mathewhe/aqua_rat huggingface dataset:
Question: A wholesaler wishes to sell 100 pounds of mixed nuts at $1.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $1.5 * (x + y) = $1.5x + $4y
From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:
$2.5 * (x + 100 - x) = $1.5x + $4(100 - x)
If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.
You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)
Answer is A.
Answer: (A) 40
Question: A can finish a piece of work in 4 days. B can do it in 8 days. They work together for two days and then A goes away. In how many days will B finish the work?
(A) 4
(B) 5
(C) 6
(D) 2
(E) 8
Rationale: 2/4 + (2 + x)/8 = 1 => x = 2 days
Answer: D
Answer: (D) 2
Question: If each term in the sum a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: Min value of 'n' can be 10 i.e 4*22+6*12 => 22+22+22+22+2+2+2+2+2+2 = 100
Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options
(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits
ANSWER:C
Answer: (C) 40
Question: Two trains start from the same station at the same time and travel in opposite directions. One
train travels at an average rate of 40 mph, the other at 65 mph. In how many hours will they be
315 miles apart?
(A) 1 hour
(B) 2 hours
(C) 3 hours
(D) 4 hours
(E) 5 hours
Rationale: First we’ll make the d=rt chart. But we won’t fill in the d.
d = r x t
Train 1 40 x
Train 2 65 x
The reason we have an x in the time column is because they left at the same time and will be 315
at the same time. In other words, their times are equal.
Now, the big question. Are there distances equal? Since they do not meet the criteria in a TYPE
A problem, the answer is no. That means the sum of the distances must be equal to a number.
D1 + D2 = #
40x + 65 = 315
105x = 315
x = 3 It will take three hours.
correct answer C
Answer: (C) 3 hours
Question: At a party, there were five times as many females as males and six times as many adults as children. Which of the following could be the number of people at the party?
(A) 384
(B) 258
(C) 216
(D) 120
(E) 77
Rationale: Five times as many females as males --> F = 5M.
Three times as many adults as children --> (F + M) = 6C.
The number of people at the party = F + M + C = 6C + C = 7C.
The number of people at the party must be a multiple of 7. The only answer choice which is a multiple of 7 is E.
Answer: E.
Answer: (E) 77
Question: The average of first ten prime numbers:
(A) 5.6
(B) 11.2
(C) 12.9
(D) 6.3
(E) 7.4
Rationale: Explanation:
The first ten prime numbers is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Average = 129/10 = 12.9
Answer: Option C
Answer: (C) 12.9
Question: One out of every 500 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 12 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
(A) 2,000
(B) 5,000
(C) 10,000
(D) 30,000
(E) 52,000
Rationale: out of 500 only 1 bulb is defective.So for 10 defective bulbs, we must have 5000 bulbs
Now out of these 10 bulbs, 2 bulbs, have broken glass
i.e 2 broken glass out of 5000 bulbs
12 broken glass will be from 30000 bulbs
Answer is D
Answer: (D) 30,000
Question: The local carpenter made a beautiful table for my father. He told him that the type of wood which he used costs G dollars per kg, and that the table only weight F kilograms. If the carpenter worked for D hours on the table and makes E dollars per hour, how much profit will my father make when he sells the table for V dollars?
(A) V-GF-DE
(B) V+GE-DF
(C) V-(GF-DE)
(D) G(V-DE)+F
(E) (FG+DE)+V
Rationale: The wood will cost= GF dollars
The carpenter will be payed an amount= DE dollars
Hence, the cost price= GF+DE dollars
The selling price= V dollars
And the profit= V-(GF+DE)
The answer is A
Answer: (A) V-GF-DE
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
(A) 1 hr
(B) 7 hr
(C) 9 hr
(D) 4 hr
(E) 9 hr
Rationale: Let the duration of the flight be x hours. Then,
600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr.
Answer: A
Answer: (A) 1 hr
Question: In a rectangular axis system, what is the area of a parallelogram with the coordinates: (4,4), (7,4), (5,9), (8,9) ?
(A) 21.
(B) 28.
(C) 5.
(D) 49.
(E) 52.
