BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Need Help in DS problems

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 190
Joined: Thu Jan 14, 2010 8:29 pm
Thanked: 2 times

Need Help in DS problems

by phoenix9801 » Thu Jun 10, 2010 2:27 am
Would you please use Picking Numbers and/or Straightforward Math to solve these questions Please be simple. (not Algebra). Thanks.


1- If R,S, and T are nonzero integers, is R^5 S^3 T^4 ?

(1) R T is negative

(2) S is Negative


2- If X is a positive integers, is square root X an integer?

(1) square root 4x is an integer

(2) Square root 3x is not an integer
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 147
Joined: Tue Aug 25, 2009 7:57 pm
Location: New York City
Thanked: 76 times
Followed by:17 members
GMAT Score:770

by Rich@VeritasPrep » Thu Jun 10, 2010 3:51 am
The first question looks incomplete. Could you clarify what the question is?

For the second question:

2- If X is a positive integers, is square root X an integer?

(1) square root 4x is an integer

Plug in x=1, which works because sqrt(4*1) is an integer

Next number that works is x=4, which works because sqrt(4*4) is an integer.

Next number that works is x=9, which works because sqrt(4*9) is an integer.

If you plug in x=1,4,9 back into the prompt, you'd find that sqrt(x) will always be an integer.

But the faster way to realize this is to notice that you can break sqrt(4x) down:

sqrt(4x) = sqrt(4) * sqrt(x) = 2*sqrt(x)

So (1) basically tells us that 2*sqrt(x) is an integer. If x is an integer, then the only way 2*sqrt(x) could be an integer is if sqrt(x) is an integer. SUFFICIENT.



(2) Square root 3x is not an integer

Plug in x=1, which works because sqrt(3*1) is not an integer.

If we plug x=1 back into the prompt, we find that sqrt(x) is an integer.

Plug in x=2, which works because sqrt(3*2) is not an integer.

If we plug x=2 back into the prompt, we find that sqrt(x) is not an integer.

INSUFFICIENT
Rich Zwelling
GMAT Instructor, Veritas Prep
Top
Master | Next Rank: 500 Posts
Posts: 190
Joined: Thu Jan 14, 2010 8:29 pm
Thanked: 2 times

by phoenix9801 » Thu Jun 10, 2010 3:57 am
raz1024 wrote:The first question looks incomplete. Could you clarify what the question is?

For the second question:

2- If X is a positive integers, is square root X an integer?

(1) square root 4x is an integer

Plug in x=1, which works because sqrt(4*1) is an integer

Next number that works is x=4, which works because sqrt(4*4) is an integer.

Next number that works is x=9, which works because sqrt(4*9) is an integer.

If you plug in x=1,4,9 back into the prompt, you'd find that sqrt(x) will always be an integer.

But the faster way to realize this is to notice that you can break sqrt(4x) down:

sqrt(4x) = sqrt(4) * sqrt(x) = 2*sqrt(x)

So (1) basically tells us that 2*sqrt(x) is an integer. If x is an integer, then the only way 2*sqrt(x) could be an integer is if sqrt(x) is an integer. SUFFICIENT.



(2) Square root 3x is not an integer

Plug in x=1, which works because sqrt(3*1) is not an integer.

If we plug x=1 back into the prompt, we find that sqrt(x) is an integer.

Plug in x=2, which works because sqrt(3*2) is not an integer.

If we plug x=2 back into the prompt, we find that sqrt(x) is not an integer.

INSUFFICIENT
For question 1 it says [yes there was a typo]

1- If R,S, and T are nonzero integers, is R^5 S^3 T^4 Negative?

(1) R T is negative

(2) S is Negative
Top
User avatar
GMAT Instructor
Posts: 147
Joined: Tue Aug 25, 2009 7:57 pm
Location: New York City
Thanked: 76 times
Followed by:17 members
GMAT Score:770

by Rich@VeritasPrep » Thu Jun 10, 2010 4:21 am
1- If R,S, and T are nonzero integers, is R^5 S^3 T^4 Negative?

T^4 will never be negative, since an even exponent is involved. R^5 and S^3 are either positive or negative depending on the signs of R and S themselves. R will have the same sign as R^5, since an odd exponent is involved. Same for S and S^3.

For the entire product to be negative, either R^5 must be positive and S^3 negative, or vice versa. If both R^5 and S^3 have the same sign, then the entire product will be positive.

So the question really becomes: Do R and S have opposite signs?

(1) R T is negative

Nothing about S. INSUFFICIENT

(2) S is Negative

Nothing about R. INSUFFICIENT

Together, (1) and (2) tell us that S is negative and RT is negative. We have the sign of S, but do we necessarily have the sign of R?

Well, we know RT is negative. That means R and T have opposite signs. We know that T^4 is positive, but T itself could be either positive or negative. Therefore, R could be either positive or negative.

INSUFFICIENT
Rich Zwelling
GMAT Instructor, Veritas Prep
Top
Senior | Next Rank: 100 Posts
Posts: 90
Joined: Thu Jan 14, 2010 5:42 am
Thanked: 2 times

by dkumar.83 » Thu Jun 10, 2010 4:24 am
1- If R,S, and T are nonzero integers, is R^5 S^3 T^4 ?

(1) R T is negative

(2) S is Negative

Lets see statement 2, S in Negative.

S^3 will be negative.
T^4 will always be positive.
R^5 will be either positive or negative, depending on the value of R which is unknown.
Hence its INSUFFICIENT.

Statement 1, RT is negative. This implies either R or T is negative. Since it doesn't touch S we, in anycase, can't say what will be S^3, hence even this is INSUFFICIENT.

Now taking both together.
S^3 is negative (from statement 1).
One out of R or T is also negative (which one is not known.) Hence its NOT POSSIBLE to find an answer using both the statements as well.
Top
Post new topic Post Reply
• Page 1 of 1