mathewhe/aqua_rat huggingface dataset:
Question: Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Monday, what was the expected day when both the brothers were to return home and when did Rohit Return?
(A) Wednesday, Sunday
(B) Tuesday, Monday
(C) Thursday, Monday
(D) Monday, Friday
(E) none
Rationale: Rajat returned on Monday -i.e. 3 days earlier
so actual day to return home is Thursday.
Rohit returned after days so Monday
ANSWER:C
Answer: (C) Thursday, Monday
Question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 35
(B) 20
(C) 47
(D) 36
(E) 30
Rationale: 1: 2/5 = 5: 2
2/7 * 70 =20
Answer:B
Answer: (B) 20
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?
(A) 1,20,000
(B) 1,10,000
(C) 1,00,000
(D) 90,000
(E) 80,000
Rationale: X * (105/100) * (105/100) * (105/100) = 138915
X = 138915/1.157625
X = 120000
ANSWER:A
Answer: (A) 1,20,000
Question: In a petting zoo, there are 50 hens, there are 40 goats, and 10 llamas with some humans. If the total number of feet are 210 more than the number of heads in the zoo, the number of humans is
(A) 1
(B) 5
(C) 10
(D) 15
(E) 20
Rationale: Explanation: Let number of humans be x. Then, Total number of feet = 2 x 50 + 4 x 40 + 4 x 10 + 2x = 2x + 300 Total number of heads = 50 + 40 + 10 + x= 100 + x. Therefore (2x + 300) = (100 + x) + 210 or x = 10. Answer: C
Answer: (C) 10
Question: A train 520 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 88 Kmph
(B) 94 Kmph
(C) 72 Kmph
(D) 16 Kmph
(E) 18 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 520/20
S = 26 M/Sec
Speed= 26*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 94 Kmph
Answer: B
Answer: (B) 94 Kmph
Question: A batsman in his 17th innings makes a score of 85, and thereby increases his average by 3. What is his average after the 17th innings? He had never been ’not out’.
(A) 47
(B) 37
(C) 39
(D) 43
(E) 42
Rationale: Average score before 17th innings
= 85 - 3 × 17= 34
Average score after 17th innings
=> 34 + 3 = 37
ANSWER:B
Answer: (B) 37
Question: What is the units digit of 17^83 × 13^82 × 11^83?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: To find : the units digit of 17^83 × 13^82 × 11^87
Let's reduce the clutter and simplify the product
(7^83) (3^82) (1^87)
7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4th power
so 7^5 has the same last digit as 7^1, 7^9, 7^13
Thus , 7^83 has the same last digit as 7^3, 7^7, 7^11 i.e.3
3 has a cyclicity of 4 : exactly the same routine as above
Thus , 3^82 has the same last digit as 3^2, 3^6, 3^10 i.e.9
Any power of 1 will result in1as the last digit
So, product of our last digits = 3 x 9 x 1 = 27....last digit is 5
Correct Option : B
Answer: (B) 5
Question: You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 2 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Solution
Start with 11 coins.
Sharon takes 2 coins from you: 11 - 2 = 9 coins.
Steven takes 4 coins from you: 9 - 4 = 5 coins.
So you have 5 at the end.
Correct answer : D
Answer: (D) 5
Question: A train 420 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 15
(B) 16
(C) 17
(D) 20
(E) 24
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 420 * 2/35 = 24 sec
Answer: Option E
Answer: (E) 24
Question: Today is Monday. After 61 days, it will be
(A) Sunday
(B) Saturday
(C) Monday
(D) Thursday
(E) Wednesday
Rationale: 61 days = 8 weeks 5 days = 5 odd days
Hence if today is Monday, After 61 days, it will be = (Monday + 5 odd days)
= Saturday
Answer is B
Answer: (B) Saturday
Question: Jonathan can type a 10 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?
