There are 1600 jelly beans divided between two jars, X and Y. If the

Question

There are 1600 jelly beans divided between two jars, X and Y. If there are 100 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?

A. 375

B. 950

C. 1150

D. 1175

E. 1350

EMPOWERgmatRichC · Accepted Answer

Hi All,

This question can certainly be solved with Algebra; with 2 variables and 2 unique equations, it's just a matter of translating the text into equations and doing "system" math.

The answers are numbers though, and there is a logical pattern in the prompt that you can use to quickly TEST THE ANSWERS.

We're told that there are a total of 1600 marbles in two jars. Jar X has 100 less than THREE TIMES the number of marbles in Jar Y. We're asked for the number of marbles in Jar X.

100 marbles is a relatively small amount, compared to the 1600 total marbles. If we ignore the "100" and do a rough estimation, Jar X would be about 1200 and Jar Y would be about 400 (which matches the information about THREE TIMES the number of marbles). Since we DO have to factor in the 100 marbles though, the number of marbles in X has to be LESS than 1200. With this deduction, the answer has to be C or D.

Let's TEST C (since it looks like the "nicer" number to deal with).

IF....
X = 1150 marbles
X + 100 = 1250
1250/3 = 416.6666 marbles
1150 + 416.66666 is NOT 1600 total marbles.
Eliminate C.

Final Answer:  D

Here's the proof though:

IF....
X = 1175 marbles
X + 100 = 1275
1275/3 = 425
1175 + 425 = 1600 marbles

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

NATABERI · Answer

x+y=1600 , X=1600-Y
x+100=3y, 1700=4Y
Y=425

x=1600-y=1600-425=1175 
D

sashiim20 · Answer

Let Jelly beans in jar  X = x  and  Y = y

x + y = 1600  ----- ( i )

Given jar  X  has  100  fewer jelly beans than three times the number of beans in jar  Y .

Therefore;  x + 100 = 3y

x = 3y - 100

Substituting value of  x  in equation ( i ), we get;

3y - 100 + y = 1600

4y = 1600 + 100 = 1700

y = \frac{1700}{4} = 425

Substituting value of  y  in equation ( i ), we get;

x + 425 = 1600

x = 1600   -   425 = 1175

Answer D

hsn81960 · Answer

Hi,
If X has 100 fewer jelly beans than three times the number of beans in jar Y.
Then why did we write X+100 ?
Shouldnt it be X-100?

Mrpd · Answer

x+y=1600 (I)

And

3*y = x-100

Reorganizing it

3*y-100 = x (II)

Subs. (II) in (I)

3*y-100+y=1600
4*y=1700
y=425

Then

x=1175

Ans (D)

hsn81960 · Answer

3*y = x-100

Reorganizing it

3*y-100 = x (II)

But if -100 go to the other side of equation, shouldnt it become +100?

Mrpd · Answer

Sorry, it's 3*y = x + 100 instead

ScottTargetTestPrep · Answer

We can let y = the number of jelly beans in jar Y; thus, there are 3y - 100 jelly beans in jar X. We can now create the equation:

3y - 100 + y = 1600

4y = 1700

y = 425

Therefore, there are 3(425) - 100 = 1275 - 100 = 1175 jelly beans in jar X.

Answer: D

saumilshah1989 · Answer

x+y=1600 , X=1600-Y
x+100=3y, 1700=4Y
Y=425

x=1600-y=1600-425=1175 
D

GmatPoint · Answer

Given, x + y = 1600
Also, x + 100 = 3*y

After subtracting the two equations,
y - 100 = 1600 - 3y
4y = 1700
y = 425

Thus, x = 1600 - 425 = 1175

Thus, the correct option is D.

Paras96 · Answer

There are 1600 jelly beans divided between two jars, X and Y. If there are 100 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?

Let the no. of jelly beans in Jar Y = n
Therefore, the no. of jelly beans in Jar X = 3n - 100

=> n + 3n - 100 = 1600
=> 4n = 1700
=> n = 425

Therefore, the no. of jelly beans in Jar X = 3n - 100 = 3x425 - 100 = 1275 - 100 = 1175

Hence D

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