The number of distinct integers in the collection

Question

GMATBusters’ Quant Quiz Question -5 
The number of distinct integers in the collection  ,  ,  ,…,  , where   denotes the largest integer not exceeding x, is 
(a) 20 
(b) 18 
(c) 17 
(d) 15
(e) 12

GMATBusters · Answer

Official Solution 
The number of distinct integers in the collection  ,  ,  ,…,  , where   denotes the largest integer not exceeding x, is

Greatest Integer Function   indicates an integral part of the real number x which is nearest and smaller integer to x. if x is an integer, then  =x. 
  =  = 100
  =   = 50
  =   =33
  = 25
  = 20
  ~ 16.something = 16
  ~14.someting =14
  ~ 12.5 =12
  ~11.11 =11
  = 10
  ~ 9.09 =9
  ~ 8.something =8
  ~ 7.something =7
  ~ 7.something =7
  ~ 6.something =6
  ~ 6.something =6
  ~ 5.something =5
  ~ 5.something =5
  ~ 5.something =5
  = 5

Hence the number of different integers is  15.

Kinshook · Answer

Asked: The number of distinct integers in the collection  ,  ,  ,…,  ,  where   denotes the largest not exceeding x, is  
(a) 20 
(b) 18 
(c) 17 
(d) 15
(e) 12

= 100
  = 50
  = 33
  = 25
  = 20
  = 16
  = 14
  = 12
  = 11
  = 10
  = 9
  = 8
  = 7
  = 7
  = 6
  = 6
  = 5
  = 5
  = 5
  = 5

Number of unique distinct integers = 12

IMO E

Hi  GMATBusters 
Please correct highlighted portion as 
where   denotes the largest  integer  not exceeding x, is

ashwini2k6jha · Answer

given, , , ,                 
ie simplifying ,100,50,33,25,20,16,14,12,11.10,9,8,7,7,6,6,5,5,5,5
Hence distinct integers=15

Raxit85 · Answer

The number of distinct integers in the collection [100/1], [(100/2], [100/3],…,[100/20] , where [x] denotes the largest integer not exceeding x, is
(a) 20
(b) 18
(c) 17
(d) 15
(e) 12

Ans. D (a) 20 (b) 18 (c) 17 (d) 15 (e) 12

techwave · Answer

Answer:D

denotes the largest not exceeding x. meaning the decimal is truncated and the resulting integer is taken into consideration.

=100

=50

=33
....
..
 =5
 =5

100,50,33,25,20,16,14,12,11,10,9,8, 7,7,6,6,5,5,5,5.
Distinct integer values = 15

Archit3110 · Answer

for the given collection of integers we get following integer values
 =1
 =50
.
.
until   it would be unique
there after at   ,   = 7
 ,  =6
  ,   ,  ,  =5

total distinct digits ; 15
IMO D

The number of distinct integers in the collection  ,  ,  ,…,  , where   denotes the largest integer not exceeding x, is
(a) 20
(b) 18
(c) 17
(d) 15
(e) 12

AnirudhaS · Answer

Answer is 15. But I solved all the 20 terms which is time consuming. Would like to know if there is any easier way to do this.

gurmukh · Answer

1/13=1/14
1/15=1/16
1/17=1/18=1/19=1/20
So 15 different integers are there.
Option D is the answer.

Posted from my mobile device

shameekv1989 · Answer

The number of distinct integers in the collection  ,  ,  ,…,  , where   denotes the largest integer not exceeding x, is
(a) 20
(b) 18
(c) 17
(d) 15
(e) 12

= 100
  = 50
  =   = 33
.....

=   = 5
  =   = 5
  =   = 5

Basically we need to take the quotient only when divided by 100. i.e. the combinations of x*y <= 100; where y is the value we are seeking

Thus, we will have all the combinations as :- 
1*100, 2*50, 3*33, 4*25, 5*20, 6*16, 7*14, 8*12, 9*11, 10*10, 11*9, 12*8, 13*7, 14*7, 15*6, 16*6, 17*5, 18*5, 19*5, 20*5

- There are 15 distinct values of y

Answer - D

GMATinsight · Answer

= 100
 = 50
  = 33
  = 25
  = 20
  = 16
  = 14
  = 12
  = 11
  = 10
  = 9
  = 8
   = 7
  = 7 
   = 6
  = 6
  = 6 
   = 5
  = 5
  = 5

i.e. 15 different integers

Answer: Option D

bM22 · Answer

Answer E

Solution
  - denotes the greatest integer not exceeding x, so all the numbers in the given will be converted to their respective decimal forms.
 when we do an approx calculation
  = 100, 
  = 50, 
  = 33,
  = 25,
  = 20,
  = 16,
  = 14,
  = 12,
  = 11,
  = 10,

= 9, 
  = 8,
  = 7,
  = 7,
  = 6,
  = 6,
  = 5,
  = 5,
  = 5,
  = 5

So we can see that starting from  , the greatest integer of   becomes constant and not distinct.

So as per me, the number of distinct integers in the collection: 12.
 Answer E

ArunSharma12 · Answer

The number of distinct integers in the collection  ,  ,  ,…,  , where   denotes the largest integer not exceeding x, is
(a) 20
(b) 18
(c) 17
(d) 15
(e) 12

= 100,  =50, =33, =25, =20...  =10.. =5 
concentrating on highlighted part, between   &   (inclusive) only 5 integer values can be distinct.
this takes the total straight down to 15.
Ans: D

The number of distinct integers in the collection

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The number of distinct integers in the collection

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards