mathewhe/aqua_rat huggingface dataset:
Question: If a cube of dimension 4 by 4 by 4 is cut into 1 by 1 by 1 after painting it by red color then which of the following is/are true.
I) Ratio of number of painted surfaces of resultant cubes to total number of surfaces is 1/4
II) Number of cubes having no faces pointed is equal to number of cubes having three faces painted.
III) Number of cubes having 2 faces painted is same as number of cubes having one face painted
(A) None
(B) II and III
(C) II only
(D) I, II & III
(E) I & III only
Rationale: Long explanation, probably too detailed
Hypercube facts (n=3 for a cube):
2^n vertices 2n−1n edges 2+E−V faces
For a cube: 8 vertices, 12 edges and 6 faces
Let G=4be the size of the original cube.
I) Ratio of number of painted surfaces of resultant cubes to total number of surfaces is 1/4
There is 1 large cube with 6 sides of G2 painted faces.
There is G3x1 cubes with 6 sides of surface area 1.
1×6×G^2/G3×6×1=G^2/G^3=G−1=1/4
True
II) Number of cubes having no faces pointed is equal to number of cubes having three faces painted.
There are always 8 vertices on a cube, each vertex is the only 1x1 block which has 3 coloured faces.
Inside the cube, there is a secondary unpainted cube. Each side of this unpainted cube is equal to the size of the original cube minus two (on each axis, there will be two 1x1 cubes on the exterior of the larger cube). The size of this cube is (G−2)3
There are (G−2)3( cubes with 0 sides painted. =23=8
There are V=23 cubes with 3 sides painted =8
True
III) Number of cubes having 2 faces painted is same as number of cubes having one face painted
There are 12 edges on a cube. Each edge consists of G cubes, two of which are the vertices of the cube (and have 3 colours), the rest have two colours.
On each exterior face, there is a square of (G−2) cubes, surrounded by 4 vertex cubes and (G−2)×4 edge cubes.
Each square consists of (G−2)^2 coloured faces. There is 1 square per face.
There are (G−2)×E cubes with 2 sides painted. =2×12=24
There are (G−2)2×F cubes with 1 side painted. =22×6=24
True
ANSWER:D
Answer: (D) I, II & III
Question: Two fill taps A and B can separately fill a cistern in 45 and 40 minutes respectively. They started to fill a cistern together but tap A is turned off after few minutes and tap B fills the rest part of cistern in 23 minutes. After how many minutes,was tap A turned-off?
(A) 9 min
(B) 10 min
(C) 12 min
(D) 7 min
(E) None of these
Rationale: Let A was turned off after x min. Then,
cistern filled by A in x min + cistern filled by B in (x + 23) min = 1
⇒ x/45+x+23/40=1
⇒ 17x + 207 = 360 ⇒ x = 9 min.
Answer A
Answer: (A) 9 min
Question: If n = 6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: If n = 6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 6p have.
p = 3 --> 6p = 18--> 18 has 3 even divisors: 2, 6, 18.
Answer: B.
Answer: (B)  Three
Question: A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
(A) 48 km/hr
(B) 56 km/hr
(C) 60 km/hr
(D) 52 km/hr
(E) None of these
Rationale: Explanation:
Method : 1
If a car covers a certain distance atxkmph and an equal distance at y kmph,
the average speed of the whole journey = 2xy/x+y kmph.
By using the same formula, we can find out the average speed quickly
Speed with which he travels from A to B = x = 40 km/hr
Speed with which he travels from B to A = x = 40×(100+50)/100 = 60 km/hr
average speed = (2×40×60)/(40+60) = 48 km/hr
Assume that distance from A to B = x km
Speed with which he travels from A to B = x = 40 km/hr
Time to travel from A to B = distance/speed = x/40 hr
Speed with which he travels from B to A = 40×(100+50)/100 = 60 km/hr
Time to travel from B to A = distance/speed = x/60
Total distance traveled = x+x = 2x
Total time taken = x/40 + x/60
Average speed = Total distance traveled/Total time taken = 2x/(x/44)+(x/60)
= 2/[(1/60)+(1/40)] = (2×2400)/(40+60) = 2×24 = 48 km/hr
Answer: Option A
Answer: (A) 48 km/hr
Question: Marcella has 24 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?
(A) 21
(B) 20
(C) 19
(D) 16
(E) 15
Rationale: Marcella has 24 pairs of shoes and loses 9 shoes.
