mathewhe/aqua_rat huggingface dataset:
Question: If a and b are positive integers such that a/b = 3.42, which of the following must be a divisor of a
(A) 57
(B) 32
(C) 45
(D) 26
(E) 20
Rationale: a/b = 3.42
a/b = 342/100
a/b = 171/50
a = 171/50*b
We require to find from the available 5 options that must be a divisor of a"
This also means which of the following 5 options can divide 171 evenly
(Ignore b as its value unknown; Ignore 50 as in denominator)
Only option A = 57 best fits in
Answer = 57
ANSWER:A
Answer: (A) 57
Question: Jerry, an electrician, worked 5 months out of the year. What percent
of the year did he work? (round answer to the nearest hundredth)
What percent 12 is 5? 12 months = 1 year
(A) 58.33%
(B) 68.33%
(C) 78.33%
(D) 88.33%
(E) 41.66%
Rationale: 1. Multiply the opposites
5 x 100 = 500
100=5/12
Divide by the remaining number
41.66% (rounded to hundredth)
correct answer E
Answer: (E) 41.66%
Question: If a quarter kg of potato cost 60 paise, how many paise will 200 gm cost ?
(A) 48 paise
(B) 54 paise
(C) 56 paise
(D) 72 paise
(E) None of these
Rationale: Solution
Let the required cost be x paise. Less weight, Less cost
∴ 250 : 200 :: 60 : x ⇔ 250 × x = (200 × 60) ⇔ x = (200x60)/250⇔ x = 48. Answer A
Answer: (A) 48 paise
Question: A number when divided by 342 gives a remainder 47. When the same number if it divided by 19, what would be the remainder ?
(A) 1
(B) 2
(C) 5
(D) 9
(E) 11
Rationale: On dividing the given number by 342, let k be the quotient and 47 as remainder.
Then, number – 342k + 47 = (19 x 18k + 19 x 2 + 9) = 19 (18k + 2) + 9.
The given number when divided by 19, gives (18k + 2) as quotient and 9 as remainder.
ANSWER D
Answer: (D) 9
Question: An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 75 km. How long did it take to reach its destination 750 km from the starting point ?
(A) 8 hrs 6 min
(B) 6 hrs 28 min
(C) 2 hrs 28 min
(D) 6 hrs 28 min
(E) 1 hrs 28 min
Rationale: Explanation:
Time taken to cover 750 km = 750/100 = 7 hrs 30 mins
Number of stoppages = 750/75 - 1 = 9
Total time of stoppages = 4 x 9 = 36 min
Hence, total time taken = 8 hrs 6 min.
Answer: A
Answer: (A) 8 hrs 6 min
Question: A 140 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) A)73
(B) B)20
(C) C)83
(D) D)40
(E) E)52
Rationale: Explanation:
1: 2/5 = 5: 2
2/7 * 140 = 40
Answer: Option D
Answer: (D) D)40
Question: In what ratio mental A at Rs.68 per kg be mixed with another metal at Rs.96 per kg so that cost of alloy (mixture) is Rs.80 per kg?
(A) 5:8
(B) 4:7
(C) 4:3
(D) 9:5
(E) 9:8
Rationale: (96-80)/(80-68)=16/12=4/3
ANSWER:C
Answer: (C) 4:3
Question: Rounded to three decimal places, 1.004^4 =
(A) 1.004
(B) 1.006
(C) 1.008
(D) 1.012
(E) 1.016
Rationale: As compared to 1, 0.004 is a very small quantity. Thus, we can write (1+0.004)^4 is nearly equal to (1+4*0.004) = 1.016.As the question asks for approximation to three decimal places, the further terms will anyways not come into picture.
E.
Answer: (E) 1.016
Question: If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 6 miles?
(A) 10/5
(B) 15/5
(C) 20/5
(D) 22/5
(E) 18/5
Rationale: 1 km is approxmately equal to 0.6 miles
So 6 km = 6*0.6 = 3.6 miles . Multiple & divide by 10
i.e 3.6*10/10 = 36/10 = 18/5
Answer : E
Answer: (E) 18/5
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
(A) 21:32
(B) 32:21
(C) 12:17
(D) 17:12
(E) 15:17
Rationale: Explanation:
Here capital is not the same.
Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio
=(20000×6+15000×6):(30000×4+50000×4)
=(20×6+15×6):(30×4+50×4)
=(20×3+15×3):(30×2:50×2)
=105:160
=21:32
Answer: Option A
Answer: (A) 21:32
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: If a - b = 3 and a(power 2) + b(power 2) = 39, find the value of ab.
(A) 15
(B) 8
(C) 4
(D) 10
(E) 3
Rationale: 2ab = (a(power 2) + b(power 2) - (a - b)(power 2)
= 39 - 9 = 30
ab = 15.
Answer is A.
Answer: (A) 15
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
(A) 124
(B) 154
(C) 166
(D) 178
(E) 190
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: (C) 166
Question: If the sum of 8 consecutive integers is x, which of the must be true?
I. x is even
II. x is odd
III. x is a multiple of 8
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III
Rationale: sum of 6 consecutive integers
= (n) + (n+1) + (n+2) + (n+3) + (n+4) + (n+5)+(n+6)+(n+7)
= 8n + 28
= even + even = even
= 4(2n+7) = divisible by 4
Hence, x is even and divisible by 4.
Answer: D
Answer: (D) I and III
Question: In a 100m, A beats B by 15m and B beats C by 10m. If A beats C by 5 sec then the speed of C.
(A) 5m/sec
(B) Speed of C can not be found with given data.
(C) 4.7m/sec
(D) 4m/sec
(E) 4.5m/sec
Rationale: When A finishes the race , B is at 85m....
and when B travels 100m, C is at 100-10 = 90m.....
so C loses 10m on B's 100m................
or C will lose 1 m for every 10m of B.....
so C will lose 8.5 m when B travels 85m.....
From above we get correlation of all three..
A is at 100, B is at 85 and C is at 85-8.5 = 76.5
So C is 100-76.5 = 23.5 m behind A...
and C also loses by 5 secs, this means C covers this 23.5m in 5 secs..
speed of C =23.5/5=4.723.55=4.7 mps
ANSWER:C
Answer: (C) 4.7m/sec
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present?
(A) 63
(B) 64.5
(C) 62.5
(D) 60.5
(E) 60
Rationale: Let required number of buckets =x
If capacity of buckets are reduced, more number of buckets are required (indirect proportion). Therefore,
25:x=(2/5):1
⇒25=2x/5
⇒x=62.5
Answer: C
Answer: (C) 62.5
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h = 9 cm
Answer: Option E
Answer: (E) 10
Question: In 10 years,A will be 5 times as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :
(A) 17.25 Years
(B) 29 Years
(C) 39 Years
(D) 49 Years
(E) 59 Years
Rationale: Solution
Let B's present age = x years.Then,A's present age =(x +9) years.
âˆ´ (x + 9)+ 10 = 5 (x - 10) â‡” x + 19 = 5x- 50 â‡” 4x = 69.
x = 17.25
Answer A
Answer: (A) 17.25 Years
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.6
(B) 31.0
(C) 31.6
(D) 31.1
(E) 31.5
Rationale: 100*(80/100)*(90/100)*(95/100)
= 68.4
100 - 68.4 = 31.6
Answer: C
Answer: (C) 31.6
Question: 25 % of 1250
(A) 330
(B) 315
(C) 312.5
(D) 370
(E) 350
Rationale: 1 % of 1250 is = 12.5025% of 1250 is = 12.50 * 25 = 312.5Answer : C
Answer: (C) 312.5
Question: What is the next number of the following sequence
8,0.5,16,4,15,0.3,50,4.5,6,.2,30,?