(A) 5 minutes
(B) 10 minutes
(C) 15 minutes
(D) 18 minutes
(E) 20 minutes
Rationale: You may set up common equation like this:
job/A+job/B+job/C=job/x
Memorize this universal formula, you will need it definitely for GMAT.
and find x from this equation
In this specific case, the equation will look like this:
10/40+10/30+10/24=10/x
If you solve this equation, you get the same answer B (10)
Answer: (B) 10 minutes
Question: How many different three-digit multiples of 5 can be composed of digits 2, 7, 4, and 5 if none of the digits is repeated?
(A) 3
(B) 6
(C) 10
(D) 12
(E) 18
Rationale: = 3c2 x 2 = 6
can you explain your method. i solved it differently
XYZ, where Z must be 5. therefore 1 variation of digit in Z.
Y can be any of the 3 possible choices.
X can be any of the 2 possible choices.
2+3+1= 6
B
Answer: (B) 6
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) 482
(B) 337
(C) 277
(D) 288
(E) 2781
Rationale: 20000(11/10)4 - 20000(6/5)2 = 482
Answer: A
Answer: (A) 482
Question: The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
(A) Rs.608
(B) Rs.6076
(C) Rs.600
(D) Rs.602
(E) Rs.601
Rationale: T.D. = B.G. x 100 = Rs. 24 x 100 = Rs. 120.
Rate x Time	10 x 2
P.W. =	100 x T.D.	= Rs. 100 x 120 = Rs. 600.
Rate x Time	10 x 2
Answer:C
Answer: (C) Rs.600
Question: two friends deepak and rajeev have agreed to meet at a definite spot on a particular day between 9pm and 10pm. the first person to come waits for some time and leaves.If the other one does not turn up by that time.If Deepak comes first,he waits for 45minutes and if Rajeev comes first,he waits for 15minutes.What is the probability of meeting between Deepak and rajeev if their arrival times are independent of eachother and each person arrives during the indicated period at random?
(A) 3/4
(B) 11/16
(C) 7/8
(D) 3/16
(E) 5/16
Rationale: deepak : 45/60 = 3/4
rajeev : 15/60= 1/4
as these are independent events
total probability = (3/4)*(1/4)
= 3/16
ANSWER:D
Answer: (D) 3/16
Question: 45% of x is greater than 1/3rd of x by 110.what is x?
(A) 100
(B) 200
(C) 300
(D) 350
(E) 943
Rationale: 45x/100-x/3=110
7x/60=110
x=943
ANSWER:E
Answer: (E) 943
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
(A) 160
(B) 175
(C) 180
(D) 195
(E) None
Rationale: EXPLANATION
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 – 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer B
Answer: (B) 175
Question: if x - y = -10,2x + 3y = 15what is the value of y?
(A) 8
(B) 6
(C) 7
(D) 6.5
(E) 5
Rationale: solution
Rearranged I--> y = x + 10
Substituted into II---> 2x + 3(x + 10) = 15
we get x = -3
Solve for Y: 2(-3) + 3(y) = 15
y = 7
Answer is C
Answer: (C) 7
Question: What percent is 3% of 5%?
(A) 60%
(B) 50%
(C) 75%
(D) 45%
(E) 30%
Rationale: Required percentage = 3%/5% * 100 = 3/5 * 100 = 60%
Answer is A
Answer: (A) 60%
Question: A train covers a certain distance at a speed of 240kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of
(A) 720km/hr
(B) 620km/hr
(C) 650km/hr
(D) 750km/hr
(E) 850km/hr
Rationale: Explanation:
Distance = 240×5 = 1200km
Required speed = (1200× 3/5) = 720km/hr
Answer: Option A
Answer: (A) 720km/hr
Question: Mohan purchased 15 kgs of rice at the rate of Rs.20 per kg and 8 kgs of pulses at the rate of Rs.20 per kg. Whaat is the total amount that he paid to the shopkeeper?