To minimize the loss of identical pairs of shoes we want Marcella to lose as many identical pairs as possible. This would yield 4 identical pairs and 1 additional shoe (destroying 5 pairs of shoes).
The 24 pairs of shoes minus the 5 'destroyed' pairs yields 19 pairs that still fulfill the requirements.
Answer: C
Answer: (C) 19
Question: 3 Years ago, the average age of a family of 5 members was 18 years. A baby having been born, the average age of the family is the same today. The present age of the baby is
(A) 1 year.
(B) 1.5 Years.
(C) 2 Years.
(D) 3 Years.
(E) 4 Years.
Rationale: We're told that 3 YEARS AGO, the average age of a family of 5 members was 17 years.
This means that the SUM of their ages was (5)(18) = 90 years.
A baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME.
This means that the sum of the ages is (6)(17) = 102 years.
We're asked for the PRESENT age of the baby.
Since each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is...
90 + (5)(3) = 108.
D
Answer: (D) 3 Years.
Question: On her annual road trip to visit her family in Seal Beach, California, Alice stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination. What was the total distance, in miles, from Alice’s starting point to Seal Beach?
(A)  250
(B)  300
(C)  350
(D)  450
(E)  400
Rationale: Let D = total distance
Traci traveled 1/3 = D/3
i.e. remaining distance = 2D/3
She traveled 1/4 th of 2D/3 = D/6
Thus:
D = (D/3) + (D/6) + 200
D = 400
ANSWER: E
Answer: (E)  400
Question: John bought 2 shares and sold them for $94 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
(A)  a profit of $10
(B)  a profit of $8
(C)  a loss of $8
(D)  a loss of $12
(E)  neither a profit nor a loss
Rationale: $ Profit of the share sold at 20% profit =
120-94
20-?
$14 profit on the sale of 1 share.
$ Loss of the share sold at 20% loss=
80-94
20-?
$26 loss on the sale of 1 share.
14-26=Loss of $12
Answer: D
Answer: (D)  a loss of $12
Question: If A is a positive integer greater than 1, what is the sum of the multiples of A from A to A^2, inclusive?
(A)  A^2(A + 1)/2
(B)  A(A + 1)(A-1)
(C)  A^2(A-1)
(D)  (x^3 + 2x)/2
(E)  x(x-1)^2
Rationale: Ans :- A
I substituted 3 in all answer choices.
Option C A were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices,
A=A^2(A + 1)/2
Answer: (A)  A^2(A + 1)/2
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, 43, 46, x
(A) 29
(B) 31
(C) 23
(D) 51
(E) 69
Rationale: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 46 + 5 = 51
Answer: (D) 51
Question: The greatest number by which the product of three consecutive multiples of 2 is always divisible is
(A) 48
(B) 76
(C) 152
(D) 162
(E) None of these
Rationale: Solution
Required number	= Product of first three multiplies of 3
= (2 Ã— 4 Ã— 6)= 48.
Answer A
Answer: (A) 48
Question: The roots of the equation ax(2)exponent) + bx + c = 0 will be reciprocal if:
(A) c = ab.
(B) a = bc
(C) c = b
(D) c = a
(E) a = b
Rationale: Let k be one of the root of the given equation.
According to the problem,
1/k will be the other root of the given equation.
We know that, product of the roots of the equation = c/a.
Therefore, k × 1/k = c/a.
or, 1 = c/a.
or, a = c [multiplying a on both sides].
The roots of the equation ax2exponent + bx + c = 0 will be reciprocal if a = c.
Therefore, a = c or c = a.
Answer: (D) c = a
Question: Find the value of 72519 x 9999 = m?
(A) 567688653
(B) 465768853
(C) 678488937
(D) 725117481
(E) 789458695
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: In an election a candidate who gets 60% of the votes is elected by a majority of 1040 votes. What is the total number of votes polled?
(A) A)4500
(B) B)5200
(C) C)6900
(D) D)7520
(E) E)6000
Rationale: Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 1040
20x/100 = 1040
x = 1040*100/20 = 5200
Answer is B
Answer: (B) B)5200
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 5 people take the trip rather than 15, how many more dollars, in terms of x, will it cost per person?