(A) 0.6
(B) 0.8
(C) 1.2
(D) 1.6
(E) 1.8
Rationale: 8,0.5,16,4,15,0.3,50,4.5,6,.2,30,X
(8,0.5,16,4),(15,0.3,50,4.5),(6,.2,30,X)
in each group, 1st/2nd=3rd & 1st*2nd=4th
8/0.5=16, 8*0.5=4
15/0.3=50, 15*0.3=4.5
6/.2 = 30, 6*.2=X => X=1.2
ANSWER:C
Answer: (C) 1.2
Question: A chair is bought for Rs.1000/- and sold at a loss of 20% find its selling price
(A) Rs.800/-
(B) Rs.510/-
(C) Rs.515/-
(D) Rs.530/-
(E) Rs.540/-
Rationale: Loss = 1000*20/100 = 200
S.P = C.P - Loss
= 1000- 200
=Rs.800/-
Answer :A
Answer: (A) Rs.800/-
Question: The speed of a boat in still water in 42 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 44 minutes is:
(A) 86.6 km
(B) 46.6 km
(C) 34.5 km
(D) 35.6 km
(E) 26.6 km
Rationale: Speed downstream = (42 + 5) = 47 kmph
Time = 44 minutes =44/60 hour = 11/15 hour
Distance travelled = Time × speed =11/15×47 = 34.5 km
ANSWER:C
Answer: (C) 34.5 km
Question: Series B(n) is such that i*B(i) = j*B(j) for any pair of positive integers (i, j). If B(1) is a positive integer, which of the following is possible?
I. 2*B(100) = B(99) + B(98)
II. B(1) is the only integer in the series
III. The series does not contain negative numbers
(A) I only
(B) II only
(C) IIII only
(D) IIIII only
(E) I, IIIII
Rationale: First thing I want to understand is this relation: i*B(i) = j*B(j) for any pair of positive integers. I will take examples to understand it.
When i = 1 and j = 2, B(1) = 2*B(2)
So B(2) = B(1)/2
When i = 1 and j = 3, B(1) = 3*B(3)
So B(3) = B(1)/3
I see it now. The series is: B(1), B(1)/2, B(1)/3, B(1)/4 and so on...
II and III are easily possible. We can see that without any calculations.
II. B(1) is the only integer in the series
If B(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except B(1)
III. The series does not contain negative numbers
Again, same series as above applies. In fact, since B(1) is a positive integer, this must be true.
I. 2*B(100) = B(99) + B(98)
2*B(1)/100 = B(1)/99 + B(1)/98 (cancel B(1) from both sides)
2/100 = 1/99 + 1/98
Not true hence this is not possible
Answer (D)
Answer: (D) IIIII only
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 80%
(B) 105%
(C) 120%
(D) 124.2%
(E) 138%
Rationale: x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,15 = 15/100
x= 80*15/100
x= 12
12/10 = 1,2 = 120%, Answer C
Answer: (C) 120%
Question: What is the ratio of y to x if (x + 3y) / ( x - y) = 7/4?
(A) -15/4
(B) -5/3
(C) -1/15
(D) 3/5
(E) 15/1
Rationale: Solving for y/x gives, 3/19 (E)
Answer: (E) 15/1
Question: A train running at the speed of 80 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 227 m
(B) 150 m
(C) 187 m
(D) 167 m
(E) 200 m
Rationale: Speed = 80 * 5/18 = 200/9 m/sec
Length of the train = speed * time = 200/9 * 9
= 200 m
Answer: E
Answer: (E) 200 m
Question: Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: E10, H13, __, N19, Q22, ... What number should fill the blank?
(A) H13
(B) I14
(C) J15
(D) K16
(E) L17
Rationale: D
K16
In this series, the letters progress by 3, and the numbers increase by 3.
Answer: (D) K16
Question: Kramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, how many cases can Kramer pack in 1 hours?
(A) 60X/Y.
(B) 120X/Y.
(C) 60Y/X.
(D) 120Y/X.
(E) (X + Y)/60.
Rationale: Kramer can pack X boxes per min.
Therefore in 1 hrs(60mins)he can pack 60X boxes.