Rationale: Delta x will give us the dimension of one side of the parallelogram = 5-4= 1 unit
Delta y will give us the dimension of the other side of parallelogram = 9-4=5 unit
Area of parallelogram = 1*5 = 5
ANSWER IS C
Answer: (C) 5.
Question: For a certain set, the value range of its members is 84.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?
(A) 18.1
(B) 21.1
(C) 36.5
(D) 42.2
(E) 84.4
Rationale: Let x and z be the smallest and largest of the original set, respectively.
z - x = 84.4
The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.
Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 84.4 / 4 = 21.1
The answer is B.
Answer: (B) 21.1
Question: A discount of 10 percent on an order of goods followed by a discount of 30 percent amounts to
(A) the same as one 45 percent discount
(B) the same as one 40 percent discount
(C) the same as one 37 percent discount
(D) the same as one 30 percent discount
(E) the same as one 25 percent discount
Rationale: 0.9*0.7*x=0.63x from initial value, meaning 0.37 or 37% discount
C
Answer: (C) the same as one 37 percent discount
Question: The interest on a certain deposit at 4.5% p.a. is Rs. 202.50 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a.?
(A) Rs. 20.25
(B) Rs. 22.50
(C) Rs. 25
(D) Rs. 42.75
(E) None
Rationale: Solution
S.I. = Rs. 202.50, R = 4.5% ,T = 1 year.
principal = Rs. (100x202.50/4.5x1)= Rs. 4500.
Now,P = Rs. 4500,R = 5% ,T = 1 year.
S.I. = Rs.(4500x5x1/1000 = Rs. 225.
∴ Difference in interest = Rs. (225 - 202.50)= Rs. 22.50.
Answer B
Answer: (B) Rs. 22.50
Question: If an amount of Rs 42,900 is distributed equally
amongst 22 persons, how much amount would each
person get?
(A) Rs 1950
(B) Rs 2000
(C) Rs 745
(D) Rs 765
(E) None
Rationale: Required amount =42900/22 = Rs 1950
Answer A
Answer: (A) Rs 1950
Question: When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 15% water?
(A) 1.2 kg
(B) 1.5 kg
(C) 1.7 kg
(D) 1.9 kg
(E) None of these
Rationale: Explanation :
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 85% (100-15).
Therefore 0.5 X Amount of flower-nectar = 0.85 X Amount of honey = 0.85 X 1 kg
Therefore amount of flower-nectar needed =
(0.85/0.51)kg=1.7 kgs
Answer : C
Answer: (C) 1.7 kg
Question: A particular library has 300 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 244 books in the special collection at that time, how many books of the special collection were loaned out during that month?
(A) 120
(B) 140
(C) 160
(D) 180
(E) 200
Rationale: The total number of books is 300.
Let x be the number of books which were loaned out.
65% of books that were loaned out are returned.
35% of books that were loaned out are NOT returned.
Now, there are 244 books, thus the number of un-returned books is 300-244 = 56 books.
0.35x = 56
x = 160
The answer is C.
Answer: (C) 160
Question: What least number should be added to 1019, so that the sum is completely divisible by 25?
(A) 4
(B) 3
(C) 2
(D) 0
(E) 6
Rationale: 1019 Ã· 25 = 40 with remainder = 19
19 + 6 = 25.
Hence 6 should be added to 1019 so that the sum will be divisible by 25
Answer: Option E
Answer: (E) 6
Question: When N is divided by T, the quotient is S and the remainder is B. Which of the following expressions is equal to N?
(A) ST
(B) S + V
(C) ST + B
(D) T(S+V)
(E) T(S – V)
Rationale: Using the rule dividend = Quotient * divisor + remainder =>ST + B C is correct
Answer: (C) ST + B
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran share in the profit?
(A) Rs 9500
(B) Rs 10,000
(C) Rs 10,500
(D) Rs 11,000
(E) Rs 14,000
Rationale: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Simran's share = Rs.24500 x	3/7	= Rs. 10,500.
ANSWER :C
Answer: (C) Rs 10,500
Question: The positive number a is q percent greater than the positive number b, which is p percent less than a itself. If a is increased by p percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: a = (1 + q%)b
b = (1-p%)a
a = (1 + q%)*(1-p%)a
So (1 + q%)(1 - p%) = 1 = No change
One easy solution to this would be q = 0 and p = 0. In that case, a = b = c. So statement II can hold.
