GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Apr 2020, 04:13

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If f(n) = 1154*1156 for some integer, n, which of the following expres

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62468
If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

27 Nov 2019, 23:05
1
12
00:00

Difficulty:

95% (hard)

Question Stats:

38% (02:17) correct 62% (02:35) wrong based on 95 sessions

### HideShow timer Statistics

Competition Mode Question

If $$f(n) = 1154*1156$$ for some integer, n, which of the following expressions could be equal to $$f(n)$$?

A. $$3n - 2$$

B. $$5n - 2$$

C. $$5n + 3$$

D. $$7n - 2$$

E. $$11n + 10$$

Are You Up For the Challenge: 700 Level Questions

_________________
Director
Joined: 30 Sep 2017
Posts: 801
GMAT 1: 720 Q49 V40
GPA: 3.8
If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

Updated on: 13 Jan 2020, 07:01
5
$$f(n)=1154∗1156=(1155-1)*(1155+1)=1155^2-1=(3^2*5^2*7^2*11^2)-1$$

We understand that the units digit of $$f(n)=1155^2-1$$ must be 4.
(B) f(n)=5n−2 --> units digit of the result is either 3 or 8
(C) f(n)=5n+3 --> units digit of the result is either 3 or 8
Thus, we confidently eliminate choices (B) and (C), since both choices NEVER yield results with units digit of 4

A. f(n)=3n−2
$$f(n)=3n−2=(3^2*5^2*7^2*11^2)-1$$
$$3n=(3^2*5^2*7^2*11^2)+1$$
$$n=(3*5^2*7^2*11^2)+1/3$$
--> $$n$$ is NOT an integer, so we confidently eliminate choice (A), since $$n$$ has to be some integer

D. f(n)=7n−2
$$f(n)=7n−2=(3^2*5^2*7^2*11^2)-1$$
$$7n=(3^2*5^2*7^2*11^2)+1$$
$$n=(3^2*5^2*7*11^2)+1/7$$
--> $$n$$ is NOT an integer, so we confidently eliminate choice (D), since $$n$$ has to be some integer

E. 11n+10
$$f(n)=11n+10=(3^2*5^2*7^2*11^2)-1$$
$$11n=(3^2*5^2*7^2*11^2)-11$$
$$n=(3^2*5^2*7^2*11)-1$$
--> $$n$$ is an integer, so we are confident that choice (E) is the CORRECT ANSWER

Originally posted by chondro48 on 28 Nov 2019, 07:45.
Last edited by chondro48 on 13 Jan 2020, 07:01, edited 2 times in total.
##### General Discussion
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6051
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

27 Nov 2019, 23:58
1
1
the last two digits = 24
options a,b,c,d wont be possible
IMO E ; 11n+10

If f(n)=1154∗1156f(n)=1154∗1156 for some integer, n, which of the following expressions could be equal to f(n)f(n)?

A. 3n−2

B. 5n−2

C. 5n+3

D. 7n−2

E. 11n+10
SVP
Joined: 20 Jul 2017
Posts: 1510
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

28 Nov 2019, 00:18
1
1
1154 = 1155 - 1 = 11k - 1, for some positive value k
& 1156 = 1155 + 1 = 11k + 1

So, 1154*1156 = (11k - 1)(11k + 1) = (11k)^2 - 1 = 11(11k^2) - 1 = 11(n + 1) - 1 = 11n + 11 - 1 = 11n + 10
--> f(n) = 1154*1156 can be expressed of the form 11n + 10 for some value of 'n'

IMO Option E
Senior Manager
Joined: 01 Mar 2019
Posts: 485
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GMAT 1: 580 Q48 V21
GPA: 4
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

28 Nov 2019, 01:01
2
f(n)=1154∗1156 = 1155^2 -1

From options its visible that
1155 is divisible by 11....
so E: 1155^2 -1-10 = 1155^2 -11= which is divisible by 11

OA:E
CR Forum Moderator
Joined: 18 May 2019
Posts: 800
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

28 Nov 2019, 04:11
1
If f(n)=1154∗1156 for some integer, n, which of the following expressions could be equal to f(n)?

For could be true questions, we only need to prove that the function is true for just one case.