(A) A)Rs.598
(B) B)Rs.594
(C) C)Rs.460
(D) D)Rs.595
(E) None of these
Rationale: Explanation:
Price of 15 kgs of rice at Rs.20/kg = 15x20 = Rs.300
Price of 8 kgs of pulses at Rs.20/kg = 8x20 = Rs.160
Therefore, Total amount = Rs.300+Rs.160 = Rs.460
Answer: Option C
Answer: (C) C)Rs.460
Question: Two men can complete a piece of work in four days. Two women can complete the same work in eight days. Four boys can complete the same work in five days. If four men, eight women and 20 boys work together in how many days can the work be completed?
(A) 1/2 day
(B) 1/7 day
(C) 3/2 day
(D) 1/4 day
(E) 7/2 day
Rationale: Two men take four days to complete the work four men would take (2 * 4)/4 = 2 days to complete it.
Similarly four women would take two days to complete it and 20 children would take one day to complete it.
All the three groups working togerther will complete 1/2 + 1/2 + 1/1 work in a day
= 2 times the unit work in a day.
They will take 1/2 a day to complete it working together.
Answer:A
Answer: (A) 1/2 day
Question: A car ferry can hold up to 60 tons of cargo. What is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average (arithmetic mean) weight of 0.75 tons and half of the vehicles are trucks with an average (arithmetic mean) weight of 4 tons?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: The weight of one car and one truck is 4.75 tons.
60/4.75 = 12 plus a remainder
The ferry could carry 12 cars and 12 trucks for a total of 24 vehicles.
The answer is D.
Answer: (D) 24
Question: There are n cities. What is the number of airlines that connected 7 different cities (airline from city A to city B is different with airline from city B to city A)?
(A) n(n-1)
(B) n(n+1)
(C) n(n-1)/2
(D) n(n-6)
(E) n2
Rationale: First of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-6). Hence, the answer is n(n-6), which makes A an answer choice.
D
Answer: (D) n(n-6)
Question: X, Y, and Z are different prime numbers. The product X^2*Y*Z is divisible by how many different positive numbers?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 12
Rationale: The exponents of X^2*Y*Z are 2, 1, and 1.
The number of factors is (2+1)(1+1)(1+1) = 12
The answer is E.
Answer: (E) 12
Question: Of the p students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?
(A)  p + w- x- y
(B)  p - w- x- y
(C)  p- w - x + y
(D)  w + x + y- z
(E)  w - x - y - z
Rationale: {Total} = {French} + {German} - {Both} + {Neither}
p = x + y - w + {Neither}
{Neither} = p + w - x - y.
Answer: A.
Answer: (A)  p + w- x- y
Question: Ravi and Kavi start a business by investing â‚¹ 4000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year.
(A) 2 : 28
(B) 5 : 28
(C) 7 : 18
(D) 1 : 18
(E) 3 : 18
Rationale: Ratio of profit = Ratio of investments
= 4000 : 72000 = 1 : 18
Answer : D
Answer: (D) 1 : 18
Question: Shruti purchased several number of three articles P, Q and R in the proportion 3 : 2 : 3. If the unit costs of the articles P, Q and R are 200, Rs. 90 and Rs. 60 respectively, how many articles of Q must have been purchased in the total purchases of Rs. 4800?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Explanation:
Let the number of articles of types P, Q and R be 3a, 2a and 3a respectively.
Thus, we get,
(200 x 3a) + (90 x 2a) + (60 x 3a) = 4800
960a = 4800
a = 5
Hence, the number of articles of type “Q” = 2x5 = 10
ANSWER B
Answer: (B) 10
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 588 as interest at the end of the loan period, what was the rate of interest?
(A) 7
(B) 6
(C) 18
(D) 24
(E) None of these
Rationale: Let rate = R% and time = R years.
Then, (1200 x R x R)/100 = 588
12R2 = 588
R2 = 49
R = 7.