Assuming p and q are not 0,
(1 + q%)(1 - p%) = 1 = No change
So if you increase something by q% (it becomes bigger) and then decrease it by p% (now you will need to decrease it by a lesser %), there is no change.
Such as, you increase 100 by 25% and it becomes 125. Then you decrease 125 by only 20% and it comes back to 100. (This should remind you of cost price, sale price, profit and margin). So q would be a higher percentage than p.
Now if you increase something by p% (the lower %) and then decrease by q% (the higher %), the value you will obtain will certainly be lower than original.
Say you increase a (100) by p% (20%) to get 120 and then decrease it by q% (25%), you will get c (90). Hence c < a is possible too.
Answer (E)
Answer: (E) II and III only
Question: what is next no. 11 23 47 83 131 191 263 347 443???
(A) 171
(B) 181
(C) 191
(D) 551
(E) 211
Rationale: 11+12*1=23
23+12*2=47
47+12*3=83
83+12*4=131
131+12*5=191
191+ 12*6=263
263+12*7=347
347+12*8=443
443+12*9=551
ANSWER:D
Answer: (D) 551
Question: The product of all the prime numbers less than 30 is closest to which of the following powers of 10 ?
(A)  10^9
(B)  10^8
(C)  10^7
(D)  10^6
(E)  15*10^5
Rationale: 2*3*5*7*11*13*17*19
2*19*3*17*5*13*7*11
38*51*65*77
By approximation
40*50*70*70
2000*4900
By approximation
3000*5000
1,500,000
E
Answer: (E)  15*10^5
Question: After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 5130. What was the number of original inhabitants?
(A) 7300
(B) 7600
(C) 7900
(D) 8200
(E) 8500
Rationale: Let the total number of original inhabitants be x.
(75/100) * (90/100) * x = 5130
(27/40) * x = 5130
x = 5130 * 40 / 27 = 7600
The answer is B.
Answer: (B) 7600
Question: A 400 meter long train crosses a platform in 45 seconds while it crosses a signal pole in 30 seconds. What is the length of the platform?
(A) 200
(B) 400
(C) 350
(D) 1800
(E) 45
Rationale: Speed = [400 / 30] m/sec = 40/3 m/sec.
Let the length of the platform be x meters.
Then, x + 400 / 45= 40/3
3(x + 400) = 1800 è x = 200 m. Answer: A
Answer: (A) 200
Question: If 5^5 × 5^x = (125)^4 , then what is the value of x?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: 5^5 × 5^x = (125)^4
5^(5+x) = 5^12
Since they have the same base we can just set the exponents equal to each other: (5+x) = 12
x=7
Ans. E) 7
Answer: (E) 7
Question: Aravamudhan, Balakrishnan and Chinnan work in a developing software company in starting level positions. However their salaries are different. Aravamudhan's salary to Balakrishnan's salary and Balakrishnan's salary to Chinnan's salary are in the ratio 4:3. If the total salary of all the three employees is Rs.29230, what is the salary of Chinnan?
(A) Rs.12640
(B) Rs.9480
(C) Rs.7110
(D) Rs.8660
(E) Rs.9660
Rationale: making them in equal proportion of Aravind:Bala:Cinnana=16:12:9
and given total salary 37*x=29230
x=790
Chinnana salary is 9*790=7110
ANSWER:C
Answer: (C) Rs.7110
Question: Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day G on which the buses leave at the same time.
(A) G=Tuesday
(B) G=Wednesday
(C) G=Thursday
(D) G=Sunday
(E) G=The busses will never leave at the same time
Rationale: The answer is E.
I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.
Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E
Answer: (E) G=The busses will never leave at the same time
Question: There are two positive integers a and b.What is the probability that a+b is odd/
(A) 3/2
(B) 6/7
(C) 1/2
(D) 7/2
(E) 4/5
Rationale: s=adding two numbers is (even+even),(even+odd),(odd+odd),(odd+even)
n(s)=4
e=(even+odd),(odd+even) are the points in the event.
n(e)=2
p(e)=n(e)/n(s)
=2/4
=1/2
Answer is option C
Answer: (C) 1/2
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick?
