Did Sanna save at least 20 percent higher last month than what she did

Question

Did Sanna save at least 20 percent higher last month than what she did the previous month?

(1) Sanna’s income last month was 20 percent greater than her income in the previous month.
(2) Sanna’s expenses last month were 10 percent greater than her expenses in the previous month.

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aditya1818 · Answer

Let the savings be S 
then question is asking is the savings at least greater than 1.2S or algebraically is new savings (>=1.2S)

Statement 1: Insufficient as no mention if savings
Statement 2: Insufficient as no mention of savings(What if the 2nd month's income was same or very less compared to previous or way too much more than previous month and so the savings can be here and there in comparison wise)

Statement 1 + statement 2:

let "I" be the income for the previous month and "E" be the expense for the previous month.
Therefore, savings for the previous month=I-E
savings for the last month= (>1.2I - >1.1E), this boils down to ((I+>0.2I)-(E+>0.1E))=(S+(>0.2I->0.1E))

(S+(>0.2I->0.1E)) again depends on the exact value of I and E to conclude that it is at least 1.2S
There again (1)+(2) is insufficient.

Answer is Option (E)

Edskore · Answer

Key Concept: Data Sufficiency — Algebraic Sufficiency vs. Assumed Insufficiency

Quick note on the existing answer: I get why (E) feels right here — it looks like we don't have enough info about actual savings. But let's work through the algebra carefully, because this question has a neat hidden sufficiency.

Set up variables:
Let I = previous month's income, E = previous month's expenses
Old savings = I − E

The question asks: Is New Savings ≥ 1.2 × Old Savings?

Statement (1) alone: Income increased 20%. No info on expenses → savings unknown. Insufficient. ✗

Statement (2) alone: Expenses increased 10%. No info on income → savings unknown. Insufficient. ✗

Statements (1) + (2) together:
New income = 1.2I
New expenses = 1.1E
New savings = 1.2I − 1.1E

We need to check: Is 1.2I − 1.1E ≥ 1.2(I − E)?

Step 1 — Expand the right side:
1.2I − 1.2E

Step 2 — Compare both sides:
Is 1.2I − 1.1E ≥ 1.2I − 1.2E?

Step 3 — Subtract 1.2I from both sides:
Is −1.1E ≥ −1.2E?
→ Is 0.1E ≥ 0?

Since expenses E must be ≥ 0, this is always true. The answer is definitively YES, regardless of the actual values of I and E.

Answer: C — both statements together are sufficient.

The trap: The instinct is to say "we don't know actual income or expense values, so (E)." But DS doesn't require you to calculate a specific number — it only needs the yes/no question to be determined. Here the algebra proves the answer is always "yes," which makes (1)+(2) sufficient.

Takeaway: In DS yes/no questions involving percentages, always try the algebra first — sometimes the variables cancel completely and give you a result that's always true (or always false), making the statements sufficient even without specific values.

ExpertsGlobal5 · Answer

Explanation:  
   
Let Sanna’s savings in the previous month be S.
Sanna’s savings in the last month is unknown.
  We need to find whether Sanna’s savings in the last month > 1.2S.  
 
 Statement (1) 
 
Let Sanna’s income in the previous month be K.
Sanna’s income in the last month = 1.2K
 
It is NOT possible to determine relation between Sanna’s savings in the previous and the last month from the given information.   Hence, Statement (1) is insufficient.  
 
 Statement (2) 
 
Let Sanna’s expense in the previous month be E.
Sanna’s expense in the last month = 1.1E
 
It is NOT possible to determine relation between Sanna’s savings in the previous and the last month from the given information.   Hence, Statement (2) is insufficient.  
 
As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements. 
 
 Statement (1) and Statement (2) combined  
 
 Intuitively: 
Since Sanna’s income increased by 20%, but the expense increased by less than 20%; hence, the saving increased by more than 20%.
 
 Mathematically: 
Sanna’s savings in the previous month (S) = Income in the previous month – Expense in the previous month = K – E 
Sanna’s savings in the previous month with a 20% increase = 1.2S = 1.2K – 1.2E. 
Sanna’s savings in the last month = Income in the last month – Expense in the last month = 1.2K – 1.1E 
 
Since 1.2K – 1.1E > 1.2K – 1.2E for all positive values as K and E, it is possible to determine with certainty that Sanna saved at least 20 percent higher last month than what she did the previous month.   Hence, Statement (1) and Statement (2) combined are sufficient.  
 
  C is the correct answer choice.

Did Sanna save at least 20 percent higher last month than what she did

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