mathewhe/aqua_rat huggingface dataset:
Question: At Joes Steakhouse the hourly wage for a chef is 22% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $8.50 per hour, how much less than a manager does a chef earn each hour?
(A) $1.40
(B) $2.40
(C) $3.315
(D) $4.40
(E) $5.40
Rationale: Manager wages per hour = $8.50
Dishwasher wages per hour = half of manager's wages. = 1/2($8.50) ==> $4.25
Chef wages per hour = 22% greater than Dishwasher wages
--> 22% of $4.25 = (22*($4.25)) /100
--> ($93.5)/100
--> $0.935
Therefore,
Chef wages per hour = $4.25 + $0.935 ==> $5.185
Difference of wages between manager and chef = $8.50 - $5.185 ==> $3.315
ANSWER:C
Answer: (C) $3.315
Question: An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1400 sculptures are not on display, how many pieces of art does the gallery have?
(A) 360
(B) 3150
(C) 540
(D) 640
(E) 720
Rationale: Too many words and redundant info there.
(i) 1/3 of the pieces of art are displayed, hence2/3 of the pieces of art are NOT displayed.
(ii) 1/6 of the pieces on display are sculptures, hence 5/6 of the pieces on display are paintings.
(iii) 1/3 of the pieces NOT on display are paintings, hence2/3 of the pieces NOT on display are sculptures.
1400 sculptures are not on display, so according to (iii) 2/3*{not on display} = 1400 --> {not on display} = 2100.
According to (i) 2/3*{total} = 2100 --> {total} = 3150.
Answer: B.
Answer: (B) 3150
Question: If x and y are positive odd integers, then which of the following must also be an odd integer? I. x^(y+2) II. x(y+4) III. (y+1)^(x-1) + 1
(A) I only
(B) II only
(C) III only
(D) I,III only
(E) All options are applicable
Rationale: let x= 5, y= 3
I. 5^5 = > Odd
II. 5*7 = > Odd
III. 4^4 +1 = > Odd
Answer : E
Answer: (E) All options are applicable
Question: Among a group of 2500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from 2500 people, what is the probability that the person selected will be one who invests in municipal bonds but not in oil stocks
(A) 7/29
(B) 7/25
(C) 7/23
(D) 7/22
(E) 7/21
Rationale: Ans: Here 2500 does not require.
From the diagram we know that only ones who invested in municipal bonds are 28%, the probability is 28 / 100
= 7/25
Answer:B
Answer: (B) 7/25
Question: The overall age of X and Y is 15 year greater than the overall age of Y and Z. Z is how many decades younger that X?
(A) 11
(B) 15
(C) 12
(D) 17
(E) 19
Rationale: B
15
(X + Y) â€“ (Y + Z) = 15
X â€“ Z = 15
Answer: (B) 15
Question: In a party attended by 11 persons, each clinch their glass with every other. How many glass clinches?
(A) 51
(B) 52
(C) 53
(D) 54
(E) 55
Rationale: Total no. of person = 11
Total no. of glass clinches = n(n-1)/2
=11*10/2
= 55
ANSWER:E
Answer: (E) 55
Question: The 280 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT
(A)  4
(B)  20
(C)  30
(D)  40
(E)  70
Rationale: Obviously the number of rows must be a factor of 280. The only option which is not a factor of 280 is C (30).
Answer: C.
Answer: (C)  30
Question: How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
(A) 62
(B) 72
(C) 55
(D) 82
(E) 62
Rationale: Explanation:
T = (660 + 165)/54 * 18/5
T = 55
Answer: Option C
Answer: (C) 55
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 177 m
(B) 189 m
(C) 120 m
(D) 178 m
(E) 188 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Answer: (C) 120 m
Question: A lawn has equally distributed grass. It takes 24 days to 70 cows and 60 days to 30 cows to eat the whole of grass. How many cows will be needed to eat the grass in 96 days.
