BTGModeratorVI wrote: ↑Fri Jul 03, 2020 7:04 am
The symbols $ and # each represent one of the following operations: addition, subtraction, multiplication or division. What is the value of 1 $ 1 # 1?
1) 2 $ 2 # 2 = 3
2) 3 $ 2 # 1 = 5
Answer:
A
Source: GMAT Prep Now
To know that value of $ and #, we must know what operation $ and # represent.
Let's take each statement one by one.
1) 2 $ 2 # 2 = 3
• Say $ = multiplication; So, we have 2 x 2 # 2 = 3.
Given that # is one among addition, subtraction, multiplication or division, 2 x 2 # 2 cannot be equal to 3. Pl. try yourself. So, $ cannot be multiplication.
• Say $ = division; So, we have (2/2) # 2 = 3 => 1 # 2 = 3
=> # must be addition.
So, we have if $ = division, then # is addition.
Thus, 1 $ 1 # 1 = 1/1 + 1 = 2 ---(1)
• Say $ = addition; So, we have 2 + 2 # 2 = 3.
# cannot be subtraction since 2 + 2 –2 ≠ 3;
# cannot be addition since 2 + 2 + 2 ≠ 3;
# cannot be multiplication since 2 + 2 x 2 ≠ 3;
# cann be division since 2 + 2/2 = 3
So, we have if $ = addition, then # is division.
Thus, 1 $ 1 # 1 = 1 + 1/1 = 2. ---(2) Same answer as we got in (1).
• Say $ = subtraction; So, we have 2 – 2 # 2 = 3.
# cannot be subtraction since 2 – 2 – 2 ≠ 3;
# cannot be addition since 2 – 2 + 2 ≠ 3;
# cannot be multiplication since 2 – 2 x 2 ≠ 3;
# cannot be division since 2 – 2/2 ≠ 3;
So, we have 1 $ 1 # 1 = 2. A unique answer. Sufficient.
2) 3 $ 2 # 1 = 5
• $ cannot be division since if were so, 3/2 = 1.5 and whatever be operations # be, it's not going to render an integer 5.
• Say $ = subtraction; So, we have 3 – 2 # 1 = 5.
Whatever operations # be, we cannot get 3 – 2 # 1 = 5.
• Say $ = multiplication; So, we have 3 x 2 # 1 = 5.
# can be subtraction since 3 x 2 – 1 = 5. Thus, 1 $ 1 # 1 = 1 x 1 – 1 = 0 ---(3)
# cannot be multiplication since 3 x 2 x 2 ≠ 5
# cannot be addition since 3 x 2 + 2 ≠ 5
• Say $ = addition; So, we have 3 + 2 # 1 = 5.
# can be subtraction since 3 + 2 – 1 = 5. Thus, 1 $ 1 # 1 = 1 + 1 – 1 = 1 ---(4)
Since the value from (3) and (4) are not the same, statement 2 is insufficient.
Correct answer:
A
Hope this helps!
-Jay
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