If there are Y boxes in one case then then the total number of cases packed by Kramer = 60X/Y
(ANSWER A)
Answer: (A) 60X/Y.
Question: Last year a worker saved 15% of her annual salary. This year, she made 20% more money than last year and she saved 25% of her salary. The amount she saved this year was what percent of the amount she saved last year?
(A) 120%
(B) 140%
(C) 160%
(D) 180%
(E) 200%
Rationale: Let x be the worker's salary last year.
Last year, she saved 0.15x.
This year, she saved 0.25(1.2x)=0.3x
0.3x/0.15x=200%
The answer is E.
Answer: (E) 200%
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4 years
(B) 8 years
(C) 6 years
(D) 2 years
(E) 10 years
Rationale: Let the ages of children be X, (X + 3), (X + 6), (X + 9) and (X + 12) years.
Then, X + (X + 3) + (X + 6) + (X + 9) + (X + 12) = 50
5X = 20
X = 4.
Age of the youngest child = X = 4 years.
ANSWER:A
Answer: (A) 4 years
Question: Score Interval Number of Scores
50-59 2
60-69 10
70-79 16
80-89 25
90-99 18
The table shows a distribution of test scores. Which score interval contains the median of the 71 scores?
(A) a) 60-69
(B) b) 70-79
(C) c) 80-89
(D) d) 90-99
(E) e) Cannot determine.
Rationale: 36th person
80-89 C
Answer: (C) c) 80-89
Question: Kala and Sudha stated a business with an investment of Rs.18000 and Rs.24000 respectively. After 3 months Gita joined in the business with an investment of Rs.20000, find share of Gita, if the difference between the profits received by Kala and Sudha is Rs.840 ?
(A) 2150
(B) 2200
(C) 2100
(D) 2250
(E) 2300
Rationale: Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10.
Investment x time.
Kala = 9 x 12 = 108.
Sudha = 12 x 12 = 144.
Githa = 10 x 9 = 180.
Or Kala : Sudha : Githa => 6 : 8 : 5.
Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a.
Difference between the profits received by Kala and Sudha
6a – 8a = 2a = 840 or a = 420.
Githa = 5a = 5 x 420 = Rs.2100.
Option C
Answer: (C) 2100
Question: A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 32% of the original number. What percent of the red candies remain?
(A) 27.5%
(B) 33.3%
(C) 35.5%
(D) 42.5%
(E) 47.5%
Rationale: Let x be the original number of each color so there are a total of 5x candies.
Kaz eats all of the green candies and half of the orange ones.
There are 0 green candies and 0.5x orange candies remaining.
He eats half of the remaining pieces of each color.
There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.
He eats red and yellow candies in equal proportions.
orange+blue+red+yellow = 0.75x + red + yellow = 1.6x
red + yellow = 0.85x
red = 0.425x, since red = yellow.
The answer is D.
Answer: (D) 42.5%
Question: (935421 x 625) = ?
(A) 584638125
(B) 584638130
(C) 584638135
(D) 584638140
(E) 584638145
Rationale: 935421 x 625 = 935421 x 54 = 935421 x 10 4
2
=	935421 x 104	=	9354210000
24	16
= 584638125
A)
Answer: (A) 584638125
Question: The number of digits of the smallest number, which when multiplied by 7 gives the result consisting entirely of nines is
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Sol.
By hit and trial, we find that a number exactly divisible by 7 and consisting entirely of nines is 999999. Number of digits in it = 6.
Answer C
Answer: (C) 6
Question: Find the remainder when 2^31 is divided by 5.
(A) 9
(B) 7
(C) 1
(D) 3
(E) 6
Rationale: 2^31=(2^10*2^10*2^10)*2=(2^10)^3 *2=(1024)^3 *2
unit digit in 2^31=unit digit in {(1024)^3*2}=(4*2)=8.
Now, 8 when divided by 5 gives 3 as remainder
2^31 when divided by 5 gives remainder =3.
Answer is D
Answer: (D) 3
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 4
(B) 8
(C) 6
(D) 2
(E) 1
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer:A
Answer: (A) 4
Question: A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 105 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?