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: g - grass at the beginning
r - rate at which grass grows, per day
y - rate at which one cow eats grass, per day
n - no of cows to eat the grass in 96 days
g + 24*r = 70 * 24 * y
g + 60*r = 30 * 60 * y
g + 96*r = n * 96 * y
Solving, n = 20.
ANSWER:A
Answer: (A) 20
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) 25
(B) 22
(C) 36
(D) 12
(E) 26
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: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2:5
(B) 2:8
(C) 2:1
(D) 2:4
(E) 2:2
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer:A
Answer: (A) 2:5
Question: A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be ?
(A) 8 days
(B) 10 days
(C) 18 days
(D) 28 days
(E) 30 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.
A)
Answer: (A) 8 days
Question: The citizens of planet nigiet are 5 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 5) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings? Express result in terms of base 10.
(A) 54
(B) 64
(C) 75
(D) 85
(E) 100
Rationale: no of 3s b/w 1-99 is 20,100-199 is 20 and so on. so leavn d range b/w 300-399 total no of 3s is(9*20=)180. no of 3s b/w 300-399 is(20+100=)120.
total no of 3s b/w 1-1000=120+180=300
in base 10 300=3*5^2=75.
ANSWER:C
Answer: (C) 75
Question: If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/t, which of the following statements could be false?
(A) n is a factor of both a and b
(B) (a*b)/n < ab
(C) ab is multiple of 2.
(D) (a*b)/n is a multiple of 2.
(E) t is a multiple of 4.
Rationale: If we divide bynand get a multiple ofaand ofb, then t must be a common factor. Answer A must be true.
Ifaandbare even integers, dividing by a factor (also an integer) results in something smaller than the productab. Answer B must be true.
If eitheraorbis even, thenabmust be even. Answer C must be true.
If both are even, the smallest either number can be is 2. Thus, the smallest common factor must be 2. Answer D must be true.
Ifbis 6 andais 2,nwould be 6, which is not 4. E can be false.
Answer: (E) t is a multiple of 4.
Question: If s, t, and p are positive numbers such that (s/(s+t))(10) + (t/(s+t))(20)=p and if s<t which of the following could be the value of p?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 30
Rationale: The answer is D. For any positive s and t, p is a number between 10 and 20. Since s < t, weight of 10 is inferior of weight of 20 -> p is > 15 -> 18 is the answer.
Answer: (D) 18
Question: From a well shuffled deck of cards, what would be the probability that you would draw a two or a spade?
(A) 4 in 12
(B) 4 in 10
(C) 4 in 13
(D) 4 in 8
(E) 4 in 16
Rationale: P(C)+P(2)-P(Cn2)
P(Cu2)=13/52 + 4/52 - 1/52 = 4/13
Answer: (C) 4 in 13
Question: What is the minimum percentage increase in the mean of set S {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A)  25%
(B)  50%
(C)  75%
(D)  100%
(E)  200%
Rationale: Mean of S is (-4-1+0+6+9)/5=2;
In order the increase to be minimal we should replace two smallest elements of S, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.
Percent increase=(4-2)/2*100=100%.
Answer: D.
Answer: (D)  100%
Question: In measuring the sides of a rectangle, one side is taken 5% in excess, and the other 4% in deficit. Find the error percent in the area calculated from these measurements.
(A) 0.11%
(B) 0.7%
(C) 0.4%
(D) 0.6%
(E) 0.8%
Rationale: Let x and y be the sides of the rectangle. Then, Correct area = xy.
Calculated area = (105/100) x (96/100) y = (504/500 )(xy)
Error In measurement = (504/500)xy- xy = (4/500)xy
Error percentage = [(4/500)xy (1/xy)100] % = (4/5) % = 0.8%.
Answer is E.
Answer: (E) 0.8%
Question: Of the goose eggs laid at a certain pond, 1/2 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
(A) 800
(B) 840
(C) 880
(D) 920
(E) 960
Rationale: Let x be the number of eggs that were laid.
