mathewhe/aqua_rat huggingface dataset:
Question: Half a number plus 7 is 11.What is the number?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let x be the number. Always replace "is" with an equal sign
(1/2)x + 7 = 11
(1/2)x = 11 - 7
(1/2)x = 4
x = 8
correct answer is A
Answer: (A) 8
Question: A boat goes 100 km downstream in 10 hours, and 30 m upstream in 15 hours. The speed of the stream is?
(A) 22 1/7
(B) 22 1/4
(C) 22 1/2
(D) 4
(E) 22 1/3
Rationale: 100 --- 10 DS = 10
? ---- 1
30 ---- 15 US = 2
? ----- 1 S = (10 - 2)/2
= 4 kmp Answer: D
Answer: (D) 4
Question: The size of a flat-screen tablet is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 8-inch flat-screen tablet than a square 7 -inch flat-screen tablet?
(A) 7.6
(B) 7.3
(C) 7.2
(D) 7.5
(E) 8.0
Rationale: If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.
square 8-inch flat-screen television
The diagonal (hypotenuse) = 8
So, we can apply the Pythagorean Theorem to get x² + x² = 8²
Simplify: 2x² = 8²
Divide both sides by 2 to get: x² = 8²/2
Since the area of the square = x², we can see that the area of this square is 8²/2
square 7-inch flat-screen television
The diagonal (hypotenuse) = 7
So, we can apply the Pythagorean Theorem to get x² + x² = 7²
Simplify: 2x² = 7²
Divide both sides by 2 to get: x² = 7²/2
Since the area of the square = x², we can see that the area of this square is 7²/2
DIFFERENCE IN AREAS =8²/2-7²/2
= (8²- 7²)/2 = (64-49)/2 =15/2=7.5
D
Answer: (D) 7.5
Question: Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four green stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?
(A) 120
(B) 350
(C) 1470
(D) 2,520
(E) 5,040
Rationale: Number of ways to choose 2 colors among 7 - 7c2
Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))
Now the order,
the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4
[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]
Total number of combinations - 7c2 * 2* 7c4 = 1470
C
Answer: (C) 1470
Question: A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining
work in 3 days. How long does it need for B if he alone completes the work?
(A) 3512
(B) 3612
(C) 3712
(D) 3812
(E) None of these
Rationale: Explanation:
Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 � 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 (1/2) days
Answer: C
Answer: (C) 3712
Question: Three cottage of the same type were advertised to be let in a area. Three men made separate applications for a cottage. What is the probability that each of them applied for the same cottage.
(A) 1/7
(B) 2/9
(C) 1/9
(D) 4/9
(E) 2/27
Rationale: Since each of the cottage has same probability of getting selected so for each men probability of selecting a cottage out of 3 cottages 1/3
Let us consider case where all 3 men choose cottage no 1
So for First men it will be 1/3,second men 1/3 and third men also 1/3
So probability of selecting cottage no 1 is 1/3*1/3*1/3= 1/27
And since there are 3 such cottage so probability that each men select the same cottage is 3*1/27 or 1/9
Ans is C
Answer: (C) 1/9
Question: Lavanya can read a book in L minutes. What part of the book can he read in 10 minutes?(L>10)
(A) (k - 8)/k
(B) 10/L
(C) 8 + k
(D) k-8
(E) 8/k
Rationale: Option B
Explanation:
Part of the book he can read in 1 minute = 1/L
Part of the book he can read in 10 minutes =10/L.
Answer: B
Answer: (B) 10/L
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 227
(B) 266
(C) 230
(D) 288
(E) 271
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer: C
Answer: (C) 230
Question: Jackie, Mark, Dave line up at a ticket window. In how many ways can they arrange themselves so that Dave is third in line from the window?
(A) a 24
(B) b 12
(C) c 9
(D) d 6
(E) e 2
Rationale: E
Dave's position is fixed. Now we need to arrange all others around Dave.
There are 2x1= 2 ways to arrange 2 people.
Answer: (D) d 6
Question: A thief is spotted by a policeman from a distance of 150 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?
(A) 350m
(B) 200m
(C) 400m
(D) 600m
(E) None of them
Rationale: Relative speed of the policeman = (10-8) km/hr =2 km/hr.
Time taken by police man to cover
(150m/1000) x 1/2 hr = 3/40 hr.
In 3/40 hrs, the thief covers a distance of 8 x 3/40 km = 3/5 km = 600 m
Answer is D
Answer: (D) 600m
Question: A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is
(A) 285
(B) 337
(C) 878
(D) 227
(E) 291
Rationale: Explanation:
Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (510 * 5 + 240 * 25) / 30 = 8550/30 = 285.