(A)  x/6
(B)  x/16
(C)  x/40
(D)  3x/40
(E)  3x/22
Rationale: Just plugging in values
X= 75
Cost per person if we consider 5 = 15
Cost per person if we consider 15 = 5
Difference between costs is 10 dollars.
Plugging in the value of x into the answer choices, let's see which one yields a result of 10. And that is E.
Answer: (E)  3x/22
Question: If a(a + 5) =6 and b(b + 5) =6, where a ≠ b, then a + b =
(A) −5
(B) −9
(C) 2
(D) 46
(E) 48
Rationale: i.e. if a = 1 then b = -6
or if a = -6 then b = 1
But in each case a+b = -6+1 = -5
Answer: option A
Answer: (A) −5
Question: Working alone at its constant rate, pump F pumped out ¼ of the water in a tank in 2 hours. Then pumps G and H started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump G, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump H, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?
(A) 6
(B) 12
(C) 15
(D) 18
(E) 24
Rationale: Rate of pump F = 1/8
3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4
Rate of F + Rate of G + Rate of H = 1/4
Rate of G + Rate of H = 1/4 - 1/8 = 1/8
G takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully.
Rate of G = 1/24
1/24 + Rate of H = 1/8
Rate of H = 1/8 - 1/24 = 1/12
Time required to pump out all the water by H = 12 hrs
Answer: B
Answer: (B) 12
Question: In a horticultural experiment, 200 seeds were planted in plot I and 300 were planted in plot II. If 57 percent of the seeds in plot I germinated and 42 percent of the seeds in plot II germinated, what percent of the total number of planted seeds germinated?
(A) 45.5%
(B) 46.5%
(C) 48.0%
(D) 49.5%
(E) 51.0%
Rationale: Plot I: 57% of 200 seeds germinated, hence 0.57*200 = 114 seeds germinated.
Plot II: 42% of 300 seeds germinated, hence 0.42*300 = 126 seeds germinated.
Thus (germinated)/(total) = (114 + 126)/(200 + 300) = 240/500 = 48% seeds germinated.
Answer: C
Answer: (C) 48.0%
Question: A pharmaceutical company received $8 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
(A) 8%
(B) 15%
(C) 45%
(D) 52%
(E) 79%
Rationale: Solution:
This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.
We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales, and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.
First 20 Million
royalties/sales =8/20
Next 108 Million
royalties/sales = 9/108 = 1/12
Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents.
First 20 Million
royalties/sales = (8/20) x 60 = 24
Next 108 Million
royalties/sales = 9/108 = (1/12) x 60 = 5
We can plug 24 and 5 into our percent change formula:
(new – old)/old x 100
[(5 – 24)/24] x 100
-475/6 x 100
At this point we can stop and consider the answer choices. Since we know that 475/6 is just a bit less than ½, we know that -475/6 x 100 is about a 79% decrease.
Answer E.
Answer: (E) 79%
Question: The length of rectangle is thrice its breadth and its perimeter is 64 m, find the area of the rectangle?
(A) 432 sq m
(B) 192 sq m
(C) 452 sq m
(D) 428 sq m
(E) 528 sq m
Rationale: 2(3x + x) = 64
l = 24 b = 8
lb = 24 * 8 = 192
ANSWER:B
Answer: (B) 192 sq m
Question: Which of the following is a possible length for side AB of triangle ABC if AC = 4 and BC = 9?
I. 5
II. 9 √3
III. 12.5
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
Rationale: (9-4) < AB < (9+4)
The answer is C.
Answer: (C) III only
Question: A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 850.50. If each member of the club paid at least $ 42, then what is the greatest possible number of members in the club?
(A) 19
(B) 21
(C) 20
(D) 23
(E) 25
Rationale: Given: Each person spends $42.
By looking at the options, we see that if there were 20 members, each person will spend atleast $42.
If there were 21 members, each person will spend $41.3
Hence the greatest number of members = 20. Option C
Answer: (C) 20
Question: Coins are to be put into 6 pockets so that each pocket contains at least one coin. At most 2 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?
(A) 16
(B) 13
(C) 17
(D) 22
(E) 28
Rationale: 2 in each, so let each contain just 1 coin;
Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);
Total: 1+1++2+3+4+5=16
Answer: A
Answer: (A) 16
Question: If x and g are integers and 2x–g= 11, then 4x+ g CANNOT be
(A)  –5
(B)  1
(C)  13
(D)  17
(E)  551
Rationale: 2x-g=11....g=2x-11
4x+g=4x+2x-11=6x-11
6x-11=-5...x=1
6x-11=1... x=2
6x-11=13...x=4
6x-11=17..X is not integer
6x-11=551..X is not integer
I think the choice E is 55 not 551. Otherwise both DE CANNOT be solution=D
Answer: (D)  17
Question: The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability R that the next couple the maitre 'd seats will not order dessert?