(2/5)(3/4)(1/2)x = 120
(6/40)x = 120
x = 800
The answer is A.
Answer: (A) 800
Question: In a fuel station the service costs $2.10 per vehicle and every liter of fuel costs $0.60. Assuming that you fill up 3 mini-vans and 2 trucks, what will be the total cost, if a mini-van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty?
(A) $287.50
(B) $290.40
(C) $293.30
(D) $296.20
(E) $299.10
Rationale: The service cost of 3 vans and 2 trucks is 5*2.10 $10.50
The fuel in 3 vans is 3*65 = 195 liters
The fuel in 2 trucks is 2*65*2.2 = 286 liters
The total fuel (vans + trucks) = 481 liters
The total fuel cost is 481*0.6 = $288.60
The total cost is $288.60 + $10.50 = $299.10
The answer is E.
Answer: (E) $299.10
Question: If x + (1/x) = 5, what is the value Q of x^2 + (1/x)^2?
(A) Q=21
(B) Q=22
(C) Q=23
(D) 24
(E) 27
Rationale: Squaring on both sides,
x^2 + (1 /x)^2 + 2(x)(1/x) = 5^2
x^2 + (1 /x)^2 = 23
Answer: C
Answer: (C) Q=23
Question: For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 25 true?
(A) 1
(B) 3
(C) 5
(D) 2
(E) 9
Rationale: Answer D
(a+b)(a-b)=25
5cases For (a+b), (a-b)
25, 1
5, 5
Answer D
Answer: (D) 2
Question: Find a 8 digit number that if multiplied by the number 9 or any of its multiplications products (18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.
(A) 12435687
(B) 12345679
(C) 10000000
(D) 99999999
(E) 11111111
Rationale: B
The number is: 12345679
12345679 * 9 = 111111111
12345679 * 18 = 222222222
12345679 * 27 = 333333333
Answer: (B) 12345679
Question: 25 people went to a hotel for combine dinner party 15 of them spent Rs. 5 each on their dinner and rest spent 4 more than the average expenditure of all the 25. What was the total money spent by them.
(A) 1628.4
(B) 1534
(C) 1492
(D) 158.25
(E) None of these
Rationale: Solution: Let average expenditure of 25 people be x.
then,
25x = 15*5+10*(x+4);
Or, 25x = 15*5+10x+20;
Or, x = 6.33;
So, total money spent = 6.33*25 = Rs. 158.25.
Answer: Option D
Answer: (D) 158.25
Question: In how many ways can the letters of the word CODD be arranged?
(A) 15
(B) 16
(C) 12
(D) 13
(E) 10
Rationale: CODD has 4 words, but d is repeated two times. Thus ways = 4! / 2! = 12 ways
C
Answer: (C) 12
Question: {1/(5-√24)}^2 =
(A) a. 16+16√15
(B) b. 31- 10√15
(C) c. 49 - 10√24
(D) d. 32- 4√15
(E) e. 32 + 4√15
Rationale: 1 / (25 - 10 root24 + 24)
= 1 / (49 - 10 root24)
Multiply numeratordenominator by (49 + 10 root24)
= (49 - 10root24)
Answer = C
Answer: (C) c. 49 - 10√24
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 90 m
(B) 100 m
(C) 120 m
(D) 140 m
(E) 150 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
ANSWER:C
Answer: (C) 120 m
Question: A pump can fill a tank with water in 8 hours. Because of a leak, it took 9 hours to fill the tank. The leak can drain all the water in ?
(A) 15hr 10min
(B) 16hr 20min
(C) 17hr 30min
(D) 72hr
(E) 14hr 25min
Rationale: Work done by the leak in 1 hour = 1/8 - 1/9 = 1/72
Leak will empty the tank in 72 hrs =
Answer is D
Answer: (D) 72hr
Question: Of the integers between 200 and 799, inclusive, how many do not have digit 2 and 5?