Answer: A
Answer: (A) 285
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 4
(B) 9
(C) 12
(D) 49
(E) 40
Rationale: Explanation: Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x <-> 14 x x = 6 x 21
x = (6 x 21)/14
x = 9
Answer B
Answer: (B) 9
Question: The unit digit in the product 1256*6785*4587*9785 is?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Unit digit in the given product = unit digit in 6*5*7*5 = 0
Answer is A
Answer: (A) 0
Question: 15 people entered a theater before Sujit. 7 people entered the theater between Sujit and Suraj and 20 people entered the theater after Suraj. If Suraj entered the theater before Sujit then how many people are there in the theater?
(A) 28
(B) 36
(C) 44
(D) 40
(E) Cannot be determined
Rationale: Explanation:
If Suraj entered before Sujit, then the number of people in the theater will be 28.
ANSWER IS A
Answer: (A) 28
Question: A man has Rs. 240 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 90
(B) 70
(C) 45
(D) 80
(E) 60
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 240
16x = 240
x = 15.
Hence, total number of notes = 3x = 45.
Answer is C.
Answer: (C) 45
Question: The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.4 kg. the weight of the new student is ?
(A) 10.6 kg
(B) 3 kg
(C) 11 kg
(D) 14.9 kg
(E) None
Rationale: Answer
Weight of new student = Total weight of all 20 students - Total weight of initial 19 students
= (20 x 14.4 - 19 x 15) kg
= 3 kg.
Correct Option: B
Answer: (B) 3 kg
Question: After decreasing 24% in the price of an article costs Rs.608. Find the actual cost of an article?
(A) 128
(B) 277
(C) 800
(D) 2688
(E) 1991
Rationale: CP* (76/100) = 608
CP= 8 * 100 => CP = 800
Answer: C
Answer: (C) 800
Question: The reciprocal of the hcf and lcm of two are 1/15 and 1/312 .if one of the number is 24 then other no. is
(A) 126
(B) 136
(C) 146
(D) 156
(E) 195
Rationale: reciprocal of the hcf and lcm of two are 1/15 and 1/312
so, HCF = 15 , LCM = 312
LCM * HCF = product of two numbers = a*b => b = LCM * HCF / a
so, other = 15*312 / 24 = 195
ANSWER:E
Answer: (E) 195
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 8 years?
(A) 6%
(B) 2.5%
(C) 4%
(D) 5%
(E) 3.5%
Rationale: 150 = (750*8*R)/100
R = 2.5%
Answer: B
Answer: (B) 2.5%
Question: 0.9*0.007= ­­­­­­­­­­_________
(A) 0.063
(B) 0.0063
(C) 0.63
(D) 0.00063
(E) 63
Rationale: 9*7=63
Sum of decimal places= 4
So, 0.9*0.007= 0.0063
ANSWER:B
Answer: (B) 0.0063
Question: The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-fourth of the males and one-half of the females in the class?
(A) 128
(B) 136
(C) 144
(D) 152
(E) 160
Rationale: 1/4*2/5 + 1/2*3/5 = 2/20 + 6/20 = 2/5
The number of degrees is 2/5 * 360 = 144 degrees
The answer is C.
Answer: (C) 144
Question: Andy solves problems 70 to 125 inclusive in a Math exercise. How many problems does he solve?
(A) 56
(B) 52
(C) 51
(D) 50
(E) 49
Rationale: 125-70+1= 56
'A' is the answer
Answer: (A) 56
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
(A) 112
(B) 100
(C) 882
(D) 262
(E) 221
Rationale: 70 = (P*4*7/2)/100
P = 500.Answer: B
Answer: (B) 100
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 400 resolutions.
(A) 561.68 m
(B) 562.68 m
(C) 563.68 m
(D) 564.68 m
(E) 565.68 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 400 resolutions.
= 500 * 2 * 22/7 * 22.4
= 56268 cm
= 562.68 m
Answer: B
Answer: (B) 562.68 m
Question: For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 80, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement?
(A) K+40
(B) 2K+40
(C) (80+K)/2
(D) (80-K)/2
(E) 2(80-K)
Rationale: Let y be the years of service at the company.
After y years of service, Sue's age will be K + y.
Sue can retire when (K+y) + y = 80
y = (80 - K)/2
Then Sue's age will be K + y = K + (80 - K)/2 = (80+K) / 2
The answer is C.
Answer: (C) (80+K)/2
Question: In a family, there are six members A, B, C, D, E and F.
