CATS and 3 DOGS, 4 animals are to be randomly selected. What is the probability that equal numbers of cats and dogs will be selected?
(A) 1/5
(B) 2/5
(C) 4/5
(D) 3/5
(E) 1
Rationale: Using the first example, here is the probability of THAT EXACT sequence occurring:
CCDD = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10
Each of the other 5 options will yield the exact SAME probability....
eg
CDCD = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10
So we have 6 different options that each produce a 1/10 chance of occurring.
6(1/10) = 6/10 = 3/5
Final Answer:
D
Answer: (D) 3/5
Question: In the Land of Oz only one or two-letter words are used. The local language has 68 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?
(A) 65
(B) 66
(C) 67
(D) 131
(E) 136
Rationale: The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...
The number of 1 letter words (X) that can be made from 68 letters is 68;
The number of 2 letter words (XX) that can be made from 68 letters is 68*68, since each X can take 68 values.
Total: 68+68*68.
Similarly:
The number of 1 letter words (X) that can be made from 67 letters is 67;
The number of 2 letter words (XX) that can be made from 67 letters is 67*67, since each X can take 67 values.
Total: 67+67*67.
The difference is (68+68*68)-(67+67*67)=136.
Answer: E.
Answer: (E) 136
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 3 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) s.4528
(B) s.4520
(C) s.4527
(D) s.4530
(E) s.2718
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)
= 906 sq.ft.
Total cost = 906 * 3
= Rs.2718
Answer:E
Answer: (E) s.2718
Question: HDFC bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?
(A) 1:5
(B) 625:3125
(C) 100:105
(D) 100^4:105^4
(E) 725:3225
Rationale: Hi Bunuel,
Here is my approach: is this correct?
HDFC bank offers an interest of 5% per annum compounded annually on all its deposits.
Interest earned in 4 year= 10000(1+0.05)^4
Interest earned in 5 year= 10000(1+0.05)^5
Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105
Hence Ans:C
Answer: (C) 100:105
Question: X, Y, and Z are consecutive numbers and X > Y > Z. Also, 2X + 3Y + 3Z = 5Y + 8. What is the value of Z?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.
2X + 3Y + 3Z = 5Y + 8
2Z+4+3Z+3+3Z = 5Z+5+8
3Z = 6
Z = 2
The answer is A.
Answer: (A) 2
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 248
(B) 289
(C) 240
(D) 242
(E) 229
Rationale: Speed = [54 * 5/18] m/sec
= 15 m/sec.
Length of the train
= (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36
= 15
x + 300 = 540
x = 240 m.
Answer: C
Answer: (C) 240
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 2287
(B) 27
(C) 299
(D) 287
(E) 150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m
Answer: E
Answer: (E) 150
Question: 2034 - (1002 / 20.04) = ?
(A) 2984
(B) 2983
(C) 2982
(D) 2981
(E) 1984
Rationale: 2034-50 =1984
Answer : E
Answer: (E) 1984
Question: George does 3/5th of a piece of work in 9 days. He then calls in Paul , and they finish the work in 4 days. How long would Paul take to do the work by himself?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: 100% work will be done by George in 15 days
(1/15)9+(1/15+1/x)4=1
solving this eqn.
we get x=30
hence Paul take to do the work in 30 days
ANSWER:A
Answer: (A) 30
Question: mr. depak has $419,774 in his bank account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among her six best friends?
Options:
(A) $1
(B) $2
(C) $3
(D) $4
(E) $6
Rationale: To find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends,
he needs to make the total divisible by 6
Simply add the individual digits of the total = 4+1+9+7+7+4 = 32
If you add 4 , the number is divisible by 6 (32+ 4)
Correct Option : D
Answer: (D) $4
Question: If y exceeds x by 20%, then x is less than y by?
(A) 16%
(B) 16 1/3 %
(C) 16 2/3 %
(D) 16 3/5 %
(E) 16 4/5 %
Rationale: Explanation:
X=100	y=120
120------20
100-------? => 16 2/3%
ANSWER IS C
Answer: (C) 16 2/3 %
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) 5409
(B) 54087
(C) 5400
(D) 546
(E) 5401
Rationale: 100x + 400 = 12(x – 5)
x = 50
100 * 50 + 400 = 5400
Answer: C
Answer: (C) 5400
Question: Three grades of milk are 1 percent, 3 percent and 2 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
(A) y + 3z
(B) (y +z) / 4
(C) 2y + 3z
(D) 3y + z
(E) 3y + 4.5z
Rationale: Soln:
The resulting equation is
=> (.01x + .03y + .02z)/(x+y+z) = 1.5/100
=> x + 3y +2z = 1.5x + 1.5y + 1.5z
taking x to one side and y and z to other side we get
=> x = 3y + z
Ans is D
Answer: (D) 3y + z
Question: Mrs. Rodger got a weekly raise of $165. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $ 165.
(B) $ 146
(C) $ 147
(D) $ 148
(E) None
Rationale: Solution:
Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 165.
So after completing the 1st week she will get $ (x+165).
Similarly after completing the 2nd week she will get $ (x + 165) + $ 165.
= $ (x + 165 + 165)
= $ (x + 330)
So in this way end of every week her salary will increase by $ 165.
Answer A
Answer: (A) $ 165.
Question: C individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?
(A) dx / C
(B) x / (C-d)
(C) d / (C-dx)
(D) x / (C(C-d))
(E) dx / (C(C-d))
Rationale: Number of individuals = C
Amount paid by each individual = n
Total expected amount = Charity's goal = nC = x
n = x/C
Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dx/C --> Additional amount
Number of individuals who are paying = C - d
Additional amount has to be divided among the (C - d) individuals --> dx/C(C - d)
Answer: E
Answer: (E) dx / (C(C-d))
Question: A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 49
(B) 50
(C) 12
(D) 13
(E) 77
Rationale: Speed of the train relative to man = (200/10) m/sec = (20) m/sec. [(20) * (18/5)] km/hr = 72 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 72 ==> x = 77 km/hr.
Answer: Option E
Answer: (E) 77