(A)  316
(B)  256
(C)  410
(D)  426
(E)  520
Rationale: Options for the first digit 6-2(2 and 5)=4;
Options for the second digit 10-2=8;
Options for the third digit 10-2=8;
Total numbers possible 4*8*8=256.
Answer: B.
Answer: (B)  256
Question: In a class of 50 students, 20 play Rugby, 15 play Cricket and 11 play Football. 7 play both Rugby and Cricket, 4 play Cricket and Football and 5 play Rugby and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
(A) 46
(B) 667
(C) 45
(D) 24
(E) 10
Rationale: Notice that7 play both Rugby and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Rugby/Football.
[color=#ffff00]{Total}={Rugby}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more checkADVANCED OVERLAPPING SETS PROBLEMS
[/color]
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Rugby and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Rugby and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
Answer: E.
Answer: (E) 10
Question: A fill pipe can fill 2/5 of cistern in 30 minutes in how many minutes, it can fill 4/5 of the cistern?
(A) 48 min
(B) 63 min
(C) 25 min
(D) 30 min
(E) 60 min
Rationale: 2/5 of the cistern can fill in 30 min
4/5 of the cistern can fill in = 30*5/2*4/5= 60min
Answer is E
Answer: (E) 60 min
Question: Find the ones digit of 73^355
(A) 3
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: The units digit of 73^355 will be the same as the units digit of 3^355.
3^1=3 --> the units digit is 3;
3^2=9 --> the units digit is 9;
3^3=27 --> the units digit is 7;
3^4=81 --> the units digit is 1;
3^5=243 --> the units digit is 3 AGAIN;
...
So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 355=352+3=(multiple of 4)+2, then the units digit of 3^355 will be the third number in the pattern thus 7.
Answer: D.
Answer: (D) 7
Question: The ratio of radius of a circle and the side of a square is 2 : 5. Find the ratio of their areas:
(A) 2 : 1
(B) 4 : 25
(C) 8 : 77
(D) 4 : 121
(E) None
Rationale: radius/side = 2/5
â‡’ area of circle/area of square= 4/25
Answer: B
Answer: (B) 4 : 25
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
(A) 7 months
(B) 10 months
(C) 9 months
(D) 11 months
(E) 13 months
Rationale: 7*5: 5*x = 7:10
x = 10
ANSWER:B
Answer: (B) 10 months
Question: A can do a job in 15days and B in 20days. If they work on it together for 3 days, then the fraction of the work that is left is?
(A) 2/15
(B) 8/15
(C) 13/20
(D) 1/12
(E) 6/13
Rationale: A's 1 day work = 1/15
B's 1day work = 1/20
A+B 1day work = 1/15 + 1/20 = 7/60
A+B 3days work = 7/60*3 = 7/20
Remaining work = 1 - 7/20 = 13/20
Answer is C
Answer: (C) 13/20
Question: In a certain company, a third of the workers do not have a retirement plan.60% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
(A) 80
(B) 95
(C) 180
(D) 120
(E) 210
Rationale: Set up equation:
x = total number of workers
120 = 0,4 * 2/3 * x + 0,4* 1/3 * x
120 = 12/30 x
x = 300
300 - 120 = 180
Answer C
Answer: (C) 180
Question: There are two concentric circles with radii 8 and 4. If the radius of the outer circle is increased by 25% and the radius of the inner circle decreased by 25%, by what percent does the area between the circles increase?
(A) 75
(B) 80
(C) 85
(D) 90
(E) 95
Rationale: The area of a circle is piR^2, where R is the radius.
The area of the big circle is 64pi.
The area of the small circle is 16pi.
The area A1 between the circles is 48pi.
When the big circle's radius increases, the new area is 100pi.
When the small circle's radius decreases, the new area is 9pi.
The area A2 between the circles is 91pi.
The ratio of A2/A1 is 91/48 = 1.9 which is an increase of 90%.
The answer is D.
