Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 03 May 2015, 04:36

### 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 June
Open Detailed Calendar

# X and y are integers, are they even?

Author Message
TAGS:
Manager
Joined: 03 Jul 2006
Posts: 178
Followers: 1

Kudos [?]: 8 [0], given: 0

X and y are integers, are they even? [#permalink]  05 Oct 2006, 17:07
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
PS: not sure of the answers

1)X and y are integers, are they even?

1). 2y-x=x^2-y^2

2). X is even.

IMO: C

2)M=O+P+Q, where O, P, and Q are consecutive positive integer; M=R*S*T, where R, S and T are positive consecutive integers. What is the remainder when M is divided by 5?
1). When O is divided by 5, the remainder is 1
2). When R is divided by 5, the remainder is 1

??
Manager
Joined: 28 Aug 2006
Posts: 245
Location: Albuquerque, NM
Followers: 1

Kudos [?]: 1 [0], given: 0

For first question

X(X+1) = Y(Y+2)

LHS is always even since either X is even or X + 1 is even (X is odd in that case)

Thus RHS has to be even and Y has to be even

Thus statement 1 tells only about Y and two about X thus together the answer is C

Let me work on the second question
Manager
Joined: 28 Aug 2006
Posts: 245
Location: Albuquerque, NM
Followers: 1

Kudos [?]: 1 [0], given: 0

For second question, the answer is D

P has to be of the form 5n + 1 so does r

the sum is 15 N +6 leaves a remainder 1 when divided by 5

and product = 125 n^3 + 150 n^2 + 60 N +6 leaves a remainder 1 when divided by 5
Manager
Joined: 01 Oct 2006
Posts: 242
Followers: 1

Kudos [?]: 5 [0], given: 0

O and R can have either 1 or 6 in unit's digit.
1)
if O is of the form X1 (i.e unit's digit 6, rest can be any numbers)
M= O+P+Q = X1+X2+X3 = Y6.
The unit's digit of M will be 6, so when M is divided by 5 remainder is 1.
if O is of the form X6:
M=O+P+Q = X6+X7+X8= Y1
remainder will be 1.
so, (1) is enough to answer

2) When R is of form X1
M=RxSxT = X1.X2.X3 = Z6 // so M%5 = 1
When R is of form X6:
M= X6.X7.X8 = Z6 // so M%5 = 1

hence D is the answer. Either of them is enough to answer
SVP
Joined: 05 Jul 2006
Posts: 1519
Followers: 5

Kudos [?]: 115 [0], given: 39

1)X and y are integers, are they even?

1). 2y-x=x^2-y^2

2). X is even.

from one

2y-x (could be even or odd)

x^2 - y^2 ( could be even or odd).........insuff

from two

insuff

both together
x is even

thus 2y-x is even

and thus x^2 - y^2 = even - ??? = even thus y^2 is even and hus x,y even

2)M=O+P+Q, where O, P, and Q are consecutive positive integer; M=R*S*T, where R, S and T are positive consecutive integers. What is the remainder when M is divided by 5?
1). When O is divided by 5, the remainder is 1
2). When R is divided by 5, the remainder is 1

M=O+P+Q

FROM ONE IF O = 5X+1 THUS
P AND Q ARE 5X+2 , 5X+3

ADD THE REMAINDERS = 6 DEVIDE BY FIVE REMAINDER IS 1....SUFF

M=R*S*T

R = 5X+1 THUS S,T ARE 5X+2, 5X+3

(5X+1)(5X+2) = 25X^2+ 15X + 2

(25X^2+ 15X + 2)(5X+3) = 125X^3+75X^2+10X+75X^2+45X+6

THUS REMAINDERR IS 6/5 = 1 .......SUFF

Similar topics Replies Last post
Similar
Topics:
1 If x and y are integers, is y an even integer? 5 05 Jul 2014, 02:05
1 Is (x-y)*(x+y) an even integer? 5 26 May 2011, 09:19
3 Is (x-y)*(x+y) an even integer? 3 18 Feb 2011, 05:41
6 If X and Y are integers, is Y an even integer? 6 26 Dec 2008, 23:34
Is X*Y*Z an even integer 1. X * Y is an even integer 8 01 Jul 2008, 21:10
Display posts from previous: Sort by