GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Dec 2018, 12:08

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• ### Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# If x, y, b and t are all positive integers, x = y/5 + 2

Author Message
TAGS:

### Hide Tags

Current Student
Affiliations: Scrum Alliance
Joined: 09 Feb 2010
Posts: 79
Location: United States (MI)
Concentration: Strategy, General Management
GMAT 1: 600 Q48 V25
GMAT 2: 710 Q48 V38
WE: Information Technology (Retail)
If x, y, b and t are all positive integers, x = y/5 + 2  [#permalink]

### Show Tags

Updated on: 04 Sep 2015, 06:14
3
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:42) correct 34% (02:33) wrong based on 73 sessions

### HideShow timer Statistics

If x, y, b and t are all positive integers, $$x = \frac{y}{5} + 2$$, and $$t = \frac{b}{7} + 4$$, is $$b(t^{xy})$$ an even number?

(1) 3.5t - 2 is even
(2) b/t is even

Source: - Prep4GMAT iOS app

_________________

Originally posted by hideyoshi on 03 Sep 2015, 12:35.
Last edited by hideyoshi on 04 Sep 2015, 06:14, edited 1 time in total.
CEO
Joined: 20 Mar 2014
Posts: 2631
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If x, y, b and t are all positive integers, x = y/5 + 2  [#permalink]

### Show Tags

03 Sep 2015, 18:20
hideyoshi wrote:
If $$x,y,b$$ and $$t$$ are all positive integers, $$x = \frac{y}{5} + 2$$, and $$t = \frac{b}{7} + 4$$, is $$b(t^{xy})$$ an even number?

1). $$3.5t - 2$$ is even
2). $$\frac{b}{t}$$ is even

When you specify the tag for source of "source-other please specify", make sure to specify the source.

x=y/5 +2,
t=b/7 + 4,

is $$b(t^{xy})$$ = even ?

Per statement 1, 3.5t-2 = even ---> 7t/2-2=even ---> 7t/2 = even +2 = even ----> 7t = even*2 = even ---> t has to be even

Also, from the given statements, t=b/7 + 4 ----> 7t=b+28 ---> even - 28 = b ----> b = even . Thus for whatever values of x,y, $$bt^{xy}$$ = even . Thus this statement is sufficient.

Per statement 2, b/t=even ---> 2 cases possible (think of 6/3 or 4/2)

case 1: b=even, t=odd
case 2: b = even, t = even

Thus, in either of the 2 cases, b = even and hence for whatever values of x,y, $$bt^{xy}$$ = even . Thus this statement is sufficient.

Both statements are sufficient individually, making D as the correct answer.
Math Expert
Joined: 02 Sep 2009
Posts: 51280
Re: If x, y, b and t are all positive integers, x = y/5 + 2  [#permalink]

### Show Tags

03 Sep 2015, 22:14
hideyoshi wrote:
If x, y, b and t are all positive integers, $$x = \frac{y}{5} + 2$$, and $$t = \frac{b}{7} + 4$$, is $$b(t^{xy})$$ an even number?

(1) 3.5t - 2 is even
(2) b/t is even

Similar questions to practice:
if-r-s-and-t-are-all-positive-integers-what-is-the-remainder-of-2-p-187298.html
if-r-s-and-t-are-all-positive-integers-what-is-the-136746.html
_________________
Board of Directors
Joined: 17 Jul 2014
Posts: 2616
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If x, y, b and t are all positive integers, x = y/5 + 2  [#permalink]

### Show Tags

18 Feb 2016, 19:07
hideyoshi wrote:
If x, y, b and t are all positive integers, $$x = \frac{y}{5} + 2$$, and $$t = \frac{b}{7} + 4$$, is $$b(t^{xy})$$ an even number?

(1) 3.5t - 2 is even
(2) b/t is even

Source: - Prep4GMAT iOS app

we need to remember that:
e-e=e
o-o=e.
e-o=o
o-e=o

the question really asks whether t is even, since we know 100% that x and y are positive integers. thus, xy must be a positive integer, and the power will neither be negative nor fractional.

1. 3.5t-2=e.
only e-e=e. this only means that 3.5t is even. it can be even only when t is even.
sufficient.

2. b/t=e
b=7t-28
b/t=7-28/t.
this is even.
we know that even is only when o-o.
thus, it must be true that 28/t is odd.
therefore, we know for sure that t must be even.
(possible variations: 28/1; 28/2; 28/4 - we can see that only the last one actually satisfies the condition)
sufficient.

D
Math Expert
Joined: 02 Aug 2009
Posts: 7112
Re: If x, y, b and t are all positive integers, x = y/5 + 2  [#permalink]

### Show Tags

18 Feb 2016, 19:19
mvictor wrote:
hideyoshi wrote:
If x, y, b and t are all positive integers, $$x = \frac{y}{5} + 2$$, and $$t = \frac{b}{7} + 4$$, is $$b(t^{xy})$$ an even number?

(1) 3.5t - 2 is even
(2) b/t is even

Source: - Prep4GMAT iOS app

we need to remember that:
e-e=e
o-o=e.
e-o=o
o-e=o

the question really asks whether t is even, since we know 100% that x and y are positive integers. thus, xy must be a positive integer, and the power will neither be negative nor fractional.

1. 3.5t-2=e.
only e-e=e. this only means that 3.5t is even. it can be even only when t is even.
sufficient.

2. b/t=e
b=7t-28
b/t=7-28/t.
this is even.
we know that even is only when o-o.
thus, it must be true that 28/t is odd.
therefore, we know for sure that t must be even.

(possible variations: 28/1; 28/2; 28/4 - we can see that only the last one actually satisfies the condition)
sufficient.

D

Hi,
Although you are correct with your solution
just two points on your solution ..
1) is $$b(t^{xy})$$ an even number?
this means any of the b or t, if even, is sufficient... and just not only t
2) related to the above point
since b/t is even as per statement 2, this clearly means b is even and we dont require to see any further if t is even or not..
since b is even, the eq $$b(t^{xy})$$ will be even

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Non-Human User
Joined: 09 Sep 2013
Posts: 9207
Re: If x, y, b and t are all positive integers, x = y/5 + 2  [#permalink]

### Show Tags

19 Oct 2017, 03:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x, y, b and t are all positive integers, x = y/5 + 2 &nbs [#permalink] 19 Oct 2017, 03:00
Display posts from previous: Sort by