A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How is E related to C ?
(A) Sister
(B) Daughter
(C) Cousin
(D) Mother
(E) Father
Rationale: Explanation:
A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E. who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A.
Clearly. E is the daughter of C.
Answer: B)
Answer: (B) Daughter
Question: It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 100 pages?
(A) 12
(B) 18
(C) 20
(D) 24
(E) 30
Rationale: If it takes 4 more minutes for A to print 40 pages than it takes B,
it takes 5 more minutes for A to print 50 pages than it takes B.
Thus if b is the number of minutes than B takes to print 50 pages,
we can write:
1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)
6(2b+5)=b(b+5)
b^2-7b-30=0
(b-10)(b+3)=0
b=10
Thus it takes A 15 minutes to print 50 pages and 15*100/50=30 minutes to print 100 pages (ANSWER E)
Answer: (E) 30
Question: In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
(A) 20
(B) 30
(C) 25
(D) 600
(E) None of these
Rationale: The toys are different; The boxes are identical.
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways:
Case i. 2, 2, 1
Case ii. 3, 1, 1
Case i:
Number of ways of achieving the first option 2, 2, 1.
Two toys out of the 5 can be selected in 5C2 ways. Another 2 out of the remaining 3 can be selected in 3C2 ways and the last toy can be selected in 1C1 way.
However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2.
Therefore, total number of ways of achieving the 2, 2, 1 option is:C
Answer: (C) 25
Question: Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. The area left ungrazed by the horses is:
(A) 1050 sq.m
(B) 3850 sq.m
(C) 950 sq.m
(D) 1075 sq.m
(E) 1065 sq.m
Rationale: area ungrazed is given by
total area - 4*area grazed by each horse
= 70*70 - 4*(90/360)*pi*(70/2)^2
as the angle made by the horse is 90 degree, so applying the area of the sector,= theta/360*pi*radius^2 above
= 70*70 - pi*(70/2)*(70/2)
= 70*70 { 1- pi/4}
= 70*70{6/(7*4)} , expanding pi = 22/7
= (70*70*6) / (7*4)
= 1050 sq m
ANSWER:A
Answer: (A) 1050 sq.m
Question: Set V consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set V, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: V = {3,-8,Y,19,-6}
B = {k,-3,0,16,-5,9}
Y > 21
So L = Median of V = 3
M = Mode of Set B
Z = (3)^M
If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor
=> M = 0
Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B.
Answer - C
Answer: (C) 0
Question: What is 15 percent of 58?
(A) 6.9
(B) 7.4
(C) 8.7
(D) 9.3
(E) 10.4
Rationale: (15/100) * 58 = 8.7
The answer is C.
Answer: (C) 8.7
Question: Pipes A and B can fill a tank in 3 and 4 hours. Pipe C can empty it in 4 hours. If all pipes are opened together, then the tank will be filled in?
(A) 3hr
(B) 1/2hr
(C) 1hr
(D) 9/7hr
(E) 5/3hr
Rationale: Net part filled in 1 hour = 1/3 + 1/4 - 1/4 = 1/3
The tank will be full in 3 hr
Answer is A
Answer: (A) 3hr
Question: A 125 meter long train crosses a man standing on the platform in 5 sec. What is the speed of the train?
(A) 229
(B) 108
(C) 278
(D) 126
(E) 90
Rationale: S = 125/5 * 18/5 = 90 kmph
Answer: E
Answer: (E) 90
Question: There are 1500 military people in a division of the army. There is one Officer for every 24 soldiers in that division. Now the question is how many officers are in the division?
(A) 22
(B) 35
(C) 37
(D) 73
(E) 60
Rationale: E
60
24 soldiers + 1 officer makes a group of 25 people. Now number of such groups = 1200/25= 60.
Answer: (E) 60
Question: A company blends two varieties of tea from two different tea gardens, one variety costing 20 per kg and other 25 per kg, in the ratio 5 : 4. He sells the blended tea at 23 per kg. Find his profit percent
(A) 5% profit
(B) 3.5% loss
(C) 3.5% profit
(D) No profit, no loss
(E) None of these
Rationale: Let the quantity of two varieties of tea be 5x kg and 4x kg, respectively.
Now, SP = 23 × 9x = 207x
and CP = 20 × 5x + 25 × 4x = 200x
Profit % = 7x/200x×100=3.5%
Answer C
Answer: (C) 3.5% profit
Question: For each positive integer,the quantitySn is defined such thatSn+1=(Sn)^2 -S(n+1).in addition ,S2=1.then which of the following must be true.