1154*1156 = 1,324,024

Testing with f(n)=3n-2
3n-2=1,334,024
3n=1,334,022
n=444,674
Since f(n) is defined for integers and the function f(n)=3n-2 yields an integer when equated to 1154*1156, then f(n) is true for 3n-2, when n=444,674

Manager
Joined: 31 Oct 2015
Posts: 95
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

28 Nov 2019, 05:22
2
1154x1156= 1334024

Of the five answer choices, We notice that the last term is -2 in three of the options. But after adding -2, the resulting number 1334026 is not divisible by 5 or 3 or 7. Therefore eliminate A,B and D.

We add -10 to the number and notice that the result,1334014 is divisble by 11. (divisibility test : difference between sum of odd digits and even digits should be divisble by 11)

VP
Joined: 24 Nov 2016
Posts: 1360
Location: United States
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

28 Nov 2019, 06:51
2
Quote:
If f(n)=1154∗1156 for some integer, n, which of the following expressions could be equal to f(n)?

A. 3n−2
B. 5n−2
C. 5n+3
D. 7n−2
E. 11n+10

$$f(n)=1154*1156=1155^2-1^2=1155^2-1$$

A. $$3n−2=1155^2-1…3n=1155^2+1…1155=factor(3)…1≠factor(3)$$
B. $$5n−2=1155^2-1…5n=1155^2+1…1155=f(5)…1≠f(5)$$
C. $$5n+3=1155^2-1…1155=f(5)…-1-3=-4…-4≠f(5)$$
D. $$7n−2=1155^2-1…1155=f(7)…-1+2=1…1≠f(7)$$
E. $$11n+10=1155^2-1…1155=f(11)…-1-10=-11…-11=f(11)…f(n)=11n+10=valid$$

Ans (E)
Senior Manager
Joined: 01 Feb 2017
Posts: 250
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

28 Nov 2019, 12:02
IMO, Ans A.

Both 1154 and 1156 when divided by 3 leaves a remainder of 2.

Posted from my mobile device
Director
Joined: 25 Jul 2018
Posts: 642
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

28 Nov 2019, 16:09
1
$$f(n) = 1154*1156= (1155 —1)(1155 +1)= 1155^{2}—1$$

$$1155^{2} —1= 11*11*105*105—1$$

E) $$11n + 10= 11n + 11—1= 11(n+1)—1$$

Posted from my mobile device
Intern
Joined: 23 Sep 2019
Posts: 38
Location: India
If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

13 Jan 2020, 09:09
1
f(n)=1154∗1156=(1155−1)∗(1155+1)=1155^2−1

A. 3n−2
B. 5n−2
C. 5n+3
D. 7n−2
E. 11n+10

For all options, put ->
3n - 2 = 1155^2−1
or
5n - 2 = 1155^2−1
and so on.

Except for E - 11n+10, you'll get a fraction for every other answer and since n is an integer, E is the answer.

Senior Manager
Joined: 01 Feb 2017
Posts: 250
If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

14 Jan 2020, 12:28
1154/3, Remainder= 2
1156/3, Remainder= 1
So, 1154*1156/3, Remainder= 2*1= 2
Therefore 3n+2 or 3n-1 can be the functions and not 3n-2 as we need to remove this Remainder to make it divisible by 3.

Similarly,
1154/5, Remainder= 4
1156/5, Remainder= 1
So, 1154*1156/5, Remainder= 4*1= 4
Therefore 5n+4 or 5n-1 can be the functions and not 5n-2 or 5n+3 as we need to remove this Remainder to make it divisible by 5.

Similarly,
1154/7, Remainder= 6
1156/7, Remainder= 1
So, 1154*1156/7, Remainder= 6*1= 6
Therefore 7n+6 or 7n-1 can be the functions and not 7n-2 as we need to remove this Remainder to make it divisible by 7.