(A) 6, 8 and 12
(B) 12, 8 and 6
(C) 8, 6 and 12
(D) 12, 6 and 8
(E) 6, 12 and 8
Rationale: Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2, respectively. So
x+2x+x+2=26
4x=24
x=6
Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.
So answer is E.
Answer: (E) 6, 12 and 8
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/36
(C) 31/27
(D) 31/28
(E) 31/18
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T)
= 1 - 1/32
= 31/32
Answer: A
Answer: (A) 31/32
Question: If 70 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A) 45%
(B) 40%
(C) 35%
(D) 30%
(E) 25%
Rationale: 70% answered the first question correctly and 20% answered neither correctly.
Then 10% missed the first question but answered the second question correctly.
Then the percent who answered both correctly is 55% - 10% = 45%.
The answer is A.
Answer: (A) 45%
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 4 men and 5 women will do that task.
(A) 13/14
(B) 13/10
(C) 13/18
(D) 13/16
(E) 13/11
Rationale: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
4 m + 5 w =13 w
Answer is 13/14
Answer: A
Answer: (A) 13/14
Question: Find the surface area of a 12 cm x 4 cm x 3 cm brick.
(A) 84 cu cm.
(B) 124 cu cm.
(C) 164 cu cm.
(D) 192 cu cm.
(E) None
Rationale: Sol.
Surface area = [2(12 x 4 + 4 x 3 + 12 x 3)]
= (2 x 96)
= 192 cu cm.
Answer D
Answer: (D) 192 cu cm.
Question: 1397 x 1397=?
(A) 1951609
(B) 1981709
(C) 18362619
(D) 2031719
(E) None of them
Rationale: =(1397)^2
=(1400 - 3)^2
=(1400)^2+3^2-2 x 1400 x 3
=1960000+9-8400
=1960009-8400
=1951609
Answer is A
Answer: (A) 1951609
Question: A merchant marks his goods up by 40% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
(A) 21%
(B) 26%
(C) 69%
(D) 31%
(E) 19%
Rationale: Let the price be 100.
The price becomes 140 after a 40% markup.
Now a discount of 10% on 140.
Profit=126-100
26%
answer B
Answer: (B) 26%
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 33
(B) 289
(C) 48
(D) 77
(E) 12
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer: C
Answer: (C) 48
Question: The H.C.F. of two numbers is 20 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 280
Rationale: Clearly, the numbers are (20 x 13) and (20 x 14).
Larger number = (20 x 14) = 280. Answer: Option E
Answer: (E) 280
Question: A man's speed with the current is 12 km / hr and the speed of the current is 2 km / hr. The man's speed against the current i
(A) 8 km / hr
(B) 9 km / hr
(C) 10 km / hr
(D) 12.5 km / hr
(E) None
Rationale: Sol.
Man's rate in still in water = (12- 2) km / hr = 10km / hr.
Man's rate against the current = (10 - 2) km / hr = 8 km / hr.
Answer A
Answer: (A) 8 km / hr
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The
present age of his son is
(A) 20 years
(B) 21 years
(C) 22 years
(D) 24 years
(E) 26 years
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years
=> (x + 24) + 2 = 2(x + 2)
=> x + 26 = 2x + 4
So, x = 22
Answer: Option C
Answer: (C) 22 years
Question: If f(x)=4x−1 and g(x)=2x+1 for all integers, which of the following is a possible value of g(f(x))?
(A) -23
(B) -17
(C) 0
(D) 8
(E) 20
Rationale: g(f(x)) = 2*f(x)+1 = 2*(4x-1)+1 = 8x-1
Of these five options, only -17 has the form 8x-1.
The answer is B.
Answer: (B) -17
Question: In a tree, 1/5 of the birds are robins while the rest are bluejays. If 1/2 of the robins are female and 2/5 of the bluejays are female, what fraction of the birds in the tree are male?
(A) 9/25
(B) 12/25
(C) 17/25
(D) 29/50
(E) 33/50
Rationale: The fraction of birds that are male robins is (1/2)(1/5)=1/10.
The fraction of birds that are male bluejays is (3/5)(4/5)=12/25.
The total fraction of male birds is 1/10 + 12/25 = 29/50.
The answer is D.