(A) a)S4 +S3 +1=0
(B) b)(S1)^2 +S4 +2=0
(C) c) ifS1=-1thenS4 is also equal to-1.
(D) d) ifS4 =-7thenS1=-2.
(E) e) ifS1 =-3thenS4=-7
Rationale: Since all the answers include S4, let's start from there.
S4=S2^2-S3
S3=S1^2-S2
Substituting S3 into the first equation we get:
S4=S2^2-(S1^2-S2)
Since S2=1
S4=1-(S1^2-1)
S4=2-S1^2
We need S1^2 in order to calculate S4.
E) provides S1 and from there we can calculate S4:
S4=2-(-3)^2
S4=-7
Correct.
As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer.
For example:
If S4=-7 then S1=3 :
if we substitute S4 with - 7 we get:
-7=2-S1^2
S1^2=9
now S1 can be +/-3 !!
A
Answer: (A) a)S4 +S3 +1=0
Question: A theater is opening and has free seating. There are 15 people who want to watch a movie, and the theater has 10 seats: 1 near the exit, 4 on the first row, 4 in middle row, and 1 in the last row. Only 4 people are claustrophobic and can sit near the exit and they cannot sit anywhere. The other people can sit anywhere. How many different groupings are possible?
(A) 98340
(B) 788922
(C) 138600
(D) 383848
(E) 458569
Rationale: 4C1 select 1 from 4 claustrophobic people;
11C4 select 4 for first row from 11 people (as 4 people can only sit near the exit 15-4=11);
7C4 select 4 for middle row from 7 people (as 4 can only sit near exit and 4 we've already selected for first row 15-4-4=7);
3C1 select 1 last row seat from 3 people (again as 4 can only sit near exit and 4 we've already selected for first row, 4 for second row 15-4-4-4=3)
Total # of selection=4C1*11C4*7C4*3C1=138600
Answer: C.
Answer: (C) 138600
Question: Last year, for every 100 million vehicles that traveled on a certain highway, 100 vehicles were involved in accidents. If 2 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
(A) 500
(B) 1500
(C) 2500
(D) 2000
(E) 1000
Rationale: To solve we will set up a proportion. We know that “100 million vehicles is to 100 accidents as 2 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 2,000 million rather than 2 billion. Creating a proportion we have:
100/100 = 2,000/x
Cross multiplying gives us:
100x = 2,000 * 100
x = 20 * 100 = 2000
Answer : D
Answer: (D) 2000
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
(A) 15
(B) 87
(C) 99
(D) 77
(E) 55
Rationale: 90 * 10/60
= 15 kmph
Answer:A
Answer: (A) 15
Question: A person crosses a 400m long street in 6 minnutes. What is his speed in km per hour?
(A) 5.8km/hr
(B) 7.2km/hr
(C) 9km/hr
(D) 2.5km/hr
(E) 4km/hr
Rationale: Speed = 400/6*60 = 1.11m/sec
=1.11*18/5
=4km/hr
Answer is E
Answer: (E) 4km/hr
Question: A number increased by 10% gives 550. The number is
(A) 250
(B) 500
(C) 450
(D) 500
(E) 520
Rationale: Formula = TOTAL=100% ,INCRESE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 10 % = 110 %
110 % -------> 550 (110 ×5 = 550)
100 % -------> 500 (100 × 5= 500)
B)
Answer: (B) 500
Question: A shopkeeper fixes the marked price of an item 32% above its cost price. The percentage of discount allowed to gain 7% is
(A) 18.94%
(B) 18.93%
(C) 18.92%
(D) 18.91%
(E) None of these
Rationale: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 132
Required gain = 7%,
So Selling price = Rs 107
Discount = 132 - 107 = 25
Discount% = (25/132)*100 = 18.93%
Option B
Answer: (B) 18.93%
Question: The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 540. What is the banker's discount?
(A) 1240
(B) 1120
(C) 1190
(D) 1290
(E) None of these
Rationale: Explanation :
TD = (BG ×100)/TR = (540×100)/(6×12) = (90×100)/12 = (15×100)2/ = Rs. 750
BG = BD – TD
=> 540 = BD - 750
=> BD = 540 + 750 = 1290 Answer : Option D
Answer: (D) 1290
Question: If the units digit of n^33 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47
(A) Only I
(B) Only II
(C) Only III
(D) I and II
(E) II and III
Rationale: Given n^33 units digit is 7.
If at all we have to get 7 as units digits only 3 and 7 series has 7
3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81
7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)
We have n^33 - then divide 33 by 4 = remainder 1.
Then we have for only 7^1 - we have units digit as 7.
