RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: One used-car salesperson receives a commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 4 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?
A.$ 5,000
B.$ 6,000
C.$ 8,000
D.$ 10,000
Answer: A.$ 5,000
Explanation: This question can be solved by TESTing THE ANSWERS.
We're given the pay rate of two different salespeople who sell cars:
1) A commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price.
2) A straight commission of 6 percent of the car’s final sale price.
We're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?
Let's TEST Answer B: $6,000
1st salesperson = $200 + .04(6,000 - 1,000) = $200 + .04(5,000) = $200 + $200 = $400
2nd salesperson = .06(6,000) = $360
These totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than $6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to $6,000 though...
Let's TEST Answer C: $8,000
1st salesperson = $200 + .04(8,000 - 1,000) = $200 + .04(7,000) = $200 + $280 = $480
2nd salesperson = .06(8,000) = $480
These totals are the SAME, so this must be the answer.
Final Answer:
A
Question: A first grade teacher uses ten flash cards, each numbered from 1 to10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?
A.70
B.210
C.336
D.840
Answer: A.70
Explanation: This is a combinations problem so you need to use the correct formula:
10-2 cards =8 total cards. all possible permutations of 4 chosen from 8 cards are 8!/4!(8!-4!) = 8!/4!*4! =8*7*6*5*/4*3*2*1* =70
ANS:A
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 70.
A.3
B.4
C.12
D.32
Answer: D.32
Explanation: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.
Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form
n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc
and
n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc
So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)
Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form
n = 5a + 1
and
n = 7b + 3
Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.
Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)
Now this question is exactly like the question above. So when you divide n by 70, remainder will be -4 i.e. n will be 4 less than a multiple of 70. So you must add 4 to n to make it a multiple of 70
D
Question: A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $100,000 in the first year, an increase in annual salary of 30% over the previous year for the next two years, and a bonus of $50,000 on signing. Team L offered a three-year contract providing for an annual salary of $150,000 in the first year, an increase in annual salary of 10% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?
A.$32,500
B.$47,500
C.$82,500
D.$92,000
Answer: B.$47,500
Explanation: Team K's contract = $100,000 + $100,000*1.3 + $100,000*1.3*1.3 + $50,000 = $449,000
Team L's contract = $150,000 + $150,000*1.1 + $150,000*1.1*1.1 = $496,500
The difference = $47,500.
Answer: B.
Question: 40% of a 70% vinegar solution is replaced with water. From the resulting solution, again 10% is replaced with water. This step is repeated once more. What is the concentration of vinegar in the final solution obtained?
A.34%
B.23%
C.42%
D.28%
Answer: A.34%
Explanation: A quick answer: (70)(0.6)(0.9)(0.9)
Imagine you have 100 ml of 70% vinegar solution.
In step 1, 40% of the vinegar solution is replaced with water. This means 60% of the original vinegar quantity remains. Hence the resultant concentration is (70)(0.6) = 42%
Next, 10% of this solution is replaced with water and the process is repeated. Both the times, 90% of the previous vinegar quantity remains. Thus, 42x0.9x0.9 = 34%
This gives the final concentration as 70x0.6x0.9x0.9 = 34%
Answer: A
Question: How many integers between 362,855 and 852,755have tens digit 1 and units digit 3?
A.4,888
B.4,898
C.4,889
D.4,869
Answer: C.4,889
Explanation: There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...
The difference between 362,855 and 852,755 is 852,755-362,855=489,900 - one number per each hundred gives 133,900/100=4,889 numbers.
Answer: C.
Question: What is the decimal equivalent of (1/5)^2?
A.0.0016
B.0.04
C.0.16
D.0.25
Answer: B.0.04
Explanation: (1/5)² = (1/5)(1/5)= 1/25
APPROACH #1: use long division to divide 25 into 1 to get 1/25 = 0.04
B
Question: What is the prime factors’ number of 48?
A.2
B.3
C.4
D.5
Answer: D.5
Explanation: prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...
So, 24 = 2^4*3^1
prime factors’ number will be 4+1 = 5.
Hence, answer is D.
Question: A truck carrying cans of soup contains A stacks. Each stack contains B cases, and each case contains C cans. How many cans of soup are contained in 3 trucks?
A.3AB/C
B.3AC/B
C.3ABC
D.AB/3C
Answer: C.3ABC
Explanation: There are C cans in each case.
There are BC cans in each stack.
There are ABC cans in each truck.
There are 3ABC cans in 3 trucks.
The answer is C.
Question: What is the present worth of Rs. 330 due in 2 years at 5% simple interest per annum?
A.128
B.277
C.120
D.300
Answer: D.300
Explanation: Let the present worth be Rs. x. Then,
S.I. = (330 - x)
(x * 5 * 2) / 100 = (330 - x)
10x = 33000 - 100x
110x = 33000 => x = 300.