Answer: (D) 90
Question: You and your friend spent a total of $15 for lunch. Your friend spent $1 more than you. How much did your friend spend on their lunch?
(A) $9
(B) $8
(C) $4
(D) $6
(E) $5
Rationale: My lunch = l, my friends lunch = l+1
(l)+(l+1)=15
l+l+1-1=15-1
2l=14
l=7
My friends lunch l+1 = 7+1=$8, the answer is B
Answer: (B) $8
Question: There is a 100 pound watermelon laying out in the sun. 99 percent of the watermelon's weight is water. After laying out for a few hours 98 percent of the watermelon's weight is water.
How much water evaporated?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 10
Rationale: In the beginning it is 99 pounds water and 1 pound other stuff. At the end the 1 pound other stuff is 2 percent so the total weight is 50 pounds. 50 pounds - 1 pound other stuff = 49 pounds water. So 99 pounds - 49 pounds = 50 pounds water lost.
Answer: (D) 50
Question: 5 identical snow plows can clear an iced parking lot in 4 hours. How long would it take 6 such snow plows to clear the same parking lot?
(A) 3 hour, 10 minutes
(B) 2 hours, 30 minutes
(C) 3 hours
(D) 7 hours, 30 minutes
(E) 10 hourss
Rationale: 6/5 as many plows will take 5/6 as many hours --> 4*5/6=10/3 hours =3 hours, 10 minutes.
Answer: A.
Answer: (A) 3 hour, 10 minutes
Question: In a class of 210 students, 70 did not opt for math. 55 did not opt for science and 42 did not opt for either. How many students of the class opted for both math and science?
(A) 123
(B) 125
(C) 127
(D) 137
(E) 148
Rationale: 210 students total
70 did not opt for math
55 did not opt for science
42 did not opt for either
Total of 140 students in math and 13 did not opt for sci but did for math
140-13=127
127 students of the class opted for both math and science
Answer:C
Answer: (C) 127
Question: A boy is playing with a wheel of 16 inches diameter rotating at x inches/min. Another boy is playing with a wheel of 32 inches diameter moving at the rate of y inches/min. Fin the value of x in terms of y if both the wheels cover the distance at same time.
(A) 2y/4
(B) 3y/7
(C) 4y/8
(D) 2y/10
(E) 1y/2
Rationale: t=S1/V1=S2/V2
or 16/x=32/y
or x=16y/32=y/2
Answer is E
Answer: (E) 1y/2
Question: A departmental store charges the commission of 15 percent on the first sale of items worth $50,000 and then an additional 10 percent on any sale price that exceeds the initial $50,000. If the department store earned $26,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?
(A)  $235,000
(B)  $365,000
(C)  $115,000
(D)  $240,000
(E)  $160,000
Rationale: 26,000 = 0.15 *(50000) + 0.10 (x - 50000)
26000 - 7500 = 0.10 (x-50000)
185000 = x - 50000
x = 2,35,000
Answer : A
Answer: (A)  $235,000
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4 pumps work in order to empty the tank in 1 day?
(A) 10
(B) 12
(C) 8
(D) 15
(E) 18
Rationale: Explanation:
Let the required hours needed be x
More pumps, less hours (Indirect proportion)
More Days, less hours (Indirect proportion)
Hence we can write as
(pumps)3:4
(days) 2:1}: : x : 8
⇒3×2×8=4×1 × x
⇒3×2×2= x
⇒x=12
Answer: Option B
Answer: (B) 12
Question: A set of numbers has the property that for any number t in the set,t+4 is in the set. If -3 is in the set, which of the following must also be in the set? I. 9 II. 2 III. 4
(A) II,III only
(B) I only
(C) I,III only
(D) II only
(E) III only
Rationale: question is asking for must be there elements.
According to the question if t is there t+4 must be there.
if -3 is the starting element the sequence is as follows.
S ={-3,1,5,9....}
if -3 is not the starting element the sequence is as follows
S = {...-7,-3,1,5,9...}
By observing the above two sequences we can say that 9 must be there in set S.