Hence 47^33 = 7 (units).
Option C is correct answer
Answer: (C) Only III
Question: √(49)2
(A) 7
(B) 14
(C) 49
(D) 21
(E) None of these
Rationale: explanation
√(49)2 =?
or, ? = 49
Answer C
Answer: (C) 49
Question: If the sales tax be reduced from 4 (1/4) % to 1 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 4500?
(A) Rs. 156.66
(B) Rs. 150.23
(C) Rs. 123.75
(D) Rs. 135.06
(E) None of these
Rationale: Explanation:
Required difference = (4 (1/4) of Rs. 4500) - (1(1/2) of Rs.4500)
= (17/4 – 3/2) % of Rs. 4500
= (11/4) x (1/100) x 4500
= Rs. 123.75
ANSWER C
Answer: (C) Rs. 123.75
Question: Sixteen percent of the programmers in a startup company weigh 200 pounds or more. Twenty-five percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less. What percent of the programmers in the startup company weigh between 100 and 200 pounds?
(A) 15%
(B) 20%
(C) 25%
(D) 63%
(E) 75%
Rationale: Initially 84% and 16% split
80% is further divided as 25% and 75%
Q is asking about that 75%
let total be '100' then that 75% is (3/4)∗84
so, the required % is [(3/4)∗84/100]∗100 = 63%
ANSWER:D
Answer: (D) 63%
Question: If the average (arithmetic mean) of five consecutive negative integers is 12k – 1, what is the difference between the greatest and least of the five integers?
(A) 4K
(B) 4k^2 -4k
(C) 4-4k
(D) 4
(E) 4k+4
Rationale: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 12k - 1
=> n = 60k - 5
Greatest = n + 2 = 60k - 5 + 2 = 60k - 3
Least = n - 2 = 60k - 5 - 2
=> Difference = 60k - 3 - (60k - 7)
= 4
Answer - D
Answer: (D) 4
Question: The maximum length of a pencil that can be kept in a rectangular box of dimensions 8cm×6cm×2cm, is :
(A) 2√13 cm
(B) 2√14 cm
(C) 2√26 cm
(D) 10√2 cm
(E) None of these
Rationale: Explanation:
Length of pencil = √(8)2+(6)2+(2)2 cm = √104 cm = 2√26 cm
Correct Option: C
Answer: (C) 2√26 cm
Question: An inspector rejects 0.05% of the meters as defective. How many will he examine to reject 2?
(A) A)1500
(B) B)2000
(C) C)2500
(D) D)3000
(E) E)4000
Rationale: Let the number of meters to be examined be x
Then, 0.05% of x = 2
(5/100)*((1/100)*x = 2
x = 4000
Answer is E
Answer: (E) E)4000
Question: the average distance between the sun and a certain planet is approximatly 3.7 10^13 inches. which of the following is the closest to the average distence between sun and the planet in kelometers? (1 km is approx 3.9 x 10^4 inches)
(A) 9.5 x(10)^7
(B) 9.5 x(10)^9
(C) 9.5 x(10)^4
(D) 9.5 x(10)^3
(E) 9.5 x(10)^8
Rationale: No need to solve entire problem.
Distance in KM = 37*(10)^13/39*(10)^4 which is -370*(10)^12/39*(10)^4 = 9.5 x(10)^8
Answer : E
Answer: (E) 9.5 x(10)^8
Question: In the Hillside summer camp there are 50 children. 85% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?
(A) 20.
(B) 45.
(C) 50.
(D) 30.
(E) 25.
Rationale: Given there are 50 students , 84% of 50 = 42 boys and remaining 8 girls.
Now here 84% are Boys and 16% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 8%..
If we add 50 to existing 45 then the count will be 92 and the girls number will be 8 as it.
Now boys are 92% and girls are 8%. ( out of 100 students = 92 boys + 8 girls ).
IMO option C is correct.
Answer: (C) 50.
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
(A) 6620
(B) 6627
(C) 6626
(D) 6622
(E) 6629
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer:A
Answer: (A) 6620
Question: There are some birds in cage, 1/3rd fly away . Then 2/5th of the remaining left the cage , then 2/3rd of the remaining left the cage . At last 8 were remaining . How many birds were in total ?
(A) 60
(B) 27
(C) 28
(D) 26
(E) 91
Rationale: Sol:
If x birds were there in total , then
x × (1 – 1/3)× (1 – 2/5) ×(1 – 2/3) = 8
x×2/3 × 3/5 × 1/3 = 8
x = 60
Answer:A
Answer: (A) 60