Answer: Option A
Answer: (A) 7
Question: A normal six-sided die bearing the numbers 1, 2, 3, 4, 5, and 6 is thrown until the running
total surpasses 6. What is the most likely total that will be obtained?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: The total before the last throw could be any number between one and six. The last
throw will also be a number between one and six but with equal probability. Seven is the only
final total that can come from each of these possibilities. Therefore seven is the most likely
final total.
correct answer A
Answer: (A) 7
Question: Mike earns $12per hour and Phil earns $6 per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?
(A) 50%
(B) 32.5%
(C) 37%
(D) 37.5%
(E) 40%
Rationale: What % less of 12 is 6
let it be x % less ,then
=12(1-x/100)=6
1-x/100=6/12
x=100/2
x=50%
Ans A
Answer: (A) 50%
Question: A man can row 4.2 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?
(A) 1.9
(B) 1.7
(C) 1.4
(D) 1.5
(E) 1.1
Rationale: Speed of boat in still water (b) = 4.2 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.4 km/hr.
Answer: C
Answer: (C) 1.4
Question: A candidate scoring 25% in an examination fails by 30 marks , while another candidate scores 50 % mark, gets 20 marks more than the minimum pass marks . Find the minimum pass marks. Find the minimum pass percentage.
(A) 40
(B) 50
(C) 60
(D) 25
(E) 30
Rationale: x/4+30 = x/2-20
maximum marks = 200
min pass marks = 200/4+30 = 80
=>80/200*100=40%
ANSWER A
Answer: (A) 40
Question: If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss.
(A) $35
(B) $43
(C) $50
(D) $65
(E) $72
Rationale: Cost of 20 lollipops = $90
Sold each lollipop for $2
So he sold 20 lollipops for $(20 × 2) = $40
Loss = $(90 – 40) = $50
Therefore, loss = $ 50.
Answer: (C) $50
Question: Michelle has $80 to buy a new outfit. She found a skirt for $20, a blouse
for $25, and a belt for $8. How much does she have left to buy shoes?
(A) $27 left.
(B) $37 left.
(C) $47 left.
(D) $57 left.
(E) $67 left.
Rationale: 80 – 20 – 25 – 8 = 27
She has $27 left.
correct answer A
Answer: (A) $27 left.
Question: A container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water. What is the ratio of alcohol to water in the resulting solution?
(A) 2:5
(B) 3:7
(C) 3: 5
(D) 4:7
(E) 7:3
Rationale: Container 1 has 12 ounces in the ratio 1:2
or,
x+2x=12 gives x(alcohol)=4 and remaining water =8
container 2 has 8 ounces in the ratio 1:3
or,
x+3x=8 gives x(alcohol)=2 and remaining water =6
mixing both we have alcohol=4+2 and water =8+6
ratio thus alcohol/water =6/14=3/7
ANSWER:B
Answer: (B) 3:7
Question: The ratio of men to women in a class is 4 to 3. If 2 men and 7 woman drop out of the class and the ratio of men to women after the drop out is 2 to 1, then how many men are currently in the class?
(A) 22
(B) 20
(C) 18
(D) 19
(E) 24
Rationale: Equation on the basis of question
4x-2/3x-7=2/1
x=6
Original number of men = 4*6=24
Original Number of Women = 3*6=18
Current number of men = 24-2=22 (Answer)
Current number of women = 18-7=11
Ratio = 22/11= 2/1 ( Just to verify)
Ans A
Answer: (A) 22
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 35% but the selling price
remains constant, approximately what percentage of the selling price is the profit
(A) 68%
(B) 80%
(C) 90%
(D) 100%
(E) None of above
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 135% of Rs. 100 = Rs. 135
New S.P. = Rs. 420.
Profit = Rs. (420 - 135) = Rs. 285
Required percentage = (285/420) * 100
= 68%(approx)
Answer: A
Answer: (A) 68%
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) 3989
(B) 2772
(C) 2500
(D) 2888
(E) 1551
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500
Answer: C
Answer: (C) 2500
Question: A factory produced 2300 TV sets in its first year of production. 4500 sets were produced in its second year and 500 more sets were produced in its third year than in its second year. How many TV sets were produced in three years?