Answer: D
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
A.1:3
B.3:1
C.1:2
D.3:2
Answer: D.3:2
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
Therefore, 27x + 17y/(x+y)= 23
=27x + 17y = 23x + 23y
=4x = 6y
=x/y	= 3/2.
Answer is D.
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.87. How much was lent at 5%?
A.228
B.299
C.300
D.500
Answer: C.300
Explanation: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 87
5x/100 + 90 â€“ 6x/100 = 87
x/100 = 3
=> x = 300
Answer:C
Question: The average speed of a train is 87kmph. The train was scheduled to start at 9am in Bangalore, and as per schedule it has to reach a destination of 348km away from Bangalore at 1:45pm same day and a halt was scheduled onthe way. For how long was the halt scheduled?
A.45 minutes
B.50 minutes
C.55 minutes
D.60 minutes
Answer: A.45 minutes
Explanation: Speed of train = 87 kmph and distance it covers is 348 km.
Time taken to cover the distance= Distance/Speed
= 348/87= 4 hours.
But total time taken by train to reach destination is = 1:45 pm – 9 a.m =4 hours 45 minutes.
Time of halt = Total time – take taken without halt
= 4 hours 45 minutes – 4 hours = 45 minutes A)
Question: A code is to be made by arranging 7 letters. Four of the letters used will be the letter A, one of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?
A.42
B.210
C.420
D.840
Answer: D.840
Explanation: we have 7 letters out of which 3 are of one kind, 2 are of another kind..
so total ways = 7!/3!1!=840
ans D
Question: The two lines y = x and x = -3 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?
A.16
B.3/√2
C.8
D.2√2
Answer: B.3/√2
Explanation: 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-3, -3) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(3 × 3) = 9/2; so z = 9/2.
The next step requires us to find the length of a side of a cube that has a face area equal to 9/2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 9/2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 9/2. Clearly s = √9/2 = 3/√2 , oranswer choice (B).
Question: If the average of 55, 48, 507, 2, 684 and y is 223, then what is y?
A.701
B.120
C.42
D.868
Answer: C.42
Explanation: y=42, because:
(55+48+507+2+684+y)/6 = 223
(55+48+507+2+684+y)/6 *6 = 223*6
(55+48+507+2+684+y)-1296= 1338-1296
y=42
So the correct answer is C, 42.
Question: If p/q =4/5, then the value of 1/7 + {(2q - p) / (2q + p)} is ?
A.4 / 7
B.34
C.1
D.2
Answer: A.4 / 7
Explanation: Answer
Given Exp. = 4 / 7 + {(2q - p) / (2q + p)}
Dividing numerator as well as denominator by q,
Exp = 1/7 + {2-p/q) / (2 + p/q)}
= 1/7 + {(2 - 4/5) / (2 + 4/5)}
= 1/7 + 6/14
= 1/7 + 3/7
=4/7
Correct Option: A
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
A.Rs.187
B.Rs.199
C.Rs.189
D.Rs.176
Answer: C.Rs.189
Explanation: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100]
= Rs.189.
Answer: C
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
A.388
B.105
C.288
D.266
Answer: B.105
Explanation: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer:B
Question: A fair coin with sides marked heads and tails is to be tossed seven times. What is the probability that the coin will land tails side up more than four times?
A.29/128
B.56/256
C.65/256
D.70/256
Answer: A.29/128
Explanation: More than 5 times tails = 6times +7times+5times = 7C6 + 7C7 + 7C5= 29
2 2 2 2 2 2 2
2^8 times total events and 29 events where tails side up .
So probability = 29/2^7 = 29/128 (Answer A)
Question: After decreasing 24% in the price of an article costs Rs.532. Find the actual cost of an article?
A.118
B.677
C.700
D.2688
Answer: C.700
Explanation: CP* (76/100) = 532
CP= 7 * 100 => CP = 700
Answer: C
Question: What should come in place of the question mark(?) in the following equation?
4 1⁄2 × 4 1⁄3 - 8 1⁄3 ÷ 5 2⁄3 = ?
A.8
B.18 1⁄34
C.1 33⁄34
D.7⁄17
Answer: B.18 1⁄34
Explanation: ? = 9⁄2 × 13⁄3 - 25⁄3 × 3⁄17
= 39⁄2 - 25⁄17 = 663−50/34=61334=18 1/34
Answer B
Question: The compound ratio of 5:6, 3:2 and 4:5 is?
A.3:5
B.2:7
C.1:1
D.1:4
Answer: C.1:1
Explanation: Answer: Option C
5/6 : 3/2 : 4/5 = 1:1
Question: If Y < X and XM < YM, what must be true
A.M < X.
B.M < Y.
C.M < 0.
D.X < 0.
Answer: C.M < 0.
