If 100

Question

If 100<x<199 and 10<y<100, then the product xy CANNOT be equal to:

A. 19,104
B. 19,303
C. 19,356.732
D. 19,502
E. 19,909

chetan2u · Accepted Answer

ans E.. 
Don't get overwhelmed with huge numbers. 
As numbers are in some order, the answer will be either A and E as we look for the range.

100<x<199 and 10<y<100
 Lowest: x=100 and y=10
Largest: x=199 and y=100 
 100*10<xy<199*100 
 1000<xy<19900

the values of xy has to be between 1000 and 19900
All options except E are within the given range.

only E is higher than possible values...

vedavyas9 · Answer

max value of x - 198
max value of y - 99

max value of xy - 19602

only E is greater

EMPOWERgmatRichC · Answer

Hi vedavyas9,

On Test Day, you have to be very careful about your assumptions.

In this question, we are NOT told that X and Y have to be integers, so you cannot assume that they are.

X could be 198.999999999999etc
Y could be 99.99999999999etc

While this might seem like a nitpick point (as it didn't matter on this question), you WILL be tested on this concept/possibility on Test Day, so you have to remember what restrictions the question gave you (and what it did NOT give you).

GMAT assassins aren't born, they're made,
Rich

vedavyas9 · Answer

totally forgot that point EMPOWERgmatRichC . will keep that in mind. Thank you

LaxAvenger · Answer

For the same reason you can just test with

x= 199
y=100

x*y = 19900

still lower than 19909

buddyisraelgmat · Answer

100<x<199 
and 
10<y<100

Since ALL +ve & same sign  , directly multiply,

1000< xy< 19900

The only product which does NOT lie between 1000 and 19900 is E (19,909)

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Correct Answer: (E)

Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 100 * 10. The largest value must be less than 199 * 100. This means that 1000 < xy < 19,900. (E) is outside of this range, so it is not a possible product of xy.

PareshGmat · Answer

Maximum possible value of x = 198

Maximum possible value of y = 99

xy = 99 * 198 = (100-1)^2 * 2

= (10000 - 200 + 1)*2

= 9801 * 2

= 19602

Only option E is out of range

Answer = E

tallyho_88 · Answer

i have done this question using a simple logic.
the ans has to be E because it is the largest no. if the option would have been d then e would also would have been out of range. We need only one no. out of range and hence E.

tallyho_88 · Answer

one quick way that i solved this is to check which is the biggest no. E has to be the only option...for instance if the answer would have been D then E would also have been out of range. We have to select only one option. Hence, E. 
Correct me if i'm wrong.

chetan2u · Answer

Yes your approach is correct BUT ensure that the lowest number is also within the lower limit..
say I gave you a choice as 909 and removed E..
you won't choose the largest here..

so NONE of central values can be the answer..
JUST check for smallest and largest..

MuditG · Answer

if one factorizes the first option it comes to 2^5 * 3 * 199 = 96 * 199 = 19104
y can be equal to 96 but x cannot be 199 as it has to < 199.

So xy cannot equal 19104 also.

stonecold · Answer

Highest value => 1000
Lowest value => 199900
Since it does not satisfy the boundary condition => Smash E

Heseraj · Answer

Should the upper domain of the two sets (X and Y) be equal to 199 and 99, one can have: 199*(100-1)=19900-199=19701 (the Max product of any two number within the two sets.

CEdward · Answer

If 100<x<199 and 10<y<100, then the product xy CANNOT be equal to:

A. 19,104
B. 19,303
C. 19,356.732
D. 19,502
E. 19,909

It is immediately clear that the answer choices are very large...close to 19900. The inequality suggests that even if x could equal 199 and y could equal 100 (they can't)...the maximum value they can take on is 19900. The only number that clearly defies this logic is 19909.

Answer is E.

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If 100<x<199 and 10<y<100, then the product xy CANNOT be equal to:

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If 100<x<199 and 10<y<100, then the product xy CANNOT be equal to:

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