(A) 8%
(B) 9%
(C) 11%
(D) 12.5%
(E) 14.28%
Rationale: Typical dosage is Dose : weight :: 2: 15.
Now if weight is 105 (Multiplying factor is 7: (105/15)) then typical dosage would be 2 *7 = 14 cc.
Dosage = 18 cc. Dosage is greater by 2 cc.
% dosage is greater: (2 / 14)*100 = 14.28 %
E is the answer.
Answer: (E) 14.28%
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 3.5, 6.5, 9.5, 12.5, ... What number should come next?
(A) 4.7
(B) 3.6
(C) 4.9
(D) 15.5
(E) 4.4
Rationale: 15.5
In this simple addition series, each number increases by 3.0
Answer : D
Answer: (D) 15.5
Question: The number of arrangements that can be made with the letters of the word MEADOW so that the vowels occupy the even places?
(A) 54
(B) 72
(C) 42
(D) 15
(E) 36
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways.
Hence the total ways are 6 * 6 = 36.
Answer:E
Answer: (E) 36
Question: If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 21?
(A) 101
(B) 187
(C) 191
(D) 221
(E) 251
Rationale: ok, not sure if this is the best explanation, but here is my way of solving this :
tn +1 = tn + n,
t 3 = 14
so:
t 4 = t 3 + 3
t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4
....
so we get
t 21 = t 3 + 3 + 4 + 5 + 6....+ 19+20
the 3 + 4 + 5 + ... + 19 +20 sequence is equal the sequence 1 + 2 + ... + 19,+20 minus 1 + 2 at the beginning (so, minus 3)
and the 1 + 2 ... + 19 +20 sequence is equal to n*(n+1)/2 with n being 20, so equal to 20 * 21 / 2 = 210
so :
t 21 = t 3 + 210 - 3
t 21 = 14 + 210 - 3 = 210 + 11 = 221, hence answer D
Answer: (D) 221
Question: On a baseball team, 4 players including Alice want to play 1st base, 2nd base, or 3rd base. Before every game, the coach chooses a name randomly from a bag and this person plays 1st base. Then the coach chooses the next name randomly and this person plays 2nd base. The coach then chooses a third name randomly and this person plays 3rd base. What is the probability that Alice plays 1st, 2nd, or 3rd base?
(A) 3/4
(B) 5/6
(C) 7/8
(D) 9/16
(E) 11/16
Rationale: The total number of ways to choose three players is 4C3=4.
Excluding Alice, the number of ways to choose three players is 3C3=1.
P(Alice is not chosen)=1/4.
P(Alice is chosen)=1 - 1/4 = 3/4.
The answer is A.
Answer: (A) 3/4
Question: Out of a list of mailing addresses, company A has x addresses, company B has y addresses, and companies A and B combined have a total number of addresses equal to 3 times as many as company A has. How many mailing addresses belong to both companies?
(A) x
(B) y
(C) x + y
(D) y - 2x
(E) x - 2y
Rationale: Let s denote the shared addresses between A and B.So A will have distinct x - s addresses and B will have y - s addresses
.
Given "A and B combined have a total number of addresses equal to 3 times as many as company A has"
i.e, x + y - s = 3 x (s is subtracted because it's captured twice)
solve for s and it gives, y - 2x.
Answer is D
Answer: (D) y - 2x
Question: Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
(A) 3! ways
(B) 8! ways
(C) 7! ways
(D) 10! ways
(E) 11! ways
Rationale: Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: (B) 8! ways
Question: 9 pirates found a treasure chest with 347298 dimaonds. In order to evenly divide the diamonds, how many more would they need to find?
(A) 0
(B) 9
(C) 4
(D) 5
(E) 3
Rationale: To find the solution you must first add the digits of 347298. 3+4+7+2+9+8=33. The closest number divisible by 9 is 36. 33+3=36. Therefore they would need to find 3 more diamonds. Answer E.