Explanation: X>Y, bus as soon as M is multiplied to both sides inequality sign changes.
This is only possible when -ve is multiplied on both sides. That means M is -ve
C is the answer
Question: Seven friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 7-person seating arrangements are possible?
A.1800
B.3600
C.5400
D.7200
Answer: B.3600
Explanation: The number of ways to arrange 7 people in a row is 7!
From this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 5 other friends is 6! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 7 friends with the 2-person unit together is 6!*2
The total number of permutations where these two friends are not seated next to each other is 7! - 6!*2 = 5*6! = 3600
The answer is B.
Question: A dealer professing to sell his goods at cost price, uses 900gm weight for 1 kg. His gain percent is
A.13%
B.12 1/3%
C.11 1/9%
D.10%
Answer: C.11 1/9%
Explanation: Gain % = ( Error/ (( True value) - Error)) *100 %
= (1000gm -900gm) / (1000 -100)* 100 %
= 100/900*100%
= 100/9
= 11 1/9 %
ANSWER:C
Question: In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 65% average total marks, it is necessary for him in third yearly examination to secure marks :
A.300
B.350
C.400
D.475
Answer: D.475
Explanation: total marks:1500 for three exams
65% of 1500=975
first exam marks=45% of 500=225
second exam marks=55% of 500=275
let X be the third exam marks
225 + 275 + X =975
X=475
ANSWER:D
Question: It's Valentine's day and Alan has promised to cook his girlfriend Alana her favorite meal: fish fingers and custard. Alana will be arriving in one hour exactly. Alan only has a microwave. The fish fingers take 13 minutes to defrost in the microwave and 6 minutes to cook in the microwave. The custard must be prepared after the fish fingers and takes 24 minutes to cook in the microwave and then 6 minutes to cool sufficiently so as not to burn someone's tongue. It will take Alan 1 minute to plate the food. However, Alan is on his Xbox and really wants to play one more game of his football video game before Alana arrives. What is the maximum length of each half of the match that Alan can play to ensure the meal is ready for Alana's arrival?
A.5 minutes
B.6 minutes
C.7 minutes
D.8 minutes
Answer: A.5 minutes
Explanation: Alana will arrive in 60 minutes.
The total meal preparation time is 13 (fish finger defrost) + 6 (fish finger cook) + 24 (custard cook) + 6 (custard cool) + 1 (plate time) = 50 minutes.
Alan therefore has 10 minutes (60-50 = 10) to play his football video game.
As football matches have two halves, Alan have select 5 minute halves (10/2 = 5)
ANSWER: A
Question: A contractor is engaged for 30days on the condition that he receives Rs.25 for eachday he works &is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was heabsent?
A.5
B.10
C.17
D.25
Answer: B.10
Explanation: 30 * 25 = 750
425
-----------
325
25 + 7.50 = 32.5
325/32.5 = 10
B
Question: In the recent, education conference in US, out of 500 men, 800 women, 1000 children present inside the building premises, 30% of the men, 25% of the women and 35% of the children were Russian. Find the percentage of people who were not Russian?
A.63.50%
B.65.23%
C.62.30%
D.69.57%
Answer: D.69.57%
Explanation: Solution: Number of Russian men present there = 500*30/100 = 150
Russian women = 800*25/100 = 200
Russian children = 1000*35/100 = 350.
Total member present in education conference = 500+800+1000 = 2300
Total Russian = 150+200+350 = 700
Hence, % of Russian present there = 700*100/2300 = 30.43%
% of people who were not Russian = 100-30.43 = 69.57%.
Answer D
Question: Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 5 books to the left of the atlas and 4 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?
A.53
B.57
C.58
D.61
Answer: A.53
Explanation: 100%. There are total of 30+33-1=62 books and 4+5=9 books are removed, thus 62-9=53 books are left.
Answer: A.
Question: Suppose that there are n points in the plane and that each of these
points is joined to exactly three of the others by straight line segments.
Then a possible value of n would be
A.11
B.15
C.18
D.27
Answer: C.18
Explanation: Count the number of pairs (p,l) where p is one of the n points and l is a line
segment joining p to one of the other n-1 points. Each point is joined to exactly 3 other
points by line segments so that the total number of pairs is 3n (three line segments for
each of the n points). On the other hand, if there are m total line segments, then each line
segment joins exactly two points so that the total number of pairs (p,l) is 2m (two pointsfor each of the m line segments). Thus, we must have 3n = 2m. But this means that n
must be even. The only even choice given is 18, so this must be the answer.
