Let 35,043 = a
& 25,043 = b

So, A = a(b+387)
& B = (a+387)b

Find out A - B = ab + 387a - ab - 387b
i.e. A - B = 387(a-b)
i.e. A - B = +ve value

Hence, A > B
answer is A

Solve such questions based on assumption,

Col. A: 35,043 x 25,430
re-write as 35 x 25.4 x \(10^6\) = 889 x \(10^6\)

Col. B: 35,430 x 25,043
re-write as 35.4 x 25 x \(10^6\) = 885 x \(10^6\)

Hence, option A

Hi,

You can solve this using a calculator without writing a single number on paper using the below steps:
1. Type Qty A i.e. 35,043∗25,430 and press equal to and then press M+ this is to store the value in the calculator , something similar to saving files.
2. Type Qty B on calculator i.e 35,430∗25,043 and press equal to and press M- (See the below note to know the difference between M+ & M-).

Now, using M+ and M- is similar to using a + &- rather, you don't have to type in the values it automatically gets calculated.
Eg. you type in 2 on the calculator and press M+ and then type in 1 and press M- and then in order to view the final calculation of the two numbers press MRC (Memory recall) you'll get the value as 1. Instead of 1 if you type 3 you'll get -1.

Similarly if you get a negative value the value stored in M->M+ whereas if you get a positive value, the value stored in M+>M-(You better try this to get a clearer picture)

Thus for this question, I get a positive value (M+>M-) I stored QTY A in M+

IMO A

Note: M+ stores the value as they are displayed on calculator whereas M- adds a "-" sign to the value. So be diligent while using M- to perform operation.

Happy to help!

Is there M- on the on-screen calculator of GRE?

I DO NOT REMEMBER THIS, FRANKLY

Hi,

Apologies!! There is no M- in the GRE on screen calculator.

Here's another solution that uses matching operations AND allows us to use the on-screen calculator
Given:
Quantity A: \((35,043)(25,430)\)
Quantity B: \((35,430)(25,043)\)

Divide both quantities by \(1000\) to get:
Quantity A: \((35.043)(25,430)\)
Quantity B: \((35.430)(25,043)\)

Divide both quantities by \(1000\) (again) to get:
Quantity A: \((35.043)(25.430)\)
Quantity B: \((35.430)(25.043)\)

At this point, the numbers are small enough to use the calculator to get following
Quantity A: \(891.143...\)
Quantity B: \(887.273...\)

Answer: A

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Here’s a fast and effective way to solve this without calculator

Step 1: Break Down the Numbers
First, re-write each quantity by splitting the numbers into their large, round parts and the smaller "leftovers."

• Quantity A: (35,000 + 43) * (25,000 + 430)
• Quantity B: (35,000 + 430) * (25,000 + 43)

Step 2: Recognize the Common Terms
If you were to expand these using the FOIL method, you'd notice that the First (`35,000 * 25,000`) and Last (`43 * 430`) products are the same for both quantities. Since they are identical, we can ignore them for the comparison.

Step 3: Compare the "Cross-Products"
The only parts that differ are the "Outer" and "Inner" terms (the cross-products). Let's isolate them for each quantity:

• Quantity A's Cross-Products: (35,000 * 430) + (43 * 25,000)
• Quantity B's Cross-Products: (35,000 * 43) + (430 * 25,000)

Step 4: The Final Insight
Now, just compare the two sums. Notice that in Quantity A, the largest base number (35,000) is multiplied by the largest "leftover" (430). In Quantity B, the largest base number is multiplied by the smallest "leftover" (43).

The term `35,000 * 430` is significantly larger than the other terms, which gives Quantity A a decisive advantage.

Conclusion:
Because the sum of its cross-products is larger, Quantity A is greater.