If (x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 and 2x = a + b + c, then find a ∶ b ∶ c.
  • a)
    23 ∶ 21 ∶ 22
  • b)
    23 ∶ 22 ∶ 21
  • c)
    21 ∶ 22 ∶ 23
  • d)
    22 ∶ 23 ∶ 21
Correct answer is option 'B'. Can you explain this answer?

Knowledge Hub answered  •  6 hours ago
(x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 and 2x = a + b + c,
⇒ (x – a) = (a + b + c) /2 – a = (b + c – a) /2 = 10      ---- 1
⇒ (x – b) = (a + b + c) /2 – b = (a + c – b) /2 = 11      ---- 2
⇒ (x – c) = (a + b + c) /2 – c = (a + b – c) /2 = 12      ---- 3
From equation 2 and 3,
⇒ (a + c – b) = 22
⇒ (a + b – c) = 24
⇒ a = 23
Similarly, b = 22 and c = 21
∴ a ∶ b ∶ c = 23 ∶ 22 ∶ 21

In a certain code language ‘253’ means ‘books are old’, ‘546’ means ‘man is old’ and ‘378’ means ‘buy good books’. What stands for ‘are’ in that code.
  • a)
    2
  • b)
    4
  • c)
    6
  • d)
    9
Correct answer is option 'A'. Can you explain this answer?

Engineers Adda answered  •  19 hours ago
In the first and second statements, the common code digit is ‘5’ and the common word is ‘old’. So ‘5’ means ‘old’. In the first and third statements, the common code digit is ‘3’ and the common word is ‘books’. So, ‘3’ means ‘books’.
Thus, in the first statement ‘2’ means ‘are’.

In the following question, by using which mathematical operators will the expression become correct?
7 # 6 β 6 © 7 = 84
  • a)
    ×, +, -
  • b)
    +, ×, ÷
  • c)
    ×, +, ×
  • d)
    +, ÷, +
Correct answer is option 'C'. Can you explain this answer?

Knowledge Hub answered  •  2 days ago
Following BODMAS rule,
1) ×, +, - → 7 # 6 β 6 © 7 → 7 × 6 + 6 – 7
⇒ 42 + 6 – 7
⇒ 48 – 7
⇒ 41 ≠ 84 (False)
2) +, ×, ÷ → 7 # 6 β 6 © 7
⇒ 7 + 6 × 6 ÷ 7
⇒ 7 + 5.16
⇒ 12.16 ≠ 84 (False)
3) ×, +, × → 7 # 6 β 6 © 7
⇒ 7 × 6 + 6 × 7
⇒ 42 + 42
⇒ 84 = 84 (True)
4) +, ÷, + → 7 # 6 β 6 © 7
⇒ 7 + 6 ÷ 6 + 7
⇒ 7 + 1 + 7
⇒ 15 ≠ 84 (False)
Hence, correct set of symbols is ‘×, +, × ’.

Brandon Stark asked   •  8 hours ago

Passage – I
As financial markets worldwide tumbled over concerns that Greece would default on its debt to the troika comprising the European Commission, the European Central Bank and the International Monetary Fund, the people of Greece were being presented with a Hobson’s choice by its government led by the leftist party platform, Syriza. In the midst of intense negotiations with representatives of the troika over rolling over debt payments, the Syriza government sought to extend the deadline for payments in order to allow it to put the conditionalities of the troika for a bailout extension to a referendum vote. Prime Minister Alexis Tsipras has denied that this referendum, scheduled for July 5, is on whether or not to continue within the eurozone; he says it is only on the acceptance of the troika’s demands. But with the troika unrelenting on the June 30 deadline for repayment of debts to the IMF, and Greece being in no position to pay, the referendum could more or less be on remaining in the eurozone. This presents a difficult choice for the people of Greece. After all, the Syriza was voted to power in January 2015 precisely on the promise of halting the programme of austerity imposed by creditors that has resulted in a drastic contraction of Greece’s economy and increase in unemployment. Yet, the mandate was also for negotiations to remain within the eurozone as Greek voters had realised that the Grexit would mean too much pain (at least in the near term) due to capital flight, a run on the banks and other troubles in returning to the drachma as currency. Over the past five months, Syriza representatives, true to their mandate, have sought to alter Greece’s terms of engagement with its creditors, seeking debt relief that would allow fiscal expansionary policies to spur the economy. Yet, the troika’s response has been to stonewall the proposals and instead push Greece to further the austerity measures it has pursued following the first major bailout in 2010 and another in 2012. The troika’s reasoning is simple: tolerating a Greek default would amount to sending signals to other creditor-nations about similar leniency. Instead, the troika has merely offered a five-month extension of Greece’s bailout programme with fresh funds but with persisting austerity conditions. With barely a concession to the Greek position, there remains a wide gap between the Greek people’s expectations and the EU recommendations. With Greece already having to impose capital controls and bank holidays to avoid further capital flight — measures that were supposed to be taken in the event of an exit from the EU — it begs the question whether the Grexit is inevitable.
 
Q. Which of the following can be true according to the passage?
(A) Syriza was voted to power in January 2015 precisely on the promise of halting the programme of austerity imposed by creditors.
(B) Alexis Tsipras has denied that this referendum, scheduled for July 5, is on whether or not to continue within the Eurozone.
(C) The troika’s reasoning is simple: tolerating a Greek default would amount to sending signals to other creditor-nations about similar leniency.
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