(A) 11,800
(B) 15,900
(C) 13,250
(D) 17,900
(E) 20,000
Rationale: 500 TV sets were produced in the third year than in the second year. The number of sets produced in the third year is equal to
4,500 + 500 = 5,000
The number of TV sets produced in three years is equal to sum of the number of TV sets produced in each year
2,300 + 4,500 + 5,000 = 11,800
correct answer A
Answer: (A) 11,800
Question: How many terms are in the G.P. 3, 6, 12, 24, ......., 384 ?
(A) 8
(B) 9
(C) 67
(D) 5
(E) 2
Rationale: Explanation:
Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, t = 384 => a * r^(n-1) = 384
=> 3 * 2^(n-1) = 384 => 2^(n-1) = 128 = 2^(7)
=> n-1 = 7 => n = 8.
Answer: A) 8
Answer: (A) 8
Question: A Baker decides to make a cake of 5 layers, one of strawberry, chocolate, butterscoch, vanila and pista. Baker decides not to put the layers of butterscoch and vanila next to each other as they both are white in colour. How many different type of such cakes can he make?
(A) 5! - (4!×2!)
(B) 4! - (6!×2!)
(C) 3! - (2!×4!)
(D) 4! - (4!×2!)
(E) 5! × (4!×3!)
Rationale: We can find the answer by substracting the number of arrangements in which V and B comes together from the total number of arrangements of 5 layers. Arrangements in which V and B comes next to each other: We can consider V and B as a single object having 2! Variations(VB and BV). VB, S, C, P can be arranged in 4! Ways. In total there are 4!×2! Ways of arranging 5 layers with B and V layers coming next to each other. Required answer = A. 5! - (4!×2!)
Answer: (A) 5! - (4!×2!)
Question: Two trains start from a certain place on two parallel tracks in the same directions. The speed of the trains are 45km/hr. and 40km/hr. respectively. The distance between the two trains after 45 minutes will be
(A) 2 km 500 m
(B) 2 km 750 m
(C) 3 km 750 m
(D) 3 km 250 m
(E) None of these
Rationale: Explanation:
In one hour the distance between the trains is 5 km.
In 45 mins = ¾ hour the distance would be equal to ¾ X 50
= 3.75 Km = 3 Km 750 m.
Answer D
Answer: (D) 3 km 250 m
Question: Given that R is between 0 and 1, which of the following expressions has the greatest possible value?
(A) (R-2)^4
(B) (R+14)
(C) (R+99)^(1/2)
(D) (R+1)/(R-1)
(E) (R-2)/(R-1)
Rationale: Two of these expressions include division by a term that includes R. In both cases, the value of the denominator can be made arbitrarily close to zero, making the magnitude of the expression increase without bound. However, (R+1)/(R-1) will always have a positive numerator and negative denominator, so the expression will always be negative. (R+1)/(R-1) will always have a negative numerator and negative denominator, so the value will be positive. Therefore the answer is E.
Answer: (E) (R-2)/(R-1)
Question: 550, 620, 589, 100, 560, 50, 100
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list?
(A) 200
(B) 310
(C) 480
(D) 550
(E) 570
Rationale: Yes, it can be solved with observation even without approximation in 30 sec.
Just observe given numbers: 50,100 ,100,550, 560, 580,620,
Median is very easy to tell - its 550. Now we want a number lower than 550 and greater than mean. How many numbers are lower than 550? DE are already out.
Now, we have 200, 310 and 480 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 480. (Notice, if 200 is more than mean then 480 is also. If 31 is more than mean, 480 is also. )
Hence C it is!
Answer: (C) 480
Question: A rectangle having length 89 cm and width 34 cm. If the length of the rectangle is increased by eighty percent then how much percent the breadth should be decreased so as to maintain the same area.