Is n = 18 really possible or is there some other argument that shows n must be divisible
by 23? One can justify that in fact if n is even, then one can join each of any n points
to 3 of the remaining n - 1 points by line segments. To see this, let n = 2k, and let the
points be p1,..., pn. For each j, join pj by line segments to pj-1, pj+1, and pj+k where
subscripts are to be interpreted modulo n. Thus, for example, if n = 18, then the point
p12 is joined to p11, p13, and p3 (since 12 + 9 + 3 (mod 18)) and the point p1 is joined
to p18 (since 1-1=18 (mod 18)), p2, and p10. You should convince yourself that this
construction for n even joins each point to exactly 3 others.
correct answer C
Question: A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 40 days, then together ,all will finish the work in :
A.13 1/3 days
B.12 1/3 days
C.15 days
D.20 days
Answer: A.13 1/3 days
Explanation: C alone can finish the work in 40 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
A’s 1 day’s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 day’s work = (1/60) + (1/30) + (1/40) = 9/120 = 3/40
All the three together will finish it in 40/3 = 13 and 1/3 days.
ANSWER:A
Question: Tough and Tricky questions: Number Properties.
If (z + 6)/8 is an integer, what is remainder when z is divided by 8?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: Assume the answer choices as the value of z
8/8=1
Ans A
Question: In a group of 58 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
A.20
B.10
C.9
D.8
Answer: A.20
Explanation: Each student is registered forat least one of three classesmeans thatthere are no students who are registered for none of the classes.
Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:
58 = 25 + 25 + 34 - {people in exactly 2 groups} - 2*3 + 0-->{people in exactly 2 groups}=20
Answer: A
Question: Two cars cover the same distance at the speed of 94 and 90 kmps respectively. Find the distance traveled by them if the slower car takes 2 hour more than the faster car?
A.1254
B.2827
C.2356
D.2780
Answer: B.2827
Explanation: 94(x + 2) = 90x
X = 47
60 * 47 = 2827 km
Answer:B
Question: Raju has 6 balls. Out of which 4 green 2 blue. He'll pick 2 balls.. Whats probability dat it contain 1 blue and 1 green..
A.7/15
B.8/15
C.9/15
D.11/15
Answer: B.8/15
Explanation: (2/6*4/5)+ (4/6*2/5)=8/15
ANSWER:B
Question: The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21, is?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: Let x be subtracted. Then,
6 - x
7 - x
<
16
21
21 (6 - x) < 16 (7 - x)
5x > 14
x > 2.8
Least such whole number is 3.
ANSWER:A
Question: Out of the five integral numbers C is the average of A and D. B is greater than C and less than D.Also B is the average of A and E . The middle most number in the sequence
A.A
B.B
C.J
D.C
Answer: B.B
Explanation: Explanation:
D _ C _ A --------(1)
D > B > C --------(2)
from (1) and (2)
D > B > C > A ---------(3)
Again E _ B _ A
But B > A, from (3)
So E > D > B > C > A [ Since B is the average of E and A so it is eqidistant from both E and A]
Answer: B
Question: Two buses of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
A.10 sec
B.30 sec
C.40 sec
D.20 s
Answer: D.20 s
Explanation: D
Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 sec.
Question: If s is an odd integer, which of the following must also be odd?
A.2s + 6
B.s + s
C.3s + 3
D.2s + s
Answer: D.2s + s
Explanation: Things to keep in mind:
Odd + odd = even
Odd + even = odd
Odd*odd = odd
Odd*even = even
On checking each option
A. 2s + 6
2s = even, 2s + 6 = even + even = even.
B. s + s
Odd + odd = even. This will be even
C. 3s + 3
3s = odd, 3s + 3 = odd + odd = even
D. 2s + s
2s = even, 2s + s = even + odd = odd
E. s^2 + 1
s^2 = odd, s^2 + 1 = odd + odd = even
Correct option: D
Question: If the number 481*673 is completely divisible by 9, what is the the smallest whole number in place of *?
A.4
B.5
C.6
D.7
Answer: D.7
Explanation: Let x be the smallest whole number in place of *
481x673 is completely divisible by 9
=> (4+8+1+x+6+7+3) is divisible by 9
=> (29+x) is divisible by 9
x should be the smallest whole number.
Hence, (29+x)=36
=>x=36−29=7
Answer is D.
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.83200?
A.81000
B.81028
C.105300
D.29889
Answer: C.105300
Explanation: 83200* 9/8 * 9/8 = 105300.Answer:C
Question: Find the number of divisors of 1080 excluding the divisors which are perfect squares.
A.28
B.29
C.30
D.31
Answer: A.28
Explanation: 1080 = 2^3 *3^3 *5^1
total no. of divisors = (3+1)*(3+1)*(1+1) = 32
only 4 divisors 1, 2^2=4 , 3^2=9 & 2^2*3^2=36 are perfect squares
so,number of divisors excluding perfect squares divisors = 32-4 = 28
ANSWER:A
Question: In the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 65, what is the greatest possible value of B × A?
A.0
B.5
C.10
D.15
Answer: C.10
Explanation: You should notice that 65*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*2=10 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).
Answer: C
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C