Answer : B
Answer: (B) I only
Question: If k > 0, x + 2k = y, and y + 4k = z, what is the ratio between z - x and y - x ?
(A) 1 to 4
(B) 1 to 2
(C) 2 to 1
(D) 3 to 1
(E) 4 to 1
Rationale: y-x = 2k
z-y = 4k
Let's add the two equations together:
z-x = 6k
The ratio of z-x to y-x is 6:2 = 3:1.
The answer is D.
Answer: (D) 3 to 1
Question: When a=4+(3/4) and b=4-(3/4), (2^a^2)/(2^b^2)=?
(A) 496
(B) 486
(C) 4096
(D) 456
(E) 426
Rationale: --> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=6/4 and a+b=8, 2^(a-b)(a+b)=2^(6/4)(8)=2^12=4096
Therefore, the answer is C
Answer: (C) 4096
Question: What is the remainder when you divide 2^200+2 by 7?
(A) 1
(B) 2
(C) 3
(D) 6
(E) 5
Rationale: answer is D. this is very similar to the 32^32^32+2 divided by 7 question.
Answer: (D) 6
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
(A) 4:5
(B) 4:2
(C) 4:3
(D) 4:9
(E) 4:1
Rationale: 12:9
= 4:3
Answer:C
Answer: (C) 4:3
Question: In a group of pigs and hens, the number of legs are 22 more than twice the number of heads. The number of pigs is
(A) 5
(B) 7
(C) 10
(D) 12
(E) 11
Rationale: Explanation:
Let the number of pigs be x and the number of hens be y.
Then, 4x + 2y = 2 (x + y) + 22
4x + 2y = 2x + 2y + 22
2x = 22
x = 11
Answer: E
Answer: (E) 11
Question: Laura can paint 1/x of a certain room in 20 minutes. What fraction Q of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
(A) 1/(3x)
(B) 3x/(x-3)
(C) (x – 3)/(3x)
(D) x/(x-3)
(E) (x-3)/x
Rationale: Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete Q=120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6
Answer (C)
Answer: (C) (x – 3)/(3x)
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.2120?
(A) Rs.1000.15
(B) Rs.1100.95
(C) Rs.1892.85
(D) Rs.1050.85
(E) Rs.1200.25
Rationale: 2120 = P [1 + (5*12/5)/100]
P= 1892.85
ANSWER:C
Answer: (C) Rs.1892.85
Question: The diagonal of a rhombus are 65 m and 60 m. Its area is:
(A) 1940
(B) 1950
(C) 1960
(D) 1990
(E) 1980
Rationale: Area of the rhombus = 1/2 d1d2 = ( 1/2 × 65 × 60 ) Cm(power)2
= 65 × 30 = 1950 Cm(power)2
Answer is B.
Answer: (B) 1950
Question: If 7a = 8b and ab ≠0, what is the ratio of a/8 to b/7?
(A) 16/14
(B) 8/7
(C) 1
(D) 7/8
(E) 64/49
Rationale: A nice fast approach is the first find a pair of numbers that satisfy the given equation: 7a = 8b
Here's one pair: a =8 and b =7
What is the ratio of a/8 to b/7?
In other words, what is the value of (a/8)/(b/7)?
Plug in values to get: (a/8)/(b/7) = (8/8)/(7/7)
= 1/1
= 1
C
Answer: (C) 1
Question: There are 35 students in a hostel. If the no. of students increases by 4, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) s. 99.75
(B) s. 89.75
(C) s. 72.75
(D) s. 58.75
(E) s. 49.75
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 4) = x – 1
or, 35x + 42 = 39x – 39
or, x = 20.25
Thus the original expenditure of the mess = 35 x 20.25=708.75
Therefore x-1 = 19.25
hence 42 x 19.25 = 808.50
808.50 - 708.75 = Rs. 99.75
A
Answer: (A) s. 99.75