(A) 25%
(B) 33.33%
(C) 47.33%
(D) 75%
(E) None of these
Rationale: Explanation :
Solution: (80/(89+80) * 100)% = 47.33%
Answer : C
Answer: (C) 47.33%
Question: In a game of 80 points. A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60?
(A) 9 points
(B) 6 points
(C) 8 points
(D) 10 points
(E) 11 points
Rationale: A can give B 5 points :- A / B = 80 / 75
A can give C 15 points :- A / C = 80/ 65
B can give C a points of ( B / A ) * ( A / C)
(75 / 80) * ( 80 / 65)
(75 / 65) = 15/13
As we have to find in a game of 60 , so multiply numerator and denominator with 4 such that the ratio becomes 60/52
therefore B can give C of (60-52) = 8 points
ANSWER:C
Answer: (C) 8 points
Question: In a jar there are 20 white balls, 24 green balls and 30 blue balls. How many balls must be taken out in order to make sure we have 21 balls of the same color?
(A) a)	23
(B) b)	46
(C) c)	57
(D) d)	60
(E) e)	67
Rationale: Here, we need to find minimum number of marbles to be taken out to get 21 marbles of same color.
For a instance, if we take 19 white marbles 1st and followed by 20 Green and then 20 Blue.
Total will be 19 + 20+ 20= 59 draws.
If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 21.
So Minimum we need to take 59+1 = 60 Times to get 21 marbles of same color(either Green or Blue).
Answer : D.
Answer: (D) d)	60
Question: A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 65 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?
(A)  16
(B)  20
(C)  32
(D)  40
(E)  48
Rationale: lets say x ounces of P is mixed with Q.
=> 65-x ounces of Q is present in the mixture (as the total = 65 ounces)
given total almond weight = 15 ounces
(20x/100)+(25/100)(65-x) = 15
=> x = 25
=> 65-25 = 40 ounces of Q is present in the mixture.
Answer is D.
Answer: (D)  40
Question: Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is
(A) 290/289
(B) 1/289
(C) 290/90
(D) 290/19
(E) None of these
Rationale: Explanation:
If the numbers are a, b, then ab = 17,
as 17 is a prime number, so a = 1, b = 17.
1/a2+1/b2=1/1(2)+1/17(2)
=290/289
Option A
Answer: (A) 290/289
Question: Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 10% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be
(A) 9% less than N
(B) 25% less than N
(C) equal to N
(D) 20% greater than N
(E) 25% greater than
Rationale: Correct answer is (A).
This year, the price of a tree is price1=P/N.
If this price increases by 10% it becomes price2=P/N*1.10
Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.10) i.e. N/1.1 i.e. .91%
Answer: (A) 9% less than N
Question: If 4x=6y=z, what is x+y, in terms of z?
(A) z/2
(B) 5z/12
(C) z/3
(D) 3z/5
(E) z/9
Rationale: 4x=6y=z
x = z/4
and y = z/6
x+y = z/4 + z/6 = 5z/12
Answer is B
Answer: (B) 5z/12
Question: By walking at 3/4th of his usual speed, a man reaches office 15 minutes later than usual. What is his usual time?
(A) 45min
(B) 50min
(C) 65min
(D) 60min
(E) 70min
Rationale: let T be the usual time.
time spent=4T/3
therefore, 4T/3=T+15
4T=3T+45..therefor T=45min
ANSWER:A
Answer: (A) 45min
Question: the sides of a triangle are in the ratio 37.if the perimeter is 60 cms, the longest side is
(A) 7
(B) 30
(C) 28
(D) 14
(E) 16
Rationale: Triangle property: sum of any two sides is always greater than the third one.
and Here we have been asked for longest side...
now we can have longest side as 29 or 28 but not 30
because 31>29 and 32>28 is true but 30>30 is not true
hence Answer is 28
ANSWER:C
Answer: (C) 28