Answer: (E) 3
Question: In a rectangular coordinate system, what is the square root of the area of a trapezoid whose vertices have the coordinates (2, -2), (2, 3), (20, 2), (20, -2)?
(A) 7.5
(B) 9
(C) 10.22
(D) 12.25
(E) 14
Rationale: we can form rectangle and then minus the area of triangle
18*5 -9 =81 sq rt of which is 9
ANSWER:B
Answer: (B) 9
Question: What number should replace the question mark? 5, 24, 11, 20, 17, 16, ---?
(A) 20
(B) 23
(C) 22
(D) 21
(E) 26
Rationale: Answer: B
5, 24, 11, 20, 17, 16, 23?
There are two alternate sequences: +6 and -4.
Answer: (B) 23
Question: Elena purchased Brand X pens for $4.00 apiece and brand Y for $2.80 apiece. If Elena purchased a total of 10 of these pens for $42.00, how many brand X pens did she purchase?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 4x+2.8y=42 --> multiply by 2.5 (to get the integers) --> 10x+7y=105 --> only one positive integers solutions x=5 and y=5 (how to solve: 7y must have the last digit of 5 in order the last digit of the sum to be 5).
Answer: B.
Answer: (B) 5
Question: A certain freshman class has 600 students and a certain sophomore class has 900 students. Among these students, there are 75 two-person sets of lab partners, each consisting of 1 freshman and 1 sophomore. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a set of lab partners?
(A) 1/75
(B) 1/96
(C) 1/5400
(D) 1/7200
(E) 1/54000
Rationale: there are 600*900 two people sets. (total outcomes)
75 sets are 2 people sets and lab partners ( favorable outcomes)
so the probability that the 2
students selected will be a set of lab partners = 75/(600∗900)75/(600∗900)
= 1/7200
Answer: D
Answer: (D) 1/7200
Question: A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased?
(A) 2
(B) 3
(C) 4
(D) 5
(E) Data Inadequete
Rationale: Explanation:
The equation for this problem can be made as:
5x + 7y =38
Where x is the number of watermelons and y is the number of pineapples.
Now test for 2, 3 and 4:
For y = 2
5x + 14 =38
x is not an integer
For y = 3
5x = 17
X not an integer
For y =4
X = 2
So 4 pineapples and 2 watermelons can be bought by 38 Rs.
ANSWER E
Answer: (E) Data Inadequete
Question: There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices.
(A) 120
(B) 116
(C) 140
(D) 20
(E) 190
Rationale: The number of triangle can be formed by 10 points = 10C3.
Similarly, the number of triangle can be formed by 4 points when no one is collinear=4C3.
In the question, given 4 points are collinear, Thus, required number of triangle can be formed,
= 10C3-4C3 = 120-4 = 116.
Option B
Answer: (B) 116
Question: In Bangalore there is a well known Science Institute. During a visit I asked two of the men to tell me their ages. One replied, 'One of our ages subtracted from the other's equal 30.'
Then the other man spoke . 'Our ages multiplied together equal 1624.'
What were their ages?
(A) 60 and 23
(B) 66 and 25
(C) 29 and 56
(D) 71 and 43
(E) 58 and 28
Rationale: E
Their ages were respectively 58 and 28
Answer: (E) 58 and 28
Question: 0.0006688/0.0000120 x 17.05 =?
(A) 450.1
(B) 910.1
(C) 930.1
(D) 920.1
(E) 950.1
Rationale: Explanation :
? = 0.0006688/0.0000120 x 17.05 = 950.1
Answer : Option E
Answer: (E) 950.1
Question: Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 2 years?
(A) 5x (1+n/100)^2 - x
(B) 2x (1+n/100)^4 - x
(C) 3x (1+n/100)^3 - x
(D) x (1+n/100)^2 - x
(E) x (1+n/100)^6 - x
Rationale: Amount after 2 years compounded yearly = x (1+n/100)^2
Thus profit = Final amount - original principle = x (1+n/100)^2 - x . Answer : D
Answer: (D) x (1+n/100)^2 - x