Now,
1154/11, Remainder= 10
1156/11, Remainder= 1
So, 1154*1156/11, Remainder= 10*1= 10
Therefore 11n+10 or 11n-1 can be the function as we need to remove this Remainder to make it divisible by 11.

Hence, Ans E
DS Forum Moderator
Joined: 19 Oct 2018
Posts: 1445
Location: India
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

14 Jan 2020, 12:49
chondro48 You deserve way better than Q49

chondro48 wrote:
$$f(n)=1154∗1156=(1155-1)*(1155+1)=1155^2-1=(3^2*5^2*7^2*11^2)-1$$

We understand that the units digit of $$f(n)=1155^2-1$$ must be 4.
(B) f(n)=5n−2 --> units digit of the result is either 3 or 8
(C) f(n)=5n+3 --> units digit of the result is either 3 or 8
Thus, we confidently eliminate choices (B) and (C), since both choices NEVER yield results with units digit of 4

A. f(n)=3n−2
$$f(n)=3n−2=(3^2*5^2*7^2*11^2)-1$$
$$3n=(3^2*5^2*7^2*11^2)+1$$
$$n=(3*5^2*7^2*11^2)+1/3$$
--> $$n$$ is NOT an integer, so we confidently eliminate choice (A), since $$n$$ has to be some integer

D. f(n)=7n−2
$$f(n)=7n−2=(3^2*5^2*7^2*11^2)-1$$
$$7n=(3^2*5^2*7^2*11^2)+1$$
$$n=(3^2*5^2*7*11^2)+1/7$$
--> $$n$$ is NOT an integer, so we confidently eliminate choice (D), since $$n$$ has to be some integer

E. 11n+10
$$f(n)=11n+10=(3^2*5^2*7^2*11^2)-1$$
$$11n=(3^2*5^2*7^2*11^2)-11$$
$$n=(3^2*5^2*7^2*11)-1$$
--> $$n$$ is an integer, so we are confident that choice (E) is the CORRECT ANSWER

Director
Joined: 07 Mar 2019
Posts: 910
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres  [#permalink]

### Show Tags

14 Jan 2020, 21:16
I do agree.
Some of his explanation are very good.
nick1816 wrote:
chondro48 You deserve way better than Q49

chondro48 wrote:
$$f(n)=1154∗1156=(1155-1)*(1155+1)=1155^2-1=(3^2*5^2*7^2*11^2)-1$$

We understand that the units digit of $$f(n)=1155^2-1$$ must be 4.
(B) f(n)=5n−2 --> units digit of the result is either 3 or 8
(C) f(n)=5n+3 --> units digit of the result is either 3 or 8
Thus, we confidently eliminate choices (B) and (C), since both choices NEVER yield results with units digit of 4

A. f(n)=3n−2
$$f(n)=3n−2=(3^2*5^2*7^2*11^2)-1$$
$$3n=(3^2*5^2*7^2*11^2)+1$$
$$n=(3*5^2*7^2*11^2)+1/3$$
--> $$n$$ is NOT an integer, so we confidently eliminate choice (A), since $$n$$ has to be some integer

D. f(n)=7n−2
$$f(n)=7n−2=(3^2*5^2*7^2*11^2)-1$$
$$7n=(3^2*5^2*7^2*11^2)+1$$
$$n=(3^2*5^2*7*11^2)+1/7$$
--> $$n$$ is NOT an integer, so we confidently eliminate choice (D), since $$n$$ has to be some integer

E. 11n+10
$$f(n)=11n+10=(3^2*5^2*7^2*11^2)-1$$
$$11n=(3^2*5^2*7^2*11^2)-11$$
$$n=(3^2*5^2*7^2*11)-1$$
--> $$n$$ is an integer, so we are confident that choice (E) is the CORRECT ANSWER

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Re: If f(n) = 1154*1156 for some integer, n, which of the following expres   [#permalink] 14 Jan 2020, 21:16
Display posts from previous: Sort by