(A)  20%
(B)  25%
(C)  40%
(D)  60%
(E)  75%
Rationale: could you use a venn diagram and just go with the number 100.
60 people order dessert and coffee... which is the union of D and C.
R=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.
B 25%
Answer: (B)  25%
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
(A) 33
(B) 44
(C) 39
(D) 66
(E) none of these
Rationale: Let the average after 7th inning = x
Then average after 16th inning = x - 3
inline fn_jvn therefore 16(x-3)+87 = 17x
inline fn_jvn therefore x = 87 - 48 = 39 Answer C
Answer: (C) 39
Question: If circles x and y have the same area and circle x has a circumference of 12π, half of the radius of circle y is:
(A) 16
(B) 8
(C) 3
(D) 2
(E) 1
Rationale: x be radius of circle x
y be radius of circle y
given:
pi*x^2 = pi*y^2
also,
2*pi*x = 12*pi
x = 6
thus y =6
y/2 = 3
Ans: C
Answer: (C) 3
Question: if the ratio of two number is 4:6 and LCM of the number is 280 then what is the number.
(A) 12
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: product of two no = lcm *hcf
4x*6x=280*x
x=12
ANSWER:A
Answer: (A) 12
Question: A family consists of two grandparents, two parents, and three grandchildren. The average age of the grandparents is 64 years, the average age of the parents is 39 years, and the average age of the grandchildren is 6 years. What is the average age (in years) of the family?
(A) 31
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: Total age of the grandparents = 64 Ã— 2 = 128
Total age of the parents = 39 Ã— 2 = 78
Total age of the grandchildren = 6 Ã— 3 = 18
Average age of the family = (128+78+18)/7 = 224/7 = 32 years
The answer is B.
Answer: (B) 32
Question: When positive integer x is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?
I. 8
II. 15
III. 30
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) None of the above
Rationale: ans E..
we can tell the ans w/o using examples..
the units digit of product x*n is 3..
this means x and n are odd positive integers..
therefore n cannot have an even factor so 8 and 30 are out..
n cannot have a factor ending in 5 because in that case the units digit has to be 5 or 0... so 15 is also out
Answer: (E) None of the above
Question: The probability that a man will be alive for 10more yrs is 1/3& the probability that his wife will alive for 10 more yrs is 2/5. The probability that none of them will be alive for 10 more yrs, is
(A) 1/2
(B) 1
(C) 2/3
(D) 3/4
(E) 2/5
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=2/5
Ans.(E)
Answer: (E) 2/5
Question: If the sales tax be reduced from 5 (1/3) % to 3 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 5000?
(A) Rs. 156.66
(B) Rs. 111.23
(C) Rs. 120.66
(D) Rs. 91.66
(E) None of these
Rationale: Explanation:
Required difference = (5 (1/3) of Rs. 5000) - (3 (1/2) of Rs. 5000)
= (16/3 – 7/2) % of Rs. 5000
= (11/6) x (1/100) x 5000
= Rs. 91.66
ANSWER D
Answer: (D) Rs. 91.66
Question: (5+√3+√5)^2-(√3+√5)^2=?
(A) 1+2√3+2√5
(B) 25+10√3+10√5
(C) 1-√3+√5
(D) 1+√3-√5
(E) √3+√5
Rationale: (5+√3+√5)^2-(√3+√5)^2
(5+√3)^2 + 5 +2 (5+√3) (√5) - ( 3 +5 + 2√3√5)
25+ 3+ 10√3 +5 +10 √5 + 2 √15 - 3-5 -2√15
25+10√3+10√5
B is the answer
Answer: (B) 25+10√3+10√5
Question: In 1995, the Jos spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Jos cut back their water usage. By how much must the Jos have reduce their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?
(A) a)	33 1/3 %
(B) b)	40 %
(C) c) 50 %
(D) d)	66 2/3 %
(E) e)	100 %
Rationale: Let x be the water usage and c be the cost water of Jos
We have
xc =800, c=800/x
Y(1.5c)=800 where Y is the water usage in 1996
Y= 800/ (1.5*800/x)= 1/1.5x=2/3x
Thus reduction will be x-2/3x=1/3x=A
Answer: (A) a)	33 1/3 %
Question: The perimeters of two squares are 48 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .
(A) 22 cm
(B) 24 cm
(C) 26 cm
(D) 28 cm
(E) 35.6 cm
Rationale: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 48/4 = 12 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 12*12 - 8*8
= 80 cm
So side of third square = 8.9 [because area of square = side*side]
Perimeter = 4*Side = 4*8.9 = 35.6 cm
Answer: Option E
Answer: (E) 35.6 cm
Question: If q = 40! + 1, which of the following cannot be a prime factor of q?
I. 11
II. 19
III. 37
(A) I​ only
(B) III only
(C) II and III
(D) I and II
(E) I​, II, and III
Rationale: It is related to common factors between that factorial +1 and all other numbers <40.
and it is not concerned with higher number than the factorial..
example 4!+1 = 24+1 = 25 it is div by 5..
similarly 5!+1 is div by 11 but no other number <5 , as it is co-prime with others..
all the numbers 11, 19, and 37 are smaller than 40, so none of them will be factors of 40!+1..
ans E
Answer: (E) I​, II, and III
Question: A can do a piece of work in 5 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 30
(B) 20
(C) 10
(D) 6
(E) 5
Rationale: A's 1 hour's work = 1/5 ;
(B + C)'s 1 hour's work = 1/3 ;
(A + C)'s 1 hour's work = 1/2 .
(A + B + C)'s 1 hour's work = ( 1/5 + 1/3 ) =8/15 .
B's 1 hour's work = ( 8/15 - 1/2 ) = 1/30.
Therefore A alone will take 30 hours to do the work.
A
Answer: (A) 30
Question: Two clocks are set at 3 0'clock in the morning. If one clock gains 10 minutes per hour and when it shows 6:30 in the morning what does the correct clock show?
(A) 5:30
(B) 5:25
(C) 7:00
(D) 6:15
(E) 6:00
Rationale: The faster clock gains 10 minutes per hour.
The two clocks at at 3:00 at 3 0'clock in the morning
At 4 0'clock -
The correct clock is at 4:00
The faster clock is at 4:10 (1 hour + gains 10 minutes)
At 5 0'clock -
The correct clock is at 5:00
The faster clock is at 5:20 (2 hours + gains 20 minutes)
In three hours the faster clock gains 3*10=30 minutes
When the faster clock is at 6:30 the correct clock is at 6:00 in the morning.
Answer is E
Answer: (E) 6:00
Question: The average of five results is 46 and that of the first four is 37. The fifth result is?
(A) 50
(B) 88
(C) 77
(D) 82
(E) 51
Rationale: 5 * 46 â€“ 4 * 37
= 82
Answer: D
Answer: (D) 82
Question: If 0.75 : x :: 5 : 8, then x is equal to:
(A) 1.12
(B) 1.2
(C) 1.25
(D) 1.3
(E) 1.35
Rationale: Explanation:
(x x 5) = (0.75 x 8)
x=6/5
=1.20
ANSWER IS B
Answer: (B) 1.2
Question: The number 46 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
(A) 17
(B) 16
(C) 15
(D) 10
(E) 13
Rationale: I think brute force with some common sense should be used to solve this problem.
Write down all perfect squares less than 46: 1, 4, 9, 16, 25, 36.
Now, 46 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 46 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).
We can find that 46 equals to 1+9+36=1^2+3^2+6^2=46 --> 1+3+6=10.
Answer: D.
Answer: (D) 10
Question: How much space, in cubic units, is left vacant when maximum number of 7x7x7 cubes are fitted in a rectangular box measuring 14x21x17 ?
(A) 878
(B) 879
(C) 880
(D) 881
(E) 882
Rationale: No of cubes that can be accommodated in box = (14*21*17)/(7*7*7)
12*16 in numerator can be perfectly divided by 7*7 in denominator.
side with length 17 can't be perfectly divided by 7 and hence is the limiting factor. Closet multiple of 7 less that 17 is 14. so vacant area in cube =
=14*21*(17-14)
=14*21*3
=882
Ans - E
Answer: (E) 882
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
(A) 5
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
Answer:D
Answer: (D) 7
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13