Answer: (D) 29/50
Question: The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
(A) 12 a.m
(B) 13 a.m
(C) 14 a.m
(D) 11 a.m
(E) 16 a.m
Rationale: D
11 a.m
Suppose they meet x hrs after 8 a.m. Then,
(Distance moved by first in x hrs) + [Distance moved by second in (x - 1) hrs] = 330
60x + 75(x - 1) = 330 => x = 3
So, they meet at (8 + 3) i.e., 11 a.m.
Answer: (D) 11 a.m
Question: A man can row his boat with the stream at 36 km/h and against the stream in 8 km/h. The man's rate is?
(A) 1 kmph
(B) 6 kmph
(C) 7 kmph
(D) 14 kmph
(E) 9 kmph
Rationale: Explanation:
DS = 36
US = 8
S = ?
S = (36 - 8)/2 =14 kmph
Answer: D
Answer: (D) 14 kmph
Question: The avg weight of A,B & C is 50 kg. If D joins the group, the avg weight of the group becomes 53 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 51 kg. What is the weight of A?
(A) 56
(B) 65
(C) 73
(D) 89
(E) 90
Rationale: A + B + C = 3 *50 = 150
A + B + C + D = 4 * 53 = 212 ---- (i)
So, D = 62& E = 62 + 3 = 65
B + C + D +E = 51 * 4 = 204 --- (ii)
From Eq. (i) & (ii)
A-E = 212 – 204 = 8
A = E +8 = 65 + 8 = 73
Answer : C
Answer: (C) 73
Question: Ifaequals the sum of the even integers from 2 to 120, inclusive, andbequals the sum of the odd integers from 1 to 119, inclusive, what is the value of a - b ?
(A) 60
(B) 10
(C) 19
(D) 20
(E) 21
Rationale: This is a solution from Beatthegmat:
even numbers:
(120-2)/2 + 1 = 60 even integers.
(120+2)/2 = 61 is the average of the even set.
sum = avg*(#of elements) = 61*60 =3660 = a
odd numbers:
(119-1)/2 + 1 = 60 odd integers.
(119+1)/2 = 60 is the average of the odd set.
sum = avg*(#of elements) = 60*60 = 3600 = b
a-b = 3660 - 3600 = 60. Answer : A
Answer: (A) 60
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
(A) 288
(B) 1900
(C) 1287
(D) 1271
(E) 2788
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer: B
Answer: (B) 1900
Question: Rebecca's annual income is $15,000 and Jimmy's annual income is $18,000. By how much must Rebecca's annual income increase so that it constitutes 50% of Rebecca and Jimmy's combined income?
(A) 7000
(B) 6000
(C) 5000
(D) 4000
(E) 3000
Rationale: total rebecca = x+15000; total = x+15000+18000
x+15000/x+33000 = 50/100 therefore x =3000
E
Answer: (E) 3000
Question: 48 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 66
(B) 26
(C) 42
(D) 27
(E) 21
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 48 = 21
Answer: E
Answer: (E) 21
Question: If x, y and z are three different positive integers whose sum is prime, which of the following statements could be true?
(A) x + y = z
(B) Each of x + 3, y + 3, and z + 3 is prime.
(C) Each of x + y, x + z, and y + z is prime.
(D) The average (arithmetic mean) of x, y, and z is prime.
(E) Each of x, y, and z is prime.
Rationale: the question asks could be!!!!
this means that if at least one option works, it is the answer.
3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that E is the answer.
Answer: (E) Each of x, y, and z is prime.
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
(A) Rs.19
(B) Rs.29
(C) Rs.15
(D) Rs.10
(E) Rs.13
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20
= Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people
= 140 - 50 = Rs. 90
The average amount with them = 90/6
= Rs.15.
Answer:C
Answer: (C) Rs.15
Question: Solve the given two equations and find the inequality of X and Y. (a) x^2-1=0 and (b) y^2+4y+3=0
(A) If x>y
(B) If x>=y
(C) If x<y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=+1,-1 and Y= -1,-3
Comparing we get X>=Y
B
Answer: (B) If x>=y
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 6 sec
(C) 4 sec
(D) 5 sec
(E) 9 sec
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec
Answer:B
Answer: (B) 6 sec