Numbers problems
- 1. A thief steals half the total number of loaves of bread plus 1/2 loaf from a bakery. A second thief steals half the remaining number of loaves plus 1/2 loaf and so on. After the 5th thief has stolen there are no more loaves left in the bakery. What was the total number of loaves did the bakery have at the beginning ?
Options- A. 21
- B. 11
- C. 17
- D. 31 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 31
Explanation:
Let y be the total number of loaves
a be the remaining loaves after 1st thief
b be the remaining loaves after 2nd thief
and c, d..so on after 3 and 4 th
e = 0 be the remaining loaves after 5th thief
a = y - (y/2 + 1/2)
= y/2 - 1/2
b = a - (a/2 + 1/2)
= a/2 - 1/2
c = b - (b/2 + 1/2)
= b/2 - 1/2
d = c - (c/2 + 1/2)
= c/2 - 1/2
e = d - (d/2 + 1/2)
= d/2 - 1/2
we know that, e = 0,
thus by substitution, we get
d = 1
c = 3
b = 7
a = 15
y = 31
Therefore total number of bread loaves in bakery was 31.
- 2. Maheshwari wants to buy 7 floors in an 68 storied building whose numbering stars from 1 upto 68. But she has to follow certain rules which are as follows : 1) None of the floor should be a prime number 2) None of the digit of the floor should be a prime number 3) Maheshwari cannot buy the 1st floor as it is being assigned to the architect. So how many options are left with Maheshwari to buy the floors ?
Options- A. 11
- B. 17
- C. 13
- D. 19 Also asked in: AIEEE, CAT, Bank Exams, Bank Clerk, Bank PO
Correct Answer: 17
Explanation:
Since floor starts form the 1 therefore 2 will be the 1st floor.
Form 1 to 10 only 4,6,8,9,10 are not prime.
Form 11 to 20 only 14 ,16,18 are not prime also non of their digits are prime.
From 21 to 30 each number has a prime number so it must no be consider.
In between 40 to 49 we have to consider only 40,44,46,48,49.
50 to 59 follow either of the condition so we have too neglect it.
In between 60 to 68 60,64,66,68.
total option = 17.
- 3. 25 divided by 7
Options- A. 3.571
- B. 35.71
- C. 0.351
- D. 0.0357 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 3.571
Explanation:
Here we have 25 divided by 7.
25 will not go directly in 7
Hence, we get the result in decimals.
25/7 = 3.571.
- 4. The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is
Options- A. 17
- B. 29
- C. 43
- D. none Also asked in: Bank Exams
Correct Answer: none
- 5. A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could be the length of the fence in feet? (12 inches = 1 foot).
Options- A. 17
- B. 18
- C. `19
- D. 20 Also asked in: GRE
Correct Answer: 17
Explanation:
The fence will consist of one more post than there are chains. (e.g. P-c-P-c-P).
Therefore, a total length has to be a multiple of the length of the chain plus one post (5.5) plus one post extra.We have length = (5.5n + 0.5), where n can be any positive whole number. If n= 3, length =17
- 6. What is the simplified result of following the steps below in order? 1.Add 5y to 2x 2.Multiply the sum by 3 3.Substract x+y from the product
Options- A. 5x + 14y
- B. 5x + 16y
- C. 5x + 5y
- D. None Also asked in: GRE
Correct Answer: 5x + 14y
Explanation:
Step 1 :2x + 5y
Step 2 :3(2x + 5y) = 6x + 15y
Step 3 :(6x + 15y) - (x +y) = 6x + 15y - x - y (watch that last minus sign!)
This gives 5x + 14y
- 7. K men agree to donate a gift of Rs. L to trust. If three men drop out how much more will each have to contribute towards the purchase of the gift ?
Options- A. L / (k-3)
- B. k / (L-3)
- C. 2K / 3L-K
- D. 3L / K(K-3) Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 3L / K(K-3)
Explanation:
Intial contribution = L/K
After 3 men drop, then contribution =L/K-3
The amount more to pay in contribution =
=
- 8. From the given series of numbers, if half of the second highest number is subtracted from the third highest number, what will be the value ? 519 328 746 495 837
Options- A. 146
- B. 203
- C. 345
- D. 96 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 146
Explanation:
From the given series of numbers, if half of the second highest number is subtracted from the third highest number, what will be the value ?
Now arranging the given numbers in descending order.
837 746 519 495 328
519 - 746/2 = 519 - 373 = 146.
- 9. There is a 3 digited number. 3rd digit is the square root of the 1st digit. 2nd digit is the sum of 1st and 3rd. And that number is divisible by 2,3,6,7. What is that number?
Options- A. 121
- B. 943
- C. 462
- D. None Also asked in: Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 462
Explanation:
Assume that the number is taken as XYZ.
Condition 1 => Z = sq.root(x) => Possible digits of X is 1,4,9
Condition 2 => Y = X + Z
X Y Z
1 2 1
4 6 2
9 12 3 => (wrong because it is 4 digit.)
and 121 is not divisible by 2
The answer is 462.
- 10. Find the regular polygon whose interior angel is 150 more than exterior angle. note the total sum of interior and exterior angle should be 180 at one point ?
Options- A. 12
- B. 24
- C. 36
- D. 6 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 24
Explanation:
Sum of Interior angle is 180 .
and it is given that interior angle is 150 more than exterior,
so let exterior angle is x then interior will be x+150
now , interior + exterior =180
x+150+x=180
x=15
now , number of sides of polygon = 360 / exterior angle
n = 